\r\n\tPrevalence of reading disability among school-age children depends upon the criteria used for definition; however, the prevalence of written expression disorders in estimated to be between 5 and 12 percent, the prevalence of written expression disorders is estimated to be between 7 and 15 percent, while the prevalence of dyscalculia is estimated to be between 3 and 6 percent.
\r\n
\r\n\tRisk factors for learning disorders are family history, socio-economic conditions, prematurity, presence of other developmental, mental and health conditions (e.g. behavioral disorders, autism, attention deficit and hyperactivity disorders), prenatal exposition to neurotoxic agents, genetic disorders, particular medical conditions, history of traumatic brain injury or other neurological conditions.
",isbn:"978-1-83968-588-0",printIsbn:"978-1-83968-587-3",pdfIsbn:"978-1-83968-589-7",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,hash:"0999e5f759c2380ae5a4a2ee0835c98d",bookSignature:" Sandro Misciagna",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10910.jpg",keywords:"Learning Disability Definition, Brain Plasticity, Learning Disability Evaluation, Learning Disabilities Resources, Psychoeducation Evaluation, Clinical Features, Dyslexia, Dysgraphia, Dyscalculia, Intellectual Disabilities, Autism Spectrum Disorders, ADHD",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"April 16th 2021",dateEndSecondStepPublish:"May 14th 2021",dateEndThirdStepPublish:"July 13th 2021",dateEndFourthStepPublish:"October 1st 2021",dateEndFifthStepPublish:"November 30th 2021",remainingDaysToSecondStep:"24 days",secondStepPassed:!1,currentStepOfPublishingProcess:2,editedByType:null,kuFlag:!1,biosketch:"Dr. Sandro Misciagna received his degree in medicine at the Catholic University in Rome. As a clinician, he has worked in different neurological departments in Italian hospitals, Alzheimer’s clinics, neuropsychiatric clinics, and neurological rehabilitative departments as the Neurological Department and Stroke Unit of Belcolle Hospital in Viterbo, Italy.",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"103586",title:null,name:"Sandro",middleName:null,surname:"Misciagna",slug:"sandro-misciagna",fullName:"Sandro Misciagna",profilePictureURL:"https://mts.intechopen.com/storage/users/103586/images/system/103586.jpg",biography:"Dr. Sandro Misciagna was born in Italy in 1969. He received a degree in medicine in 1995 and another in neurology in 1999 from The Catholic University, Rome. From 1993 to 1995, he was involved in research of cerebellar functions. From 1994 to 2003, he attended the Neuropsychological department involved in research in cognitive and behavioural disorders. 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\n\t\t\t
1. Introduction
\n\t\t\t
Nowadays global and extended markets have to process and manage increasingly differentiated products, with shorter life cycles, low volumes and reducing customer delivery times. Moreover several managers frequently have to find effective answers to one of the following very critical questions: in which kind of facility plant and in which country is it most profitable to manufacture and/or to store a specific mix of products? What transportation modes best serve customer points of demand, which can be located worldwide? Which is the best storage capacity of a warehousing system or a distribution center (DC)? Which is the most suitable safety stock level for each item of a company’s product mix? Consequently logistics is assuming more and more importance and influence in strategic and operational decisions of managers of modern companies operating worldwide.
\n\t\t\t
The Council of Logistics Management defines logistics as “the part of supply chain process that plans, implements and controls the efficient, effective flow and storage of goods, services, and related information from the point of origin to the point of consumption in order to meet customers’ requirements”. Supply Chain Management (SCM) can be defined as “the integration of key business processes from end-user through original suppliers, that provides product, service, and information that add value for customers and other stakeholders” (Lambert et al., 1998). In accordance with these definitions and with the previously introduced variable and critical operating context, Figure 1 illustrates a significant conceptual framework of SCM proposed by Cooper et al. (1997) and discussed by Lambert et al. (1998). Supply chain business processes are integrated with functional entities and management components that are common elements across all supply chains (SCs) and determine how they are managed and structured. Not only back-end and its traditional stand-alone modelling is addressed, but the front-end beyond the factory door is also addressed through information sharing among suppliers, supplier’s suppliers, customers, and customers’ customers.
\n\t\t\t
In the modern competitive business environment the effective integration and optimization of the planning, design, management and control activities in SCs are one of the most critical issues facing managers of industrial and service companies, which have to operate in strongly changing operating conditions, where flexibility, i.e. the ability to rapidly adapt to changes occurring in the system environment, is the most important strategic issue affecting the company success.
\n\t\t\t
As a consequence the focus of SCM is on improving external integration known as “channel integration” (Vokurka & Lummus, 2000), and the main goal is the optimization of the whole chain, not via the sum of individual efficiency maximums, but maximising the entire system thanks to a balanced distribution of the risks between all the actors.
\n\t\t\t
The modelling activity of production and logistic systems is a very important research area and material flows are the main critical bottleneck of the whole chain performance. For this reason in the last decade the great development of research studies on SCM has found that new, effective supporting decisions models and techniques are required. In particular a large amount of literature studies (Sule 2001, Manzini et al. 2006, Manzini et al. 2007a, b, Gebennini et al. 2007) deal with facility management and facility location (FL) decisions, e.g. the identification of the best locations for a pool of different logistic facilities (suppliers, production plants and distribution centers) with consequent minimization of global investment, production and distribution costs. FL and demand allocation models and methods object of this chapter are strongly associated with the effective management and control of global multi-echelon production and distribution networks.
\n\t\t\t
Figure 1.
Supply Chain Management (SCM) framework and components.
\n\t\t\t
A few studies propose operational models and methods for the optimization of SCs, focusing on the effectiveness of the global system, i.e. the whole chain, and the determination of a global optimum. The purpose of this chapter is the definition of new perspectives for the effective planning, design, management, and control of multi-stage distribution system by the introduction of a new conceptual framework and an operational supporting decision platform. This framework is not theoretical, but deals with the tangible Production Distribution Logistic System Design (PDSD) problem and the optimization of logistic flow within the system. As a consequence the proposed optimization models have been applied to real case studies or to multi-scenarios experimental analysis, and the obtained results are properly discussed.
\n\t\t\t
The remainder of this chapter is organized as follows: Section 2 presents and discusses principal literature studies on SC planning and design. Section 3 presents and describes the conceptual framework proposed by the authors for providing an effective solutions to the PDSD problem. Section 4 presents mixed integer programming models and a case study for the so called static design of a logistic network. Similarly Section 5 and 6 discuss about the fulfillment system design problem and the dynamic facility location. Finally, Section 7 concludes with directions for future research.
\n\t\t
\n\t\t
\n\t\t\t
2. Review of the literature
\n\t\t\t
In recent years hundreds of studies have been carried out on various logistics topics, e.g. enterprise resource planning (ERP), warehousing, transportation, e-commerce, etc. These studies follow the well-known definition of SC: “it consists of supplier/vendors, manufacturers, distributors, and retailers interconnected by transportation, information and financial infrastructure. The objective is to provide value to the end consumer in terms of products and services, and for each channel participant to garner a profit in doing so” (Shain & Robinson, 2002). As a consequence SCM is the act of optimizing all activities through the supply chain (Chan & Chan 2005).
\n\t\t\t
Literature contributions in SC planning and management discriminate between the strategic level on the one hand, and the tactical and operational levels on the other (Shen 2005, Manzini et al. 2007b). The strategic level deals with the configuration of the logistic network in which the number, location, capacity, and technology of the system facilities are decided. The most important tactical and operational decisions are inventory management decisions and distribution decisions within the SC, e.g. deciding the aggregate quantities and material flows for purchasing, processing, and distribution of products. Shen (2005) affirms that in order to achieve important costs savings, many companies have realized that the generic SC should be optimized as a whole, i.e. the major cost factors that impact on the performance of the chain should be considered jointly in the decision model. Even though several studies have proposed innovative models and methods to support logistic decision making concerning what to produce, where, when, how, and for which customer, etc., as yet no effective and low cost tools have been developed capable of integrating logistic problems and decision making at different levels as a support for management in industrial and service companies. Recent studies of Manzini et al. (2007b), Monfared & Yang (2007), and Samaranayake & Toncich (2007) introduce the first basis for the definition and development of effective supporting decision tools which integrates these three different levels of planning. In particular the tool proposed by Manzini et al. (2007b) is based on an original conceptual framework described in next section. In logistics and SCM the high level of significance of the generic FL problem can be obtained by taking of simultaneous decisions regarding design, management, and control of a distribution network:
\n\t\t\t
location of new supply facilities in a given set of demand points. The demand points correspond to existing customer locations;
allocation of demand flows to available or new suppliers;
configuration of the transportation network for supplying demand needs: i.e. the design of paths from suppliers to customers and simultaneously the management of routes and vehicles.
\n\t\t\t
The problem of finding the best of many possible locations can be solved by several qualitative and efficiency site selection techniques, e.g. ranking procedures and economic models (Byunghak & Cheol-Han 2003). These techniques are still largely influenced by subjective and personal opinions (Love et al. 1988, Sule 2001). Consequently, the problems of an effective location analysis are generally and traditionally categorized into one broad classes of quantitative and quite effective methods described in Table 1 (Love et al. 1988, Sule 2001, Manzini et al. 2007a).
\n\t\t\t
In particular the location allocation is the problem to determine the optimal location for each of the m new facilities and the optimal allocation of existing facility requirements to the new facilities so that all requirements are satisfied, that is, when the set of existing facility locations and their requirements are known. Literature presents several models and approaches to treating location of facilities and allocation of demand points simultaneously. In particular, Love et al. (1988) discuss the following site-selection LAP models: set-covering (and set-partitioning models); single-stage, single-commodity distribution model; and two-stage, multi-commodity distribution model which deals with the design for supply chains composed of production plants, DCs, and customers. The LAP models consider various aspects of practical importance such as production and delivery lead times, penalty cost for unfulfilled demand, and response times different customers are willing to tolerate (Manzini et al. 2007a, b). Passing to the NLP one of the most critical decision deals with the selection of specific paths from different nodes in the available network.
\n\t\t\t
So-called “dynamic location models” consider a multi-period operating context where the demand varies between different time periods. This configuration of the problem aims to answer three important questions. Firstly, where i.e. the best places to locate the available facilities. Secondly, what size i.e. which is the best capacity to assign to the generic logistic facility. Thirdly, when i.e. with regard to a specific location, which periods of time demand a certain amount of production capacity. Recent studies on FL are presented by Snyder (2006), Keskin & Uster (2007) and Hinojosa et al. (2008). ReVelle et al. (2008) present a taxonomy of the broad field of facility location modelling.
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\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Class of location problems/models
\n\t\t\t\t\t\t
Description
\n\t\t\t\t\t\t
Examples and references
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Single facility minimum location problems
\n\t\t\t\t\t\t
optimal location of a single facility designed to serve a pool of existing customers
\n\t\t\t\t\t\t
see Francis et al. (1992)
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Multiple facility location problems (MFLP)
\n\t\t\t\t\t\t
optimal location of multiple facilities capable of serving the customers in the same or in different ways.
\n\t\t\t\t\t\t
p-Median problem (p-MP), p-Centre problem (p-CP), uncapacitated facility location problem (UFLP), capacitated facility location problem (CFLP), quadratic assignment problem (QAP), and plant layout problem
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Facility location allocation problem (LAP)
\n\t\t\t\t\t\t
several facilities have to be located and flows between the new facilities and the existing facilities (i.e. demand points) have to be determined. The LAP is an MFLP with unknown allocation of demand to the available facilities.
\n\t\t\t\t\t\t
see Love et al. (1988), Manzini et al. (2007a,b)
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Network location problem (NLP)
\n\t\t\t\t\t\t
a LAP where the network (routes, distances, travel times, etc.) have to be constructed and configured.
\n\t\t\t\t\t\t
see Sule et al. (1988), Manzini et al. (2007b)
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Extensions classes of NLP and LAP
\n\t\t\t\t\t\t
Tours development problem. Vehicle routing problem (e.g. assignment procedures for the travelling salesman problem and the truck routing problem). Dynamic location models. Multi-period dynamic facility location problem. Integrated distribution network design problem (decisions regarding locations, allocation, routing and inventory).
\n\t\t\t\t\t\t
see Sule et al. (1988), Ambrosino and Scutella (2005), Gebennini et al. (2007), Manzini et al. (2007b).
\n\t\t\t\t\t
\n\t\t\t\t
Table 1.
Main classes of facility locations in logistics.
\n\t\t
\n\t\t
\n\t\t\t
3. A PDSD conceptual framework
\n\t\t\t
Limited research has been carried out into solving the supply chain problems from a “system” point of view, where the purpose is to design an integrated model for supply chains. The authors propose an original conceptual framework which is illustrated in Fig.2 and is based on the integration of three different planning levels (Manzini et al. 2007b):
\n\t\t\t
\n\t\t\t\t\t\tStrategic planning. This level refers to a long term planning horizon (e.g. 3-5 years) and to the strategic problem of designing and configuring a generic multi stage supply chain. Management decisions deal with the determination of the number of facilities, geographical locations, storage capacity, and allocation of customer demand (Manzini et al. 2006). The proposed supporting decisions approach to the strategic planning is based on a static network design as illustrated in Section 4.
\n\t\t\t\t\t\tTactical planning. This level refers to both long and short term planning horizons and deals with the determination of the best fulfillment policies and material flows in a supply chain, modelled as a multi-echelon inventory distribution system. The proposed supporting decisions approach is specifically based on the application of simulation and multi-scenario what-if analysis as illustrated in Section 5.
\n\t\t\t\t\t\tOperational planning. It refers to long and short term planning horizons. In fact, the main limit of the modelling approach based on the static network design is based on the absence of time dependency for problem parameters and variables. A period dynamic network design differs from the static problem by introducing the variable time according to the determination of the number of logistic facilities, geographical locations, storage capacities, and daily allocation of customer demand to retailers (i.e. distribution centers or production plants). The very short planning horizon is typical of a logistic requirement planning (LRP), i.e. a tool comparable to the well-known material requirement planning (MRP) and capable of planning and managing the daily material flows throughout the logistic chain.
\n\t\t\t
Figure 2.
Conceptual framework for the Production Distribution Logistic System Design problem.
\n\t\t\t
Next three sections presents effective models for approaching to the previously described planning levels for the optimization of a multi-echelon production distribution system.
\n\t\t
\n\t\t
\n\t\t\t
4. Static network design
\n\t\t\t
An effective mathematical formulation of the static (i.e. not time dependent) network design problem is based on the LAP (Manzini et al. 2006, 2007a, 2007b). The objective is to configure the distribution network by minimizing a cost function and maximizing profit. LAP belongs to the NP-hard complexity class of decision problems, and the generic occurrence requires the simultaneous determination of the number of logistic facilities (e.g. production plants, warehousing systems, and distribution centers), their locations, and the assignment of customer demand to them.
\n\t\t\t
\n\t\t\t\tFig. 3 exemplifies a distribution system whose configuration can be object of a LAP. The generic occurrence of a LAP is usually made of several entities (i.e. facilities). Fig. 4 illustrates an example of a worldwide distribution of a large number of customers within a company logistic network. In particular the generic dot represents a demand point and its colour is related to the amount of demand during a period of time T (e.g. one year). The colour of the geographic area relates to the average unit cost of transportation from a central depot located in Ohio.
\n\t\t\t
Figure 3.
Multi-stage distribution system.
\n\t\t\t
\n\t\t\t\t
4.1. Single commodity 2-stage model (SC2S)
\n\t\t\t\t
The following static model has been developed by the authors for the design of a 2-stage logistic network which involves three different levels of facilities (i.e. types of nodes): a production plant which can be identified by a central distribution center (CDC), a set of regional distribution centers (RDCs), and a group of customers which represent the points of demand.
\n\t\t\t\t
This model controls the distribution customers lead times (t\n\t\t\t\t\t\n\t\t\t\t\t\tkl\n\t\t\t\t\t where k is a generic RDC and l is the generic demand point, i.e. customer) introducing a maximum admissible delivery delay, called T\n\t\t\t\t\t\n\t\t\t\t\t\tR. In particular it is possible to measure and optimize three different portions of customers demand:
\n\t\t\t\t
part of demand delivered within lead time T\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t (defined for customer l), i.e. t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tkl\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t< T\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t;
part of demand not delivered within T\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t but within the admissible delivery delay, i.e. t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tkl\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t< T\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t+ T\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tR\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t;\n\t\t\t\t\t\t
part of demand not delivered because the delay is not admissible, i.e. t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tkl\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t> T\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t+ T\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tR\n\t\t\t\t\t\t\t.
\n\t\t\t\t\tk = 1,..,K RDC belonging to the second level of the generic logistic network;
\n\t\t\t\t
\n\t\t\t\t\tl = 1,..,L demand point belonging to the third level of the network;
\n\t\t\t\t
\n\t\t\t\t\tc’\n\t\t\t\t\t\n\t\t\t\t\t\tk\n\t\t\t\t\t transportation unit cost from the CDC to the RDC k;
\n\t\t\t\t
\n\t\t\t\t\tx’\n\t\t\t\t\t\n\t\t\t\t\t\tk\n\t\t\t\t\tproduct quantity from the CDC to the RDC k;
\n\t\t\t\t
\n\t\t\t\t\td’\n\t\t\t\t\t\n\t\t\t\t\t\tk\n\t\t\t\t\tdistance from the CDC to the RDC k;
\n\t\t\t\t
\n\t\t\t\t\tc\n\t\t\t\t\t\n\t\t\t\t\t\tkl\n\t\t\t\t\ttransportation unit cost from the RDC k to the point of demand l;
\n\t\t\t\t
\n\t\t\t\t\tx\n\t\t\t\t\t\n\t\t\t\t\t\tkl\n\t\t\t\t\tproduct quantity from the RDC k to the point of demand l;
\n\t\t\t\t
\n\t\t\t\t\td\n\t\t\t\t\t\n\t\t\t\t\t\tkl\n\t\t\t\t\tdistance from the RDC k to the point of demand l;
\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tproduct quantity delivered with an admissible delay from the RDC k to the point of demand l;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\to\n\t\t\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tproduct quantity (from the RDC k to the point of demand l) not delivered because it does not respect the maximum admissible delay;
\n\t\t\t\t\ty\n\t\t\t\t\t\n\t\t\t\t\t\tkl\n\t\t\t\t\t1 if the RDC k supplies the point of demand l. 0 otherwise;
\n\t\t\t\t
\n\t\t\t\t\tz\n\t\t\t\t\t\n\t\t\t\t\t\tk\n\t\t\t\t\t1 if the RDC k is selected by the solution of the problem; 0 otherwise;
\n\t\t\t\t
\n\t\t\t\t\tf\n\t\t\t\t\t\n\t\t\t\t\t\tk\n\t\t\t\t\tfixed cost to operate using the RDC k;
\n\t\t\t\t
\n\t\t\t\t\tv\n\t\t\t\t\t\n\t\t\t\t\t\tk\n\t\t\t\t\tvariable cost (based on the product quantity flow) for the RDC k;
\n\t\t\t\t
\n\t\t\t\t\tD\n\t\t\t\t\t\n\t\t\t\t\t\tl\n\t\t\t\t\tdemand from the point of demand l;
\n\t\t\t\t
\n\t\t\t\t\tt\n\t\t\t\t\t\n\t\t\t\t\t\tkl\n\t\t\t\t\tdelivery time from the RDC k to the point of demand l;
\n\t\t\t\t
\n\t\t\t\t\tT\n\t\t\t\t\t\n\t\t\t\t\t\tl\n\t\t\t\t\tdelivery time required by the point of demand l;
\n\t\t\t\t
\n\t\t\t\t\tpmaximum number of points of demand supplied by a generic RDC;
\n\t\t\t\t
\n\t\t\t\t\tAadditional delivery unit cost for product delivered with an admissible delay;
\n\t\t\t\t
\n\t\t\t\t\tBpenalty unit cost for units of product not delivered because they do not respect the admissible delay;
The objective function is composed of five different addends:
\n\t\t\t\t
\n\t\t\t\t\t\t\tC(CDC-RDC). It is the global transportation cost from the first level (CDC) to second level (RDCs);
\n\t\t\t\t\t\t\tC(RDC-Demand). It is the global transportation cost from the second level to the third level (points of demands);
\n\t\t\t\t\t\t\tC(DELAY). It measures the cost for the product quantities in delivery delay but delivered during admissible delay time T\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tR\n\t\t\t\t\t\t\t;
\n\t\t\t\t\t\t\tC(UNDELIVERED). It is a penalty cost associated with product quantities (from the RDCs to the points of demand) not delivered because they failed to respect the delay time T\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tR\n\t\t\t\t\t\t\t;
\n\t\t\t\t\t\t\tC(RDC). It is the cost associated with the management of the set of RDCs.
\n\t\t\t
\n\t\t\t
\n\t\t\t\t
4.2. Single commodity 3-stage model (SC3S)
\n\t\t\t\t
The previously described mixed integer programming model has also been modified in order to take into account the product levels and related flows and costs, which were previously neglected. The following presents the adopted objective function which quantifies also the transportation cost from the production level to the CDC.
The new set of constraints introduced by this model have now been omitted because they are very similar to those previously discussed.
\n\t\t\t\t
New symbols introduced by this model are:
\n\t\t\t\t
\n\t\t\t\t\ti = 1,..Iproduction plant;
\n\t\t\t\t
\n\t\t\t\t\tj = 1,..,J central distribution center CDC;
\n\t\t\t\t
\n\t\t\t\t\tc’’\n\t\t\t\t\t\n\t\t\t\t\t\tij\n\t\t\t\t\t transportation unit cost from the production plant i to the CDC j;
\n\t\t\t\t
\n\t\t\t\t\tx’’\n\t\t\t\t\t\n\t\t\t\t\t\tij\n\t\t\t\t\tproduct quantity from the production plant i to the CDC j;
\n\t\t\t\t
\n\t\t\t\t\td’’\n\t\t\t\t\t\n\t\t\t\t\t\tij\n\t\t\t\t\tdistance from the production plant i to the CDC j;
\n\t\t\t\t
\n\t\t\t\t\tc’\n\t\t\t\t\t\n\t\t\t\t\t\tjk\n\t\t\t\t\ttransportation unit cost from the CDC j to the RDC k;
\n\t\t\t\t
\n\t\t\t\t\tx’\n\t\t\t\t\t\n\t\t\t\t\t\tjk\n\t\t\t\t\tproduct quantity from the CDC j to the RDC k;
\n\t\t\t\t
\n\t\t\t\t\td’\n\t\t\t\t\t\n\t\t\t\t\t\tjk\n\t\t\t\t\tdistance from the CDC j to the RDC k;
\n\t\t\t\t
\n\t\t\t\t\tf\n\t\t\t\t\t\n\t\t\t\t\t\tj\n\t\t\t\t\tfixed operating cost using the CDC j;
\n\t\t\t\t
\n\t\t\t\t\tv\n\t\t\t\t\t\n\t\t\t\t\t\tj\n\t\t\t\t\tvariable cost (based on the product quantity flow) for the CDC j;
\n\t\t\t\t
\n\t\t\t\t\tw\n\t\t\t\t\t\n\t\t\t\t\t\tj\n\t\t\t\t\t\n\t\t\t\t\t1 if the CDC j is selected by the solution of the problem; 0 otherwise.
\n\t\t\t\t
The following new addends have been introduced into the objective function:
\n\t\t\t\t
\n\t\t\t\t\t\t\tC(PRODUCTION-CDC). It represents the global cost for the distribution of products from the first level to the CDCs level;
\n\t\t\t\t\t\t\tC\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tCDC\n\t\t\t\t\t\t\t measures the cost associated with the management of the set of CDCs.
\n\t\t\t
\n\t\t\t
\n\t\t\t\t
4.3. Multi commodity 3-stage model (MC3S)
\n\t\t\t\t
This model differs from previously illustrated because it is a multi commodity model: several different products can be simultaneously involved for supporting strategic decisions on network configuration. The objective function is:
c’’mijtransportation unit cost from the production plant i to the CDC j for the family m;
\n\t\t\t\t
x’’mijproduct quantity from the production plant i to the CDC j for the family m;
\n\t\t\t\t
d’’mijdistance from the production plant i to the CDC j for the family m;
\n\t\t\t\t
\n\t\t\t\t\tc’\n\t\t\t\t\t\n\t\t\t\t\t\tmjk,\n\t\t\t\t\t\n\t\t\t\t\tx’\n\t\t\t\t\t\n\t\t\t\t\t\tmjk,\n\t\t\t\t\t\n\t\t\t\t\td’\n\t\t\t\t\t\n\t\t\t\t\t\tmjk,\n\t\t\t\t\t\n\t\t\t\t\tc\n\t\t\t\t\t\n\t\t\t\t\t\tmkl\n\t\t\t\t\t\n\t\t\t\t\t, x\n\t\t\t\t\t\n\t\t\t\t\t\tmkl,\n\t\t\t\t\t\n\t\t\t\t\td\n\t\t\t\t\t\n\t\t\t\t\t\tmkl\n\t\t\t\t\t, etc. are similar to c’\n\t\t\t\t\t\n\t\t\t\t\t\tjk,\n\t\t\t\t\t\n\t\t\t\t\tx’\n\t\t\t\t\t\n\t\t\t\t\t\tjk,\n\t\t\t\t\t\n\t\t\t\t\td’\n\t\t\t\t\t\n\t\t\t\t\t\tjk\n\t\t\t\t\t\n\t\t\t\t\t, c\n\t\t\t\t\t\n\t\t\t\t\t\tkl\n\t\t\t\t\t\n\t\t\t\t\t, x\n\t\t\t\t\t\n\t\t\t\t\t\tkl,\n\t\t\t\t\t\n\t\t\t\t\td\n\t\t\t\t\t\n\t\t\t\t\t\tkl\n\t\t\t\t\t, etc., which were introduced in the previous objective function (12), but they refer to the generic family of products m.
\n\t\t\t
\n\t\t\t
\n\t\t\t\t
4.4. Strategic planning. Case study
\n\t\t\t\t
This section presents the results obtained by the application of previously illustrated mixed integer linear location allocation models to the rationalization and optimization of the logistic network for the distribution of components in a leading electronics Italian company (this case study is deeply presented in Manzini et al. 2006).
\n\t\t\t\t
\n\t\t\t\t\tFigure 5 illustrates the network configuration made of 4 levels (production level, central DC level, RDC level and customer level) and 3 stages (production plants-CDC, CDC-RDCs and RDCs-Customers). The model does not consider multiple periods of time according to a long-term strategic design and planning of the network.
\n\t\t\t\t
Figure 5.
Strategic planning. Network configuration in the case study.
\n\t\t\t\t
The products number several thousands and their demand is strongly fragmented; nevertheless in a first approximation the products’ mix has been reduced to a single product according to types of products which are very small and so similar that their individual quantities are unimportant. Then the model of the system does not consider multiple periods of time according to a long-term strategic design and planning. Furthermore this aggregated demand of products assumes a constant trend during a year. Finally more than 90% of the delivered products passed and passes through the CDC. As a consequence the flow of products along the system can be simply measured in tons and for the system design and optimization it is possible to apply the single commodity models illustrated above by omitting the production level in the SC2S model. Fig.6 presents the location of a pool of DCs and a set of exemplifying points of demand according to the projection of longitude and latitude values into Cartesian coordinates, useful for the determination of the distance between two generic locations.
\n\t\t\t\t
The model illustrated in Section 4.1 has been applied to optimize the so-called “actual” network (i.e. to minimize the global logistic cost function in the original configuration of the system, also called “AS-IS”, before the optimization study) for different values of T\n\t\t\t\t\t\n\t\t\t\t\t\tR\n\t\t\t\t\t. Fig.7 presents the actual/AS-IS configuration of the system, which is compared with the best system configuration obtained by the application of the linear model when T\n\t\t\t\t\t\n\t\t\t\t\t\tR\n\t\t\t\t\t is equal to 0. Fig.8 presents the results obtained when T\n\t\t\t\t\t\n\t\t\t\t\t\tR\n\t\t\t\t\t is optimized (the optimal value is 9). Finally Fig.9 compares the actual configuration of the network with the best one distinguishing the different kinds of logistic costs of objective function (1): the global cost reduction is approximately 4.22% (about € 200000 per year) of the actual annual cost.
\n\t\t\t\t
Figure 6.
Points of demand and DCs in Cartesian coordinates.
\n\t\t\t\t
Figure 7.
a) Actual configuration, b) Best configuration when TR=0.
\n\t\t\t\t
Figure 8.
Best configuration when TR=9.
\n\t\t\t\t
Figure 9.
Logistic costs comparison AS-IS vs best configuration.
\n\t\t\t\t
Figure 10.
SC3S solution, when TR=9.
\n\t\t\t\t
\n\t\t\t\t\tFig.10 shows the solution to the SC3S problem found by the linear programming solver MPL (Mathematical Programming Language by Maximal Software Inc.) introducing the production level. This solution cannot be compared directly with the solution produced by the SC2S because the second one does not quantify transportation costs from the production level. In particular, the opportunity to supply products directly from the production level to the point of demand strongly reduces the storage quantities located in the CDC. This opportunity is modelled by the introduction of a virtual DC (virtual RDC in figures 7 and 8).
\n\t\t\t\t
The previously illustrated multi-commodity model (the MC3L) is capable of distinguishing and quantifying the flows of different product families. By applying the model to the case study where M = 9, I = 7, J = 8, K = 13 and L = 351, the solution presented in fig. 11 is obtained. It is based on 3 DCs:
\n\t\t\t\t
a “virtual DC” through which products flow virtually and directly from production level to customers’ level;
a CDC, which is capable of supplying customer demand directly (e.g. Europe) through the “virtual RDC”;
2 RDCs: TW supplies the Far East, while USA supplies North and South America.
\n\t\t\t\t
This result shows that the MC3L model is effective for rapid strategic and long-term design of a complex logistic network.
\n\t\t\t\t
Figure 11.
Multi-commodity model.
\n\t\t\t
\n\t\t
\n\t\t
\n\t\t\t
5. Fulfillment system design
\n\t\t\t
Being strategic and tactical, this level refers to both long and short term planning horizons. Therefore, the solution to the problem deals with the determination of the best fulfillment policies and material flows in a SC, modelled as a multi-echelon inventory distribution system. The decisional approach is specifically based on the application of simulation and multi-scenario what-if analysis.
\n\t\t\t
The literature largely discusses the application of simulation and stochastic modelling to support the design and management of SCs (Chan & Chan 2005, 2006, Manzini et al. 2005b, Ng et al. 2003, Santoso et al. 2005). Simulation can model complex real systems incorporating many non-deterministic factors, such as uncertainty in demand, lead times, number of facility locations, assignment of customer demand, etc. In particular, thanks to a what-if approach, simulation models can provide a thorough understanding of the dynamic behaviours of a system as well as assisting evaluation of different operational strategies.
\n\t\t\t
The modelling approach of this planning level is dynamic, i.e. multi-period. So the modelled unit period of time can be the day. Every actor in the chain is modelled as a dynamic entity whose behaviour is deterministic or stochastic.
\n\t\t\t
By using the dynamic modelling of the distribution system, management can implement different fulfillment strategies. In particular, the reorder strategy for the generic stock point (i.e. facility) of the distribution network can be either push or pull, e.g. a supplier can push materials to a distribution center which supplies retailers in accordance to a pull or push strategy.
\n\t\t\t
\n\t\t\t\t
5.1. Case study. A multi-echelon 3-stage system
\n\t\t\t\t
\n\t\t\t\t\tFig.12 exemplifies a 3-stage divergent system where each stockpoint has a unique supplier but it may deliver material to multiple other stockpoints. In particular stockpoint 0 is supplied by several external sources (e.g. production facilities), and the “end stockpoints” are the entities that deliver materials directly to final customers (whose demand can be stochastic). All products are supplied via the network in order to satisfy customer demand.
\n\t\t\t\t
\n\t\t\t\t\tFig.13 illustrates the well known reorder policy usually adopted for the determination of the reorder quantity of a retailer (or a DC) in a period of time t\n\t\t\t\t\t\n\t\t\t\t\t\ti\n\t\t\t\t\t. This quantity is defined by the following equation:
\n\t\t\t\t\tt\n\t\t\t\t\t\n\t\t\t\t\t\ti\n\t\t\t\t\t\n\t\t\t\t\ti\n\t\t\t\t\t\n\t\t\t\t\t\tth\n\t\t\t\t\t reviewing period (i.e. unit period of time);
\n\t\t\t\t
\n\t\t\t\t\tI(t\n\t\t\t\t\t\n\t\t\t\t\t\ti\n\t\t\t\t\t\n\t\t\t\t\t)on-hand inventory in time t\n\t\t\t\t\t\n\t\t\t\t\t\ti\n\t\t\t\t\t;
\n\t\t\t\t
\n\t\t\t\t\tt\n\t\t\t\t\t\n\t\t\t\t\t\tl\n\t\t\t\t\t identifies the variable lead time of the generic replenishment (Fig.13).
\n\t\t\t\t
This is the order-up-to (S,s) replenishment policy whose several contributions in the literature confirm its effectiveness because it is a parametric rule which can be easily applied to represent different fulfillment policies such as the periodic review rule, the fixed order quantity rule, the economic order quantity (EOQ), etc.
\n\t\t\t\t
Figure 12.
A 3-stage divergent system. Push-pull vs pull-pull strategies.
\n\t\t\t\t
Figure 13.
S,s) policy. s’<s.
\n\t\t\t\t
The following figures present some of the results obtained from a what-if analysis conducted on the simulation of several hypothetical scenarios in order to identify some effective guidelines for designing new Demand/Supply Chain. These results also illustrate the application of some statistical techniques to the management of the performance data in accordance with the proposed framework previously illustrated. In particular, Fig.14 presents the trend of some performance indexes (LS_1, LSCent, LStot, etc.) introduced to support the validation of a fulfillment model by identifying the warm-up period (equal to 500 time periods) and the right number of repetitions (equal to 10 and in agreement with a confidence interval equal to 0.95) for each simulation run. More details are reported in Manzini et al. (2005a).
\n\t\t\t\t
Figure 14.
Validation analysis. Warm-up periods.
\n\t\t\t\t
\n\t\t\t\t\tFig.15 illustrates the results of a factorial analysis (in particular an ANOVA analysis) for an exemplifying performance index Perf1(r=1,T=500) defined as follows:
\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tS\n\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\tT\n\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tretailer service level, defined as the ratio between the whole amount of quantity delivered S(r,T) and the total amount of demand D(r,T) from all customers to r;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tC\n\t\t\t\t\t\t\t\tU\n\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\tT\n\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tretailer unit cost.
In particular the retailer unit cost is defined as the ratio between the global cost for the retailer and the global economic value of the requested demand:
\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tC\n\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\to\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\tT\n\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tglobal cost for the retailer in period T;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tcustomers demand in unit period of time t\n\t\t\t\t\n\t\t\t\t\ti\n\t\t\t\t for retailer r;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tU\n\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\tPr\n\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tprice of product for retailer r.
As a consequence the value of Perf1(r=1,T=500) measures the relationship between the generic service level (defined for a retailer-r) and the related logistic unit cost.
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Figure 15.
ANOVA Analysis.
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Figure 16.
Pareto chart of the standardized effects.
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By the multi-level factorial analysis it is possible to identify the existence of significant increasing/decreasing (or decreasing/increasing) trends, the existence of optimal values and combinations of values for system performance optimization. Fig. 16 illustrates the Pareto Chart of the Standardized effects obtained by a 2K factorial analysis conducted on another performance index. The collection of several campaigns of factorial analysis support the identification of the most critical factors and combinations of factors affecting the system performance.
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6. Network management and dynamic facility location
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This planning level is simultaneously both tactical and operational, and refers to long and short term planning horizons. In fact, the main limit of the modelling approach based on the static LAP is based on the absence of time dependency for problem parameters and variables. The multi-period dynamic LAP differs from the static problem by introducing the variable time according to the determination of the number of logistic facilities, geographical locations, storage capacities, and daily allocation of customer demand to retailers (i.e. distribution centers or production plants). The very short planning horizon is typical of a logistic requirement planning (LRP), i.e. a tool comparable to the well-known material requirement planning (MRP) and capable of planning and managing the daily material flows throughout the logistic chain.
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6.1. Multi period single commodity 2-stage model (SCMP2S)
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An original and illustrative mathematical formulation of the dynamic LAP has recently been developed by Manzini et al. (2007a) and is now discussed: it is a multi period single commodity two stages (SCMP2S) linear model based on the application of mixed integer programming. The logistic network is composed of two stages that involve the levels introduced and discussed in section 3.1. The cost-based objective function SCMP2S is:
\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t...\n\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\tK\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tRDC belonging to the second level of the logistic network;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t...\n\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tdemand point belonging to the third level of the network;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t...\n\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\tT\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tunit period of time along the planning horizon T;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t′\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tproduct quantity from the CDC to the RDC k in t;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\ton time delivery quantity i.e. product quantity from the RDC k to the point of demand l in t;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tS\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tproduct quantity not delivered from the RDC k to the point of demand l in t. The admissible period of delay is one unit of time: consequently, this quantity must be delivered in the period t + 1;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tdelayed product quantity delivered late from the RDC k to the point of demand l in t. The value of this variable corresponds to\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tS\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t; \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tI\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tstorage quantity in the RDC k at the end of the period t;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tP\n\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tproduction quantity in time period t. It is available after the lead time\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\t\t\t\to\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t; \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t1 if the RDC k supplies the point of demand l in t. 0 otherwise;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t1 if the RDC k belongs to the distribution network. 0 otherwise;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\t′\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tunit cost of transportation from the CDC to the RDC k;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t′\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tdistance from the CDC to the RDC k;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tunit cost of transportation from the RDC k to the point of demand l;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tdistance from the RDC k to the point of demand l;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tW\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tadditional unit cost of stock-out;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tunit production cost;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\ts\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tunit inventory cost which refers to t. If t is one week, the cost is the weekly unit storage cost;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tfixed operative cost of the RCD k;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tvariable unit (i.e. for each unit of product) cost based on the product quantity which flows through the RDC k;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tdemand from the point of demand l in the time period t;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tS\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tb\n\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\tg\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tstarting stock-out at the beginning (t = 0) of the horizon of time T;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tI\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tb\n\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\tg\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tstarting storage quantity in RDC k;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tmaximum number of points of demand supplied by a generic RDC in any time period;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\to\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t∑\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tL\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t∑\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tT\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\ttotal amount of customer demand during the planning horizon T;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tC\n\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\tP\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tproduction capacity available in t;\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t1 if demand from the customer l in t is not null. 0 otherwise; \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tT\n\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tdelivery time required by the point of demand l;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\t\t\t\to\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tproduction lead time;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tdelivery lead time from the CDC to the generic RDC k;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tdelivery lead time from the RDC k to the point of demand l.
The objective function is composed of various contributions:
\n\t\t\t\t
\n\t\t\t\t\t\t\tC(CDC-RDC). It measures the total cost of transportation from the first level (CDC) to the second level (RDCs);
\n\t\t\t\t\t\t\tC(RDC-Demand), i.e. the total cost of transportation from the second level (RDCs) to the third level (points of demand);
\n\t\t\t\t\t\t\tC\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tPROD\n\t\t\t\t\t\t\t, i.e. the total production cost;
\n\t\t\t\t\t\t\tC\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tSTORAGE, i.e. the total storage cost;
\n\t\t\t\t\t\t\tC\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tRDC\n\t\t\t\t\t\t\t, first addend: total amount of fixed costs for the available RDCs;
\n\t\t\t\t\t\t\tC\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tRDC\n\t\t\t\t\t\t\t, second addend: total amount of variable costs for the available RDCs;
\n\t\t\t\t\t\t\tC\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tSTOCK-OUT\n\t\t\t\t\t\t\t, i.e. the total amount of extra stock-out cost. The parameter W is a large number so that solutions capable of respecting the customer delivery due dates can be proposed.
\n\t\t\t\t
The more significant constraints are expounded as follows:
\n\t\t\t\t
(19) guarantees the conservation of logistic flows to each facility in each period of time t;
(21) states that the product quantity from the RDC k to the point of demand l is delivered according to a lead time \n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t in order to satisfy the demand of period\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t. Stock-outs are backlogged and supplied in the following period;
(25) guarantees the individual sourcing requirement: if the demand of node l in t is not null (\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t= 1), only one RDC must serve the point of demand l ; otherwise (\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t= 0) the point of demand l is not assigned to any facilities;
(26) ensures that a demand node is only assigned to an RDC if it is possible to carry out the order by the customer delivery due date.
\n\t\t\t\t
The result of this problem formulation is explained in Fig. 2 (Decisions section): daily allocation of logistic requirements, i.e. determination of number of facilities, locations, storage capacities, and allocation of demand of customers (retailers) to retailers (DCs and/or production plants).
\n\t\t\t
\n\t\t\t
\n\t\t\t\t
6.2. Multi-period model with safety stock optimization
\n\t\t\t\t
The following model extends and improves the previous one by including the optimization of safety stock (SS) at each facility that belongs to the logistic network. The SS is the minimal level of inventory (storage quantity) that a company seeks to have on hand at any unit of time t in accordance to the uncertainty of customer demand. In particular the SS level depends on the following main factors (Persona et al., 2007):
\n\t\t\t\t
customer service level. High levels ask for great quantities of SS levels;
number and locations of points of demand which are allocated to production/distribution facilities;
variance of demand at each facility.
\n\t\t\t\t
The proposed model do not consider deterministic values of customer demand and this choice strongly increases the complexity of the decision problem. In particular, a recursive solving procedure has been properly developed and illustrated by Gebennini et al. (2007).
\n\t\t\t\t
The new problem formulation is based on a non-linear analytical model capable of optimizing the SS levels within the distribution system, utilizing the notation introduced for the SCMP2S and in the following lines:
\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tassumes value 1 if the RDC k supplies the point of demand l in any unit time t which belongs to T. 0 otherwise;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tvariance of demand at the point of demand l;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t^\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tsafety factor to control customer service level;\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\t\t^\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t⋅\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tcombined variance at the RDC k serving the point of demand l.
The proposed analytical model of LAP with safety stock is:
The objective function (35) minimizes the total network costs, composed of different contributions: transportation cost from the CDC to the RDCs, transportation cost from the RDCs to the points of demand, total production cost, total inventory cost including safety stock costs, fixed and variable costs associated respectively with the location of new facilities and with their working, and finally the total amount of extra stock-out cost.
\n\t\t\t\t
Eq. (35) includes a non-linear term which represents the SS cost for the generic facility k in accordance with the following equation which quantifies a contribution to the determination of the variance of demand cumulated in k and generated by the customer l:
\n\t\t\t\t\tGebennini et al. (2007) illustrate a recursive procedure based on a linearization of Eq. (35) for the determination of an admissible solution to the non-linear model.
\n\t\t\t
\n\t\t\t
\n\t\t\t\t
6.3. Case study. Multi-period model with SS
\n\t\t\t\t
The proposed model illustrated in Section 6.2 has been applied to the optimization of the logistic network of the Italian electronics company object of the case study introduced in Section 4. A first scenario of interest, called AS-IS, refers to the availability of the whole set of actual RDCs. It has been used for a comparison with new network configurations based on the optimization of the logistic system (TO-BE scenario).
\n\t\t\t\t
The obtained optimal solution establishes strategic and operational results such as the number and configuration of RDCs to keep open and the allocation of customer requests to the available RDCs. It is made up of only three RDCs: in Taiwan, USA and Germany. Direct shipments from the CDC to customers are suggested: South Europe, Middle East, North Africa are served directly from Italy. The allocation of demand to each RDC affects the SS levels that depend on both the total demand variance and the service level the company wants to guarantee. Table 2 presents the SS level maintained at each RDC which belongs to the network in the obtained solution: scenarios AS-IS and TO-BE are compared and a
\n\t\t\t\t
Table 2.
Safety stock level for RDCs.
\n\t\t\t\t
reduction of the total amount of SSs is achieved by the application of the optimizing procedure. Other tactical results obtained for each time period within the planning horizon T concern the product flows between CDC and RDCs, the product flows between RDCs and points of demand, the operational inventory levels and the production levels.
\n\t\t\t\t
\n\t\t\t\t\tTable 3 presents the cost savings obtained by the reduction of the number of RDCs in accordance to the TO-BE system configuration. In particular the obtained savings do not affect negatively the customer service level that is supposed to be constant: the value of \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t^\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is assumed equal to 2 (i.e. the customer service level is 0.95).
\n\t\t\t\t
Table 3.
Logistic cost comparison: AS-IS vs TO-BE.
\n\t\t\t\t
Finally Table 4 presents the percentage of variation in all the cost terms of the objective function (except for the production cost, unchanged in all simulated scenarios) by passing from \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t^\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t=1 to \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t^\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t=3, i.e. by incrementing the customer service level, in case of an higher unit inventory cost that makes total inventory holding cost more significant (total inventory holding cost is now 11% of transportation cost if \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t^\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t=1, and 21% if \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t^\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t=3).
\n\t\t\t\t
Table 4.
Logistic costs variations when.
\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t^\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tpasses from 1 to 3.
\n\t\t
\n\t\t
\n\t\t\t
7. Conclusions and further research
\n\t\t\t
This chapter presents original analytical models and supporting decision tools for the optimization of multi-echelon production distribution systems. In particular strategic models and methods have been discussed, applied and compared to tactical and operational approaches and applications. Nowadays industrial and service companies need effective and reliable supporting decision tools for the rapid planning, design, and execution of new production system from a strategic, tactical and operational point of view.
\n\t\t\t
The literature continuously presents original models for product, process, and system design but these models are rarely based on integrated and system-oriented approaches, so future studies need to integrate simultaneous contributions from industrial management, OR, statistics, and IT sciences.
\n\t\t\t
The size of the generic problem rapidly exceeds the computational limits of problem mathematical formulations and the need for local optimization decisions needs to be bypassed by using a reliable, efficient and global cost-based solutions that could be effective for the whole system. For this purpose Manzini et al. (2007b) introduce a supporting decision platform for the simultaneous design and management of a SC system (i.e. a production distribution network). The proposed platform represents the first step towards developing an expert system capable of supporting the integration of planning, design, management, control and optimization activities in a flexible production distribution system. The proposed tool is composed of strongly interrelated different decision modules. They are based on the application of both optimal mathematical formulations and simulation modelling which are capable of considering stochastic production and distribution processes such as transportation, logistic costing, customer demand, etc.
\n\t\t\t
Further research is needed to develop supporting methodologies for the simultaneous design of products, process, and production distribution systems. How can the global economic impact of the introduction of a new product, a process (e.g. a manufacturing or an assembly technology) or a production system (e.g. flexible manufacturing system) be measured?
\n\t\t\t
Furthermore industrial applications are achieved because the well known computational experiments proposed by several optimal or heuristic approaches in the literature suffer from the limitation of not being comprehensive and/or being unrealistic.
\n\t\t\t
In particular further research on SC and production system planning should follow the direction traced by the development of ERP systems e.g. by providing more affective planning and optimization modules for multi-echelon production/distribution systems.
\n\t\t\t
Finally, further research could take place to develop and apply supporting decision models capable of considering product recovery activities for the purpose of recycling, re-manufacturing, and reuse. These activities are an integral part of reverse logistics and management of product returns. In fact, scarce attention has been paid to how SC decisions and actions will affect other aspects of human life, such as the environment, social justice, and sustainability of natural resources.
\n\t\t
\n\t\n',keywords:null,chapterPDFUrl:"https://cdn.intechopen.com/pdfs/745.pdf",chapterXML:"https://mts.intechopen.com/source/xml/745.xml",downloadPdfUrl:"/chapter/pdf-download/745",previewPdfUrl:"/chapter/pdf-preview/745",totalDownloads:3303,totalViews:1061,totalCrossrefCites:1,totalDimensionsCites:4,hasAltmetrics:0,dateSubmitted:null,dateReviewed:null,datePrePublished:null,datePublished:"February 1st 2008",dateFinished:null,readingETA:"0",abstract:null,reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/745",risUrl:"/chapter/ris/745",book:{slug:"supply_chain"},signatures:"Riccardo Manzini and Rita Gamberini",authors:null,sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Review of the literature",level:"1"},{id:"sec_3",title:"3. A PDSD conceptual framework",level:"1"},{id:"sec_4",title:"4. Static network design",level:"1"},{id:"sec_4_2",title:"4.1. Single commodity 2-stage model (SC2S)",level:"2"},{id:"sec_5_2",title:"4.2. Single commodity 3-stage model (SC3S)",level:"2"},{id:"sec_6_2",title:"4.3. Multi commodity 3-stage model (MC3S)",level:"2"},{id:"sec_7_2",title:"4.4. Strategic planning. Case study",level:"2"},{id:"sec_9",title:"5. Fulfillment system design",level:"1"},{id:"sec_9_2",title:"5.1. Case study. A multi-echelon 3-stage system",level:"2"},{id:"sec_11",title:"6. Network management and dynamic facility location",level:"1"},{id:"sec_11_2",title:"6.1. Multi period single commodity 2-stage model (SCMP2S)",level:"2"},{id:"sec_12_2",title:"6.2. Multi-period model with safety stock optimization",level:"2"},{id:"sec_13_2",title:"6.3. Case study. Multi-period model with SS",level:"2"},{id:"sec_15",title:"7. Conclusions and further research",level:"1"}],chapterReferences:[{id:"B1",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tAmbrosino\n\t\t\t\t\t\t\tD.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tScutellà\n\t\t\t\t\t\t\tM. 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R.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2001\n\t\t\t\t\tLogistics of Facility Location and Allocation, Marcel Dekker Inc., 0-82470-493-2 New York.\n\t\t\t'},{id:"B28",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tVokurka\n\t\t\t\t\t\t\tR.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLummus\n\t\t\t\t\t\t\tR.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2000 The role of just-in-time in supply chain management. International Journal of Logistics Management, 11\n\t\t\t\t\t1 89-97, 0957-4093\n\t\t\t\t\n\t\t\t'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Riccardo Manzini",address:null,affiliation:'
Department of Industrial Mechanical Plants, University of Bologna
Department of Engineering Sciences and Methods, University of Modena and Reggio Emilia, Italy
'}],corrections:null},book:{id:"3603",title:"Supply Chain",subtitle:null,fullTitle:"Supply Chain",slug:"supply_chain",publishedDate:"February 1st 2008",bookSignature:"Vedran Kordic",coverURL:"https://cdn.intechopen.com/books/images_new/3603.jpg",licenceType:"CC BY-NC-SA 3.0",editedByType:"Edited by",isbn:null,printIsbn:"978-3-902613-22-6",pdfIsbn:"978-953-51-5824-0",editors:[{id:"396",title:"Dr.",name:"Vedran",middleName:null,surname:"Kordic",slug:"vedran-kordic",fullName:"Vedran Kordic"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},chapters:[{id:"731",title:"Supply Chain Collaboration",slug:"supply_chain_collaboration",totalDownloads:4760,totalCrossrefCites:4,signatures:"Ana Meca and Judith Timmer",authors:[null]},{id:"732",title:"Towards a Quantitative Performance Measurement Model in a Buyer-Supplier Relationship Context",slug:"towards_a_quantitative_performance_measurement_model_in_a_buyer-supplier_relationship_context",totalDownloads:2980,totalCrossrefCites:2,signatures:"Lamia Berrah and Vincent Cliville",authors:[null]},{id:"733",title:"A Framework for Assessing and Managing Large Purchaser - Minority Supplier Relationships in Supplier Diversity Initiatives",slug:"a_framework_for_assessing_and_managing_large_purchaser_-_minority_supplier_relationships_in_supplier",totalDownloads:2169,totalCrossrefCites:2,signatures:"Nicholas Theodorakopoulos and Monder Ram",authors:[null]},{id:"734",title:"An Evaluation Framework for Supply Chains Based on Corporate Culture Compatibility",slug:"an_evaluation_framework_for_supply_chains_based_on_corporate_culture_compatibility",totalDownloads:3577,totalCrossrefCites:0,signatures:"Khalid Al-Mutawah and Vincent Lee",authors:[null]},{id:"735",title:"How Negotiation Influences the Effective Adoption of the Revenue Sharing Contract: A Multi-Agent Systems Approach",slug:"how_negotiation_influences_the_effective_adoption_of_the_revenue_sharing_contract__a_multi-agent_sys",totalDownloads:2232,totalCrossrefCites:1,signatures:"Ilaria Giannoccaro and Pierpaolo Pontrandolfo",authors:[null]},{id:"736",title:"Mean-Variance Analysis of Supply Chain Contracts",slug:"mean-variance_analysis_of_supply_chain_contracts",totalDownloads:3292,totalCrossrefCites:0,signatures:"Tsan-Ming Choi",authors:[null]},{id:"737",title:"Developing Supply Chain Management System Evaluation Attributes Based on the Supply Chain Strategy",slug:"developing_supply_chain_management_system_evaluation_attributes_based_on_the_supply_chain_strategy",totalDownloads:6813,totalCrossrefCites:1,signatures:"Chun-Chin Wei and Liang-Tu Chen",authors:[null]},{id:"738",title:"Impact of Hybrid Business Models in the Supply Chain Performance",slug:"impact_of_hybrid_business_models_in_the_supply_chain_performance",totalDownloads:2684,totalCrossrefCites:0,signatures:"C. 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1. Introduction
1.1 Synovial joints and osteoarthritis
The free moving joints within the body are known as synovial joints and have the primary purpose of allowing forces applied to the skeleton to be transmitted as smooth, low-friction movements. The joint capsule, working alongside the muscles, tendons and ligaments stabilises the joint, whilst articular (or hyaline) cartilage covering the end of the bones in combination with synovial fluid within the joint space provides the environment for smooth, well-lubricated movements [1, 2]. In addition, some joints also contain fibrocartilaginous discs between the two bones to support the other joint components and dissipate the forces experienced by the joint, for instance, intervertebral discs in the spine, or the meniscus within the knee.
Osteoarthritis affects all of the structures within the joint and is defined as a condition causing pain within the joint, loss of function and decreased quality of life for patients [3]. The disease results in the degradation of cartilage and subsequent sclerosis and lesions in the now exposed subchondral bone, along with inflammation in the joint [4]. Tears within cartilaginous structures and new interactions between cartilage and bone, along with bone and bone, make for less smooth movements, pain, stiffness and reduction in joint function.
1.2 Epidemiology and impact
The most common joints affected by osteoarthritis include those of the knee, hip and hands with osteoarthritis of the knee the most commonly occurring form, affecting over 18% of the population in England [5].
With such a large proportion of the population affected, musculoskeletal conditions including osteoarthritis have considerable impact both medically and economically. Clinically, the pain and loss of function associated with osteoarthritis result in a lower quality of life reported by patients, who require a large number of GP visits and hospital admissions [6, 7, 8].
The underlying pathophysiology of osteoarthritis is unclear, with genetics, age, gender, obesity and previous injury all contributing to varying degrees in disease development and progression. The heterogeneous nature of the disease makes targeted treatment of cause and prevention of progression a challenge, with current best practice centring on patient education and lifestyle changes surrounding exercise, use of analgesics and anti-inflammatories to manage pain and inflammation and finally joint replacement at the severe end of the spectrum of disease [9]. However, this approach, with the exception of exercise targeting weight loss and strength, does not address an underlying cause or prevent progression of disease, an aspiration of future interventions for the disease.
Ranking the sixth most common cause of disability globally in 2010 [10], musculoskeletal conditions, including osteoarthritis, impact not only the healthcare system and patients but also their families [11]. Patients and their carers are at greater risk of being out of employment [12], with only 63% of those with a musculoskeletal condition in employment compared to 82% in those without a health condition [13].
With a predicted increase in the ageing population and an increase in obesity [14, 15, 16], the burden on health services and economic impact in terms of lost work time and disability is of growing concern. There is a real need for means of non-invasive early detection of osteoarthritis, sensitive means of monitoring progression and development of efficacious treatments to prevent and improve symptoms in order to improve quality of life and reduce the numbers progressing to severe disease and requiring joint replacement.
2. Standard methods of detection
Osteoarthritis is a condition affecting a multitude of tissues within a joint, and as such, approaches which give information to the clinician on bone, muscle, cartilaginous tissue and the microenvironment within a joint are required to give a full picture of the condition of a joint. Imaging is currently the main diagnostic tool used to assess osteoarthritis. Dependent upon the form of imaging used, a variety of tissues can be examined as markers of disease state and progression.
In clinical practice, a combination of clinical presentation and X-radiography (X-ray) is used to diagnose osteoarthritis. When a patient presents as over 45 years of age, with typical symptoms of osteoarthritis including pain within the joint during activity and minimal stiffness within the joint in the morning lasting no more than 30 min, then X-ray is not indicated for diagnosis [9, 17].
However, X-ray is useful when differential diagnosis is possible, and in certain scenarios, magnetic resonance imaging is used to give additional information on damage to tissues within the joint and inform treatment options.
2.1 X-radiography
X-ray works upon the principle of differential absorbance of radiation by different tissues, with dense tissues such as the bone absorbing a large proportion of the radiation compared to soft tissues such as the muscle and connective tissue.
As a result, the bone appears bright white on images and can be studied for changes in morphology, whereas soft tissues show less differentiation and are not easily examined.
The current gold standard in the diagnosis of osteoarthritis from radiographic images involves the scoring of X-ray images using the Kellgren-Lawrence (KL) scale. The Kellgren-Lawrence is a five-point scale which categorises disease severity based upon the assessment of bony changes, appearances of osteophytes and joint space narrowing within the joint [18]. The description of the radiographic findings at different KL grades can be seen in Table 1.
Grade
Description of radiographic findings
0
No evidence of radiographic osteoarthritis
1
Doubtful narrowing of the joint space and possible osteophytic lipping
2
Definite osteophytes and possible narrowing of the joint space
3
Moderate multiple osteophytes, definite narrowing of the joint space, small pseudocystic areas with sclerotic walls and possible deformity of bone contour
4
Large osteophytes, marked narrowing of joint space, sever sclerosis and definite deformity of bone contour
Table 1.
Kellgren-Lawrence scale description of radiographic findings.
The KL scale was first described in 1957 in response to an identified need to standardise the definition of changes within an osteoarthritic joint in order to improve inter-rater reliability when reporting the disease [18]. Thorough analysis of the performance of the scale at joints throughout the body revealed that whilst correlation between the defined changes and osteoarthritis were observed at all joints bars the wrist, the greatest inter-rater agreement was found within the knee joint. Intra-rater repeatability followed a similar trend with slightly better agreement between readings. This has subsequently been reflected in the most common use of the scale in the assessment of the knee joint.
More recent comparison of radiographic scoring systems has established that for the knee joint, the KL scale has stood the test of time, with no subsequently developed grading systems outperforming the inter-rater repeatability of this scale [19]. However, whilst the limit of inter and intra-observer reliability in assessing radiographic osteoarthritis may have been reached (correlation coefficients around 0.8), it is acknowledged that a more diverse manner of assessment of osteoarthritis may be warranted to improve sensitivity when assessing disease progression and specificity for aspects of the homogeneous pathophysiology underlying the disease.
In terms of sensitivity, KL scoring of radiographs does not perform well in the detection of early disease or in the monitoring of disease progression, where large time periods are required to observe a change in category during which time symptomatic progression may have occurred [20].
Alone, radiographic assessment using the Kellgren-Lawrence scale allows direct assessment of bony changes such as osteophyte formation, however, relies on indirect measures of joint space narrowing to assess cartilaginous change. The surrogate marker of joint space narrowing in place of direct measurement of cartilage, whilst important in the sensitivity of Kellgren-Lawrence scale to disease severity, does not perform well when compared with changes observed arthroscopically [19, 21].
This may go some way to explaining the disparity in patient symptom reporting in the form of self-reported osteoarthritis, clinically diagnosed osteoarthritis and disease severity suggested using the Kellgren-Lawrence scale [22]. In addition to indirect cartilage measurements, the Kellgren-Lawrence score is based solely on the femorotibial joint. As osteoarthritis can also affect the patellofemoral joint, this could account for further disparity between symptoms and radiographic severity of disease [20].
2.2 Magnetic resonance imaging
In contrast to X-radiography, magnetic resonance imaging (MRI) can directly image a number of tissues, including the cartilage, bone and fluids such as that found in the synovium. Several approaches have been taken to the assessment of joints with suspected osteoarthritis using MRI.
A number of joint-specific semi-quantitative scoring systems have been developed using features considered important in osteoarthritis disease manifestation, including bone marrow lesions, meniscal scores and scores of cartilage loss. For the knee, the scoring systems developed include the whole-organ MRI score (WORMS), the knee osteoarthritis scoring system (KOSS), the Boston-Leeds OA knee scoring (BLOKS) and the MRI osteoarthritis knee score (MOAKS), which brings together the strengths of the WORMS and BLOKS systems whilst standardising the definitions used [23].
Quantitative analysis of specific tissues has also been used to measure thickness, area and volume of cartilage, bone area and area of the bone that is denuded, as well as combining the two to assess cartilage thickness over areas of denuded bone. Whilst concentrating on a smaller region of the joint, this approach removes some of the subjectivity associated with the semi-quantitative scores detailed above, both for MRI and X-ray scoring [23, 24, 25, 26].
The benefits of MRI for use both clinically and within research are a trade-off between increased sensitivity and specificity and protocols which are realistic for application in a given setting. Semi-quantitative MRI protocols can be performed using clinical MRI equipment, however, have the same caveats of KL scoring of X-rays in terms of inter and intra-rater reliability.
Quantitative measures of the cartilage and bone remove some of the subjective elements of semi-quantitative assessment. The changes of cartilage and bone measurements can be exceedingly small in magnitude, allowing assessment of much smaller anatomical change over shorter timeframes than those observed using X-ray. Making such small measurements presents its own challenges and is time-consuming, whilst producing such small measurements of change that relationship to clinical outcomes can be weak [27]. However, being direct in nature, quantitative measures have shown promise in improving association of imaging techniques with disease symptoms and progression compared with KL scoring of X-rays. Denuded bone area has been shown to correlate with concurrent and incident knee pain [28], whilst changes in cartilage thickness have been linked to the likelihood of disease progression to the point of needing knee joint replacement surgery [29, 30].
In addition to semi-quantitative and quantitative measurements, the use of contrast and powerful MRI imaging protocols extend the means to assess tissue, enabling assessment of components of the ultrastructure of articular cartilage and the meniscus along with the synovial fluid via compositional and diffusion MRI, respectively. This makes MRI a potentially powerful tool in assessing the impact of osteoarthritis on the entirety of a joint, as well as in identifying factors driving disease and predicting disease progression.
High-resolution MRI protocols and high doses of contrast prove most useful in research aimed at understanding of the mechanisms of osteoarthritis and assessment of disease progression or slowing with intervention. However, these are time-consuming protocols and contrast doses can far outstrip recommended doses accepted in clinical practice [31].
The added power of MRI in the assessment of osteoarthritis is most likely to remain predominantly within the research field at this point in time, as access to advanced equipment, lack of uniform protocols and the time-consuming nature of post-processing that is required limits use clinically.
2.3 Other biomarkers of osteoarthritis
Whilst X-Ray and MRI are the two primary forms of imaging used to assess osteoarthritic joints, both computer tomography (CT) and ultrasound have also been employed for this purpose, generally in a research setting, where MRI is proving to provide greatest accuracy [32]. For CT, the use is limited due to CT scans delivering a high radiation dose without delivering significantly greater sensitivity to disease progression than X-ray or MRI.
Whilst ultrasound allows direct imaging of the cartilage which is not obtained during X-ray, interpretation and observations made can vary between operators, especially at joints further from the surface of the skin. This is least marked in superficial joints, and assessment of inflammation and effusion has drawn parallels with disease severity and progression [33, 34, 35]. Therefore, ultrasound may be most useful in adding measures associated with inflammation when assessing joints of the hand rather than the knee and hip which are much deeper joints.
Finally, biochemical markers associated with inflammation and degradation of the bone and cartilage are under investigation as additional biomarkers for osteoarthritis. This presents its own challenges as whilst these markers may well be sensitive to change in internal environment, their specificity to osteoarthritis and location of degeneration are proving more of obstacle, with generally weak associations seen between biochemical biomarkers of disease and measures of use in assessing disease severity and progression [36, 37]. That said, there is some evidence that markers may be able to offer additional strength in assessing osteoarthritis severity and response to treatments with further research [38].
2.4 Current challenges in diagnosis and treatment
Individually the current means to diagnose and assess progression of osteoarthritis are limited by one or more factors, namely, subjectivity of measures including high inter- and intra-rater repeatability in semi-quantitative imaging, low sensitivity for change in disease state or low specificity for disease tissue or location.
This presents challenges when making informed clinical decisions, investigating new interventions and determining the effects of preventative measures on disease progression. The low sensitivity of current biomarkers also limits the application of stratified medicine in the approach to new treatments, an area that is of particular interest given the marked clinical and biological heterogeneity of this condition [39].
As the disease is driven by multiple pathogenic factors, it may be that a combination of multiple diagnostic measures is required to develop a sensitive biomarker for osteoarthritis. This concept is currently demonstrated through the development of computational risk factor tools based on a range of self-reported osteoarthritis risk factors, aimed at patient education and pre-emptive lifestyle intervention [40, 41, 42]. More recently, the tool for osteoarthritis risk prediction has proven inclusion of MRI measures in combination with KL scored radiographs provides a more powerful predictive tool for predicting disease progression [43]. Furthering this approach using other potential biomarkers for osteoarthritis, including imaging and biochemical markers of cartilage and bone change, may allow even greater sensitivity and specificity.
With this in mind, research has progressed in innovative approaches to develop biosensors that address aspects of osteoarthritis that are currently unmeasured. To date, all biomarkers for the disease consider circulating biochemicals or images of the knee in a static state. As the symptoms of osteoarthritis relate directly to movements of the joint, a novel approach to assessing changes in interactions between tissues during joint movement is being investigated using acoustics within the joint.
3. Acoustic medical technologies for joint health
Due to its non-invasive nature, the use of sound or vibration has found many medical applications associated with the musculoskeletal system.
For instance, as discussed above, ultrasound imaging, or ultrasonography (US), can be a useful tool in rheumatology. It is increasingly used to image and evaluate the inflammatory aspects of rheumatic diseases as an assessment tool for tendons and soft tissue [44, 45]. It has been applied to osteoarthritis specifically, having been shown to be a sensitive tool for the evaluation of synovitis (joint inflammation) and joint effusion (the flow of blood and other fluids in joints), through direct imaging and the use of Doppler signal analysis, a form of flow velocimetry [44, 45, 46, 47, 48]. Whilst US can be used for imaging musculoskeletal changes in osteoarthritis, such as changes in cartilage thickness, it is limited. It has been noted that US may be limited in assessing cartilage in larger weight-bearing joints [49] because of the inherent inability of ultrasound to pass through denser bony structures and therefore penetrate to the deeper portions of the joint [50]. The central portion of thick joints cannot be visualised with US [51], but US can detect osteophytosis (bone spurs forming around joints) at greater rates than conventional radiography. Being non-ionising and able to image soft tissues, US is a good alternative to radiographic imaging. Magnetic resonance imaging (MRI) offers excellent tissue contrast and anatomical resolution compared to US [49]. MRI can detect changes in the volumes of cartilage, whereas US is only capable of quantifying changes in thicknesses. Therefore, whilst MRI is more expensive, US is primarily only used as an alternative for anatomical imaging when there is hardware present within the patient, i.e. implants and some older cardiac defibrillators and pacemakers, which precludes the use of MRI [52].
As well as for imaging, ultrasound can be utilised directly as a treatment for OA [53, 54]. The management of OA involves the relief of pain and the maintenance or improvement of joint function. The American College of Rheumatology (ACR) and the European League Against Rheumatism (EULAR) recommend a combination of pharmacological and nonpharmacological treatments [55]. Various nonpharmacological treatments, including exercise, physical therapy, hot packs and therapeutic ultrasound (TU) etc., exist with varying evidence of efficacy. In TU, mechanical energy in the form of pulsed or continuous high-frequency vibrations is applied directly to the joint [56]. This is reputed to reduce oedema or cysts [57], as well as reduce inflammation, relieve pain and accelerate tissue repair; however, results of clinical studies are conflicting [55, 56]. The applied ultrasonic vibrations cause atomic oscillations in the tissue; the amplitude of which depends on the intensity or power of the applied beam. When applied continuously, this can result in thermal effects in the tissue, which are reduced when the beam is pulsed [56]. When the ultrasonic beam has high intensity, the atoms in the attenuating medium no longer oscillate around their equilibrium position but have a net motion along the axis of the beam [53]. This can result in damage or micro-machining due to the ultrasound-induced forces, allowing TU to be used as a surgical tool [53]. High-intensity TU can also result in the movement of particles and fluid within the tissue. This phenomenon has been used to drive pharmaceuticals, such as non-steroidal anti-inflammatory drugs (NSAIDs) and corticosteroids, into the tissue [58, 59], facilitating local delivery.
3.1 Acoustic detection
Spontaneous emission of acoustic waves and other vibrations has been recorded during the flexion and extension of joints, as well as the fracture and wear of bones and implants [60, 61]. Studies have shown that these vibrations are affected by musculoskeletal disorders in joints, making vibration monitoring a useful diagnostic tool [62]. However, joints are highly complex heterogeneous structures over a wide range of length scales. Parameters like wave velocity, dispersion and attenuation all affect how waves travel through tissues, making interpretation of the waveform complicated. The following techniques have been developed to resolve this issue:
3.1.1 Phonoarthrography
The earliest studies on the monitoring of the spontaneous emission of acoustic waves were based on the use of stethoscopes to amplify audible sounds generated within joints [63, 64]. Early joint auscultation in this manner was initially a manual process and was inherently subjective. Still, these studies showed that whilst there are ‘normal joint sounds’, the sound produced is affected by different kinds of injury and arthritis [65]. That said, this method is not yet used in primary care and has only received modest attention in the literature since its first appearance in 1902 [63, 66].
Later studies attempted to reduce the subjectivity of this method by recording the sounds using microphones in conjunction with joint measurement technologies such as goniometers and video tracking [67]. Several of these studies note that pathological signals have major frequency components at low frequencies, that is, below 1000 Hz [64, 68]. The sensitivity range of the microphones used is usually in the range 50 Hz to 15 kHz; however, it has been suggested that standard acoustic recording microphones are not appropriate for the monitoring of joint signals, being too sensitive to background noise, with vibration transducers, or contact sensors, and accelerometers being preferred [61, 69]. Studies such as that by Chu et al. employed a differential microphone pair for noise cancellation and bandpass filters to minimise low-frequency movement artefacts and high-frequency transducer noise to mitigate this issue [61]. Conversely, other studies [70] suggest that as microphones are able to detect higher frequencies and no direct contact with the body is required, the combination of signals from both microphones and accelerometers might perform better than anyone signal alone.
Data analysis in early studies generally only used traditional stationary spectrum estimation methods using oscilloscopes or narrow-band spectrum analysers, with key measures being the frequency, wavelength, wave number and amplitude [64]. However, it is clear that the signals are nonstationary in nature, especially as different signals are generated at different joint positions [69]. As a result of this observation, more sophisticated spectral analysis methods were developed. One method is short-time Fourier analysis on segmented data where it is assumed that the data is stationary within each segment. This allows trends in the frequency component of the signal to be correlated with joint angle. The determination of the segments introduces subjectivity into the analysis. Therefore, techniques to track the nonstationarities in the signal, such as adaptive segmentation, linear prediction and autoregressive moving averages (ARMA), have been incorporated into the analysis [69].
3.1.2 Vibroarthrography (VAG)
Whilst phonoarthrography is based on the sound produced during the flexion or extension of joints, in VAG all vibrations produced during movement are considered [62]. Consequently, it is more common for a single accelerometer to be used as the sensor rather than a microphone [71]. It is also very common for signals in a frequency range below 1000 Hz to be of primary focus [72], with sampling rates of the order 1–4 kHz. A key advantage of the low sampling rate is that it allows for wireless data acquisition and processing using simple microcontrollers or single-board computers [73, 74]. That said, it has been suggested [71, 75] that single signal processing may be limited and multi-channel recordings may lead to better discrimination of the severity and location of joint injury or disorder. In many cases noise mitigation is achieved through prefiltering (commonly using a bandpass filter from 10 Hz to 1 kHz) and amplification prior to digitization at a specified sampling rate [76, 77]. The digital signal may go through additional filtering, such as that conducted by Andersen et al. [78] who used a Kaiser-windowed finite impulse response (FIR) bandpass filter.
There are other rationales for using multiple sensors during VAG as it has been observed that VAG may pick up vibrations not necessarily just due to the joint directly or to external interference [79]. For instance, the 10 Hz signal generated by the rectus femoris muscle which activates during the extension of the leg could interfere with the VAG signal recorded from the skin surface over the patella [80]. As this signal may vary in a similar fashion to the VAG signal, simple bandpass filtering may not be sufficient. It may be necessary to record the vibromyogram at the rectus femoris at the same time as the VAG signal and use adaptive filtering and noise cancellation techniques to isolate the VAG signal [79].
Therefore, the VAG signal is inherently nonstationary and potentially multicomponent in nature. The nature of the VAG signal means that it is not easily analysed using common signal processing techniques. This coupled with the difficulty in ascertaining the biological origin of the source of the signal is the main barrier to its use as a common diagnostic tool. As a result, much of the recent research activity has been focussed on feature extraction and statistical pattern classification [60]. Adaptive segmentation using least-square, linear prediction and autoregression algorithms is common [81, 82]. A host of statistical measures has been considered to characterise the VAG signal, including the form factors, skewness, kurtosis and entropy [71, 76]. It has also been shown that time-frequency distribution (TFD) [81, 83] and wavelet decomposition [84] are potentially powerful techniques for analysis and may negate the need for segmentation [83] but may be susceptible to noise [85]. These advancements have mostly been driven by developments in digital signal processing technologies that sped up analysis time as well as nonstationary signal analysis techniques developed for other biological signals like EEGs [84].
Using these techniques, spectral features such as frequency, energy and their respective spreads can be classified and linked to joint position, loading and pathology. The commonly used classifiers are neural network-based classifiers and support vector machines (SVM), as well as logistic regression and rule-based techniques [62, 71]. These neural networks and SVMs are supervised learning algorithms which search for a number of independent training data patterns taken from signals measured from participants with known pathologies to characterise new signals. These classification algorithms are increasingly dependable and can perform well with a limited amount of data. A number of different variants of these algorithms and classifiers have been investigated [60, 62]. Wu et al. [73] used an SVM based on the entropy and envelope amplitude features and achieved an overall accuracy of 83.56%. Nalband et al. [86] utilised an a priori algorithm with a least-square SVM classifier and claim accuracy of 94.31% with a false discovery rate of 0.0892. Kręcisz [87] achieved accuracies of >90% using a logistic regression-based method. In each of these cases, the VAG signals were collected during knee flexion/extension motion using an accelerometer secured to the participants patella.
3.1.3 Acoustic emission (AE)
AE for biomedical applications is derived from non-destructive techniques developed for detecting damage in engineering materials, such as metals and composites [88]. AE occurs when materials locally under stress emit energy in the form of transient elastic waves. This allows for the monitoring of microcrack initiation and propagation in the bones and joints [89]—essential parts of bone remodelling [90], and wear [91, 92]. Other characteristic sounds in joints, such as the bursting of gas bubbles in synovial joints during movement, can also be detected using AE [93]. AE frequencies are usually in the ultrasonic range and so detection often involves the use of ultrasonic sensors.
A number of researchers have proposed AE sensor-based joint monitoring systems using piezoelectric films, electret or MEMS-based microphones.
Toreyin et al. [94, 95] used an off-the-shelf low-noise MEMS microphone in conjunction with gyroscope and accelerometer pairs in order to monitor sounds generated during various complex motions. The microphone used had a sensitivity range of 100 Hz to 10 kHz, and the researchers suggested that the MEMS-based microphone had a similar performance to an electret microphone [94]. The acoustic data were sampled at 100 kHz, and the inertial data (monitoring joint angle and limb movement) at 1 kHz, with the data being collected by a field programmable gate array (FPGA)-based real-time processor. It was noted that air microphones do not exhibit signal losses due to motion artefacts, but they are sensitive to ambient noise.
Teague et al. [96] compared a piezoelectric film-based contact microphone to two air microphones: one electret and one MEMS-based. The air microphones were used with a 15 Hz high-pass filter and a second-order low-pass filter with a cut-off frequency of 21 kHz and sampled at 44.1 kHz using an acoustic recorder. The piezoelectric microphone was used with a 100 Hz high-pass filter followed by a fourth order low-pass filter with a 10 kHz cut-off frequency. It was sampled at 50 kHz using custom circuits. The 100 Hz high-pass filter was chosen to attenuate the motion artefact noise. It was noted that the electret and MEMS microphones performed similarly in detecting joint sounds, although the electret sensor was significantly more expensive. They were both sensitive to ambient and interface noise, including rubbing of the tape securing the sensors. It was noted that the air microphones did not need to be in contact with the skin. Experiments with sensors positioned 5 cm off the skin captured similar acoustic signals, albeit with lower amplitude. The piezoelectric sensor was more sensitive to interface noise but less sensitive to background noise. Importantly, the contact microphone did not pick up higher frequency vibrations as distinctly as the air microphones which provided higher quality recordings as indicated by higher SNIRs.
Jeong et al. [97] used a low-noise electret microphone with a frequency range of 50 Hz to 20 kHz recorded by an audio recorder at a rate of 44.1 kHz. Signals were digitally filtered using a finite impulse response bandpass filter with a bandwidth from 1 to 15 kHz to prioritise short duration joint sounds whilst supressing interface noise.
Feng and Chen [98] developed a piezoelectric sensor comprised of a lead zirconium titanate (PZT) film deposited on titanium cantilever arrays as an acoustic sensing layer. This sensor uses a 1-mm-tall SU8 cylindrical probe on each cantilever to be in direct contact with the skin of the participant and transmit vibrations to the sensor. A thermoresponsive poly(N-isopropylacrylamide) (PNIPA) film was integrated into the sensor to apply a force to the cantilever and hence improve contact between the probe and the skin when a current is applied across it. The sensor achieved a frequency range of up to 100 kHz, with at least one strong resonant peak at 390 Hz. A sampling rate of 2 MHz was used with a 1 kHz high-pass digital filter to remove low-frequency noise signals. Testing of the sensor on a butchered porcine leg during repeated joint flexure cycles revealed the presence of well-defined peaks located between 30 and 40 kHz, 60 and 70 kHz and 70 and 80 kHz. Similar trends to that observed with commercial AE sensors (the same used in the studies by Mascaro et al. in the JAAS system described later [99]) were noted during overuse of the joint.
Choi et al. [93] developed the bone joint acoustic sensor (BJAS). This has a pin-type probe on a disk-shaped piezoceramic supported by a damped metal plate. The structure is in a metal case with the probe in direct contact with the skin. The system used in conjunction with IMUs seems to have a frequency range of 100 Hz to 25 kHz and is sampled at 50 kHz.
Shark and Goodacre developed the joint acoustic analysis system (JAAS) [99, 100]. This system uses commercial piezoelectric contact ultrasonic acoustic sensors (with high sensitivity in the range 50–200 kHz but monitored over 20–400 kHz at a 1–5 MSPS sampling rate) [100] and electro-goniometers to provide joint angle-based AE during knee joint movement (see Figure 1). These commercial AE sensors use relatively thick piezoelectric bulk blocks for AE sensing and are housed in metal shells. The housing is fixed to the skin with surgical tape to maintain a rigid contact. The AE data acquisition operates in a non-continuous recording mode to minimise data volume. When the AE PCI data acquisition board is triggered by a signal value above a pre-set threshold, a ‘hit’ is recorded corresponding to an acoustic event. Each AE hit is recorded with a set of characteristic waveform features (i.e. dominant frequency, maximum amplitude and duration), and in addition the full waveforms were also stored, digitalized at a 1 MHz sampling frequency over a maximum duration of 15 ms [99]. The number of hits during each joint motion was used to determine a correlation with OA severity defined by KL scores determined using MRI data. It was noted that the frequency response of the acoustic sensor data is characterised by two peaks with a high probability of occurrence during knee measurements using a sit-stand-sit protocol, one in the low-frequency range (20–50 kHz) and the other one around 150 kHz. The latter frequency is mainly due to a peak of sensitivity of the sensor used [99].
Figure 1.
Output from the joint acoustic analysis system (JAAS). Recording is made as the participant performs five sit-stand-sit movements. A: Acoustic ‘hits’ from a single knee recorded using a piezoelectric contact ultrasonic acoustic sensors. Each square indicates one acoustic emission captured by the system. For each ‘hit’ a waveform is also captured [D] from which waveform characteristics are calculated by the software. Alongside the acoustic emissions, joint angle [B] and weight through the leg [C] are also recorded.
4. Conclusion
Using radiographic techniques to monitor variations in joint structure and morphology is the classic method of quantifying OA. However, this technique is ionising, often requires multiple measurements as only the plane perpendicular to the radiation is observed and cannot monitor soft tissue directly. MRI can measure the thickness and volume of cartilage, but there are limitations with respect to time and cost. Ultrasound can monitor joint effusion and the thickness of cartilage, but it is not possible for ultrasound to penetrate thick bone tissue and observe the whole joint. There is the additional issue of subjectivity and the large difference in reproducibility based on the skill of those analysing the image. The use of invasive cameras in arthroscopy and joint endoscopy necessitate recovery after diagnosis. These techniques also do not facilitate measurements using dynamic movements. The use of acoustic sensors has the potential to quantify and classify joint pathology whilst removing the subjectivity of classic imaging techniques. Despite progress in detecting differences between type and severity of joint disorders, questions remain about the true origin and form of acoustic signals generated by joint structural changes. Thus, a significant part of the challenge linked to acoustic signal analysis resides in the retrieval of pertinent parameters from irrelevant information in a robust and statistically significant way [78].
As yet, whilst several protocols, sensor types and data analysis techniques have been developed, to date there is no consensus on the most adequate way to record and process vibration data [60]. The methodological aspects of acoustic assessments, such as sensor placement and outcomes measures have not been thoroughly investigated allowing doubt in the technique to remain. For instance, for knee investigations, many studies [73, 81, 101] favour what may be called an open kinematic chain configuration [102] whereby participants sit in a chair and lift their legs in a repetitive fashion, perhaps with weights attached. This has the advantage of being able to vary the load on the joint and allow for the inclusion of participants with advanced degenerative conditions or injuries affecting the limitation of the range of motion in the joint. A common alternative protocol involves repeated sit-stand-sit movements [103, 104, 105], creating a closed kinematic chain. This latter configuration perhaps has the advantage of forming a more natural loading of the knee joint. It potentially has the consequence of being inconsistent over time, as people can have the tendency of adjusting their movement to compensate for restricted or painful movement, thus changing the distribution of forces and moments acting on the knee [106]. Data comparing the protocols is limited, and there is no strong evidence for favouring one protocol over the other or indeed over alternatives, such as squatting [94, 102]. Given the protocol affects the loading of the joint and the frequency response of the vibration data generated, it also affects the potential consistency of the statistics derived therefrom and their subsequent interpretation for diagnostic and prognostic purposes. This suggests the necessity of a standard protocol if such techniques are to be used for monitoring the development of OA in an individual over time for clinical or research purposes.
Similarly, it is unclear what sort of vibrations and which frequency range is the most pertinent range to measure. In phonoarthrography acoustic waves in the audible range are of most interest. In VAG, focus is on low-frequency (<1000 Hz) vibrations, the cause and nature of which is more general. In AE, acoustic signals are of primary focus, albeit generally of a higher frequency than that used in phonoarthrography. Whilst there is a significant amount of overlap between the techniques, there are important data that can be missed if one technique is favoured. There is little evidence to suggest that one technique is inherently better than the other, simply due to the lack of comparative studies. The lack of commonality in technique makes meta-analysis difficult. One limitation that is preventing the direct comparison is the lack of technologies that allow high-quality acoustic data to be collected at high sampling rates (>5 MSPS) for significant time periods as such sensors will inherently generate vast amounts of data requiring significant processing. Multiple sensors covering the different frequency ranges of interest are likely to be the way forward, but this strategy will have the disadvantage of comparing signals recorded at different sites, making the analysis more difficult. In any case, further study relating the acoustic signal back to the biomechanics of joint pathology may provide a stronger scientific basis to the causation of the signal, instead of relying on correlations. This will reduce the subjectivity of the analysis and facilitate diagnosis and prognosis, allowing this technique to become a powerful clinical tool.
Acknowledgments
We thank the research team at Lancaster University, led by Prof. Goodacre, who helped in the development of the concepts within this chapter. We also thank the University of Cumbria for providing funding to support the publication of this chapter.
Conflict of interest
The authors declare that they have no conflict of interest.
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The renal biopsy showed a membranous nephropathy (MN). In the blood analysis the patient presented antibodies against M-type phospholipase A2 receptor (anti-PLA2R) positive at a very high titer. Given the existence of idiopathic membranous nephropathy (IMN), treatment was started with a modified Ponticelli regimen, with no response, requiring periodic ultrafiltration sessions. Rituximab induces nephrotic syndrome (NS) remission in two-thirds of patients with IMN, even after other treatments have failed. We proposed treatment with rituximab based on published evidence. In IMN, the presence of M-type anti-receptor antibodies of A2 phospholipase is considered highly specific to idiopathic forms, but the presence of such antibodies has not been shown to be associated with a particular clinical profile. Assessing circulating anti-PLA2R autoantibodies and proteinuria may help in monitoring disease activity and guiding personalized rituximab therapy in nephrotic patients with IMN.",signatures:"María Carmen Prados Soler, María Dolores Del Pino y Pino, Álvaro Pérez Fernández, Llenalia Gordillo García, María José López Ruiz and César Luis Ramírez-Tortosa",authors:[{id:"291444",title:"Dr.",name:"María Carmen",surname:"Prados Soler",fullName:"María Carmen Prados Soler",slug:"maria-carmen-prados-soler",email:"lensasu@yahoo.es"},{id:"301092",title:"Dr.",name:"María Dolores",surname:"Del Pino Y Pino",fullName:"María Dolores Del Pino Y Pino",slug:"maria-dolores-del-pino-y-pino",email:"mdpinoypino@gmail.com"},{id:"301094",title:"Dr.",name:"Álvaro",surname:"Pérez Fernández",fullName:"Álvaro Pérez Fernández",slug:"alvaro-perez-fernandez",email:"alvaroperfdez@gmail.com"},{id:"301095",title:"Dr.",name:"Llenalia",surname:"Gordillo García",fullName:"Llenalia Gordillo García",slug:"llenalia-gordillo-garcia",email:"llenaliagg@hotmail.com"},{id:"301096",title:"Dr.",name:"María José",surname:"López Ruiz",fullName:"María José López Ruiz",slug:"maria-jose-lopez-ruiz",email:"mjoselopez6@hotmail.com"},{id:"301097",title:"Dr.",name:"César Luis",surname:"Ramirez-Tortosa",fullName:"César Luis Ramirez-Tortosa",slug:"cesar-luis-ramirez-tortosa",email:"cesarl.ramirez.sspa@juntadeandalucia.es"}],book:{title:"Glomerulonephritis and Nephrotic Syndrome",slug:"glomerulonephritis-and-nephrotic-syndrome",productType:{id:"1",title:"Edited Volume"}}}],collaborators:[{id:"229083",title:"Associate Prof.",name:"Samuel N.",surname:"Uwaezuoke",slug:"samuel-n.-uwaezuoke",fullName:"Samuel N. Uwaezuoke",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/229083/images/6684_n.jpg",biography:"Born in Lagos on 4th March, 1966. Had primary education at the cities of Abakaliki, Aba and Enugu, all in South east Nigeria. Secondary education took place at Union Secondary School, Awkunanaw- Enugu (formerly, Boys\\' High School Awkunanaw) between 1977 to 1982. Read medicine at the University of Nigeria, Nsukka where a Bachelor of Medicine and Bachelor of Surgery degree was obtained in 1988. Had post-graduate medical training in the West African College of Physicians between 1991 to 1999, specializing in Pediatrics. Worked initially as a research fellow in the Institute of Child Health, U.N.T.H Enugu between 1999 and 2004 before employment as an academic staff in the College of Medicine, University of Nigeria, Nsukka. Currently an Associate Professor of Pediatrics in the institution and an Honorary Consultant Pediatrician with U.N.T.H Ituku-Ozalla, Enugu. Married to Ogonna Blessing and blessed with a daughter, Chinenye",institutionString:null,institution:{name:"University of Nigeria, Nsukka",institutionURL:null,country:{name:"Nigeria"}}},{id:"231042",title:"Associate Prof.",name:"Maria",surname:"Stangou",slug:"maria-stangou",fullName:"Maria Stangou",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"294671",title:"Dr.",name:"Jorge Enrique",surname:"Moreno Collazos",slug:"jorge-enrique-moreno-collazos",fullName:"Jorge Enrique Moreno Collazos",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"295668",title:"Prof.",name:"Diana Carolina",surname:"Zona Rubio",slug:"diana-carolina-zona-rubio",fullName:"Diana Carolina Zona Rubio",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"299733",title:"Dr.",name:"Polyvios",surname:"Arseniou",slug:"polyvios-arseniou",fullName:"Polyvios Arseniou",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"299734",title:"Dr.",name:"Stamatina",surname:"Stai",slug:"stamatina-stai",fullName:"Stamatina Stai",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"301092",title:"Dr.",name:"María Dolores",surname:"Del Pino Y Pino",slug:"maria-dolores-del-pino-y-pino",fullName:"María Dolores Del Pino Y Pino",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"301094",title:"Dr.",name:"Álvaro",surname:"Pérez Fernández",slug:"alvaro-perez-fernandez",fullName:"Álvaro Pérez Fernández",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"301095",title:"Dr.",name:"Llenalia",surname:"Gordillo García",slug:"llenalia-gordillo-garcia",fullName:"Llenalia Gordillo García",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"301096",title:"Dr.",name:"María José",surname:"López Ruiz",slug:"maria-jose-lopez-ruiz",fullName:"María José López Ruiz",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null}]},generic:{page:{slug:"our-story",title:"Our story",intro:"
The company was founded in Vienna in 2004 by Alex Lazinica and Vedran Kordic, two PhD students researching robotics. While completing our PhDs, we found it difficult to access the research we needed. So, we decided to create a new Open Access publisher. A better one, where researchers like us could find the information they needed easily. The result is IntechOpen, an Open Access publisher that puts the academic needs of the researchers before the business interests of publishers.
",metaTitle:"Our story",metaDescription:"The company was founded in Vienna in 2004 by Alex Lazinica and Vedran Kordic, two PhD students researching robotics. While completing our PhDs, we found it difficult to access the research we needed. So, we decided to create a new Open Access publisher. A better one, where researchers like us could find the information they needed easily. The result is IntechOpen, an Open Access publisher that puts the academic needs of the researchers before the business interests of publishers.",metaKeywords:null,canonicalURL:"/page/our-story",contentRaw:'[{"type":"htmlEditorComponent","content":"
We started by publishing journals and books from the fields of science we were most familiar with - AI, robotics, manufacturing and operations research. Through our growing network of institutions and authors, we soon expanded into related fields like environmental engineering, nanotechnology, computer science, renewable energy and electrical engineering, Today, we are the world’s largest Open Access publisher of scientific research, with over 4,200 books and 54,000 scientific works including peer-reviewed content from more than 116,000 scientists spanning 161 countries. Our authors range from globally-renowned Nobel Prize winners to up-and-coming researchers at the cutting edge of scientific discovery.
\\n\\n
In the same year that IntechOpen was founded, we launched what was at the time the first ever Open Access, peer-reviewed journal in its field: the International Journal of Advanced Robotic Systems (IJARS).
\\n\\n
The IntechOpen timeline
\\n\\n
2004
\\n\\n
\\n\\t
Intech Open is founded in Vienna, Austria, by Alex Lazinica and Vedran Kordic, two PhD students, and their first Open Access journals and books are published.
\\n\\t
Alex and Vedran launch the first Open Access, peer-reviewed robotics journal and IntechOpen’s flagship publication, the International Journal of Advanced Robotic Systems (IJARS).
\\n
\\n\\n
2005
\\n\\n
\\n\\t
IntechOpen publishes its first Open Access book: Cutting Edge Robotics.
\\n
\\n\\n
2006
\\n\\n
\\n\\t
IntechOpen publishes a special issue of IJARS, featuring contributions from NASA scientists regarding the Mars Exploration Rover missions.
\\n
\\n\\n
2008
\\n\\n
\\n\\t
Downloads milestone: 200,000 downloads reached
\\n
\\n\\n
2009
\\n\\n
\\n\\t
Publishing milestone: the first 100 Open Access STM books are published
\\n
\\n\\n
2010
\\n\\n
\\n\\t
Downloads milestone: one million downloads reached
\\n\\t
IntechOpen expands its book publishing into a new field: medicine.
\\n
\\n\\n
2011
\\n\\n
\\n\\t
Publishing milestone: More than five million downloads reached
\\n\\t
IntechOpen publishes 1996 Nobel Prize in Chemistry winner Harold W. Kroto’s “Strategies to Successfully Cross-Link Carbon Nanotubes”. Find it here.
\\n\\t
IntechOpen and TBI collaborate on a project to explore the changing needs of researchers and the evolving ways that they discover, publish and exchange information. The result is the survey “Author Attitudes Towards Open Access Publishing: A Market Research Program”.
\\n\\t
IntechOpen hosts SHOW - Share Open Access Worldwide; a series of lectures, debates, round-tables and events to bring people together in discussion of open source principles, intellectual property, content licensing innovations, remixed and shared culture and free knowledge.
\\n
\\n\\n
2012
\\n\\n
\\n\\t
Publishing milestone: 10 million downloads reached
\\n\\t
IntechOpen holds Interact2012, a free series of workshops held by figureheads of the scientific community including Professor Hiroshi Ishiguro, director of the Intelligent Robotics Laboratory, who took the audience through some of the most impressive human-robot interactions observed in his lab.
\\n
\\n\\n
2013
\\n\\n
\\n\\t
IntechOpen joins the Committee on Publication Ethics (COPE) as part of a commitment to guaranteeing the highest standards of publishing.
\\n
\\n\\n
2014
\\n\\n
\\n\\t
IntechOpen turns 10, with more than 30 million downloads to date.
\\n\\t
IntechOpen appoints its first Regional Representatives - members of the team situated around the world dedicated to increasing the visibility of our authors’ published work within their local scientific communities.
\\n
\\n\\n
2015
\\n\\n
\\n\\t
Downloads milestone: More than 70 million downloads reached, more than doubling since the previous year.
\\n\\t
Publishing milestone: IntechOpen publishes its 2,500th book and 40,000th Open Access chapter, reaching 20,000 citations in Thomson Reuters ISI Web of Science.
\\n\\t
40 IntechOpen authors are included in the top one per cent of the world’s most-cited researchers.
\\n\\t
Thomson Reuters’ ISI Web of Science Book Citation Index begins indexing IntechOpen’s books in its database.
\\n
\\n\\n
2016
\\n\\n
\\n\\t
IntechOpen is identified as a world leader in Simba Information’s Open Access Book Publishing 2016-2020 report and forecast. IntechOpen came in as the world’s largest Open Access book publisher by title count.
\\n
\\n\\n
2017
\\n\\n
\\n\\t
Downloads milestone: IntechOpen reaches more than 100 million downloads
\\n\\t
Publishing milestone: IntechOpen publishes its 3,000th Open Access book, making it the largest Open Access book collection in the world
We started by publishing journals and books from the fields of science we were most familiar with - AI, robotics, manufacturing and operations research. Through our growing network of institutions and authors, we soon expanded into related fields like environmental engineering, nanotechnology, computer science, renewable energy and electrical engineering, Today, we are the world’s largest Open Access publisher of scientific research, with over 4,200 books and 54,000 scientific works including peer-reviewed content from more than 116,000 scientists spanning 161 countries. Our authors range from globally-renowned Nobel Prize winners to up-and-coming researchers at the cutting edge of scientific discovery.
\n\n
In the same year that IntechOpen was founded, we launched what was at the time the first ever Open Access, peer-reviewed journal in its field: the International Journal of Advanced Robotic Systems (IJARS).
\n\n
The IntechOpen timeline
\n\n
2004
\n\n
\n\t
Intech Open is founded in Vienna, Austria, by Alex Lazinica and Vedran Kordic, two PhD students, and their first Open Access journals and books are published.
\n\t
Alex and Vedran launch the first Open Access, peer-reviewed robotics journal and IntechOpen’s flagship publication, the International Journal of Advanced Robotic Systems (IJARS).
\n
\n\n
2005
\n\n
\n\t
IntechOpen publishes its first Open Access book: Cutting Edge Robotics.
\n
\n\n
2006
\n\n
\n\t
IntechOpen publishes a special issue of IJARS, featuring contributions from NASA scientists regarding the Mars Exploration Rover missions.
\n
\n\n
2008
\n\n
\n\t
Downloads milestone: 200,000 downloads reached
\n
\n\n
2009
\n\n
\n\t
Publishing milestone: the first 100 Open Access STM books are published
\n
\n\n
2010
\n\n
\n\t
Downloads milestone: one million downloads reached
\n\t
IntechOpen expands its book publishing into a new field: medicine.
\n
\n\n
2011
\n\n
\n\t
Publishing milestone: More than five million downloads reached
\n\t
IntechOpen publishes 1996 Nobel Prize in Chemistry winner Harold W. Kroto’s “Strategies to Successfully Cross-Link Carbon Nanotubes”. Find it here.
\n\t
IntechOpen and TBI collaborate on a project to explore the changing needs of researchers and the evolving ways that they discover, publish and exchange information. The result is the survey “Author Attitudes Towards Open Access Publishing: A Market Research Program”.
\n\t
IntechOpen hosts SHOW - Share Open Access Worldwide; a series of lectures, debates, round-tables and events to bring people together in discussion of open source principles, intellectual property, content licensing innovations, remixed and shared culture and free knowledge.
\n
\n\n
2012
\n\n
\n\t
Publishing milestone: 10 million downloads reached
\n\t
IntechOpen holds Interact2012, a free series of workshops held by figureheads of the scientific community including Professor Hiroshi Ishiguro, director of the Intelligent Robotics Laboratory, who took the audience through some of the most impressive human-robot interactions observed in his lab.
\n
\n\n
2013
\n\n
\n\t
IntechOpen joins the Committee on Publication Ethics (COPE) as part of a commitment to guaranteeing the highest standards of publishing.
\n
\n\n
2014
\n\n
\n\t
IntechOpen turns 10, with more than 30 million downloads to date.
\n\t
IntechOpen appoints its first Regional Representatives - members of the team situated around the world dedicated to increasing the visibility of our authors’ published work within their local scientific communities.
\n
\n\n
2015
\n\n
\n\t
Downloads milestone: More than 70 million downloads reached, more than doubling since the previous year.
\n\t
Publishing milestone: IntechOpen publishes its 2,500th book and 40,000th Open Access chapter, reaching 20,000 citations in Thomson Reuters ISI Web of Science.
\n\t
40 IntechOpen authors are included in the top one per cent of the world’s most-cited researchers.
\n\t
Thomson Reuters’ ISI Web of Science Book Citation Index begins indexing IntechOpen’s books in its database.
\n
\n\n
2016
\n\n
\n\t
IntechOpen is identified as a world leader in Simba Information’s Open Access Book Publishing 2016-2020 report and forecast. IntechOpen came in as the world’s largest Open Access book publisher by title count.
\n
\n\n
2017
\n\n
\n\t
Downloads milestone: IntechOpen reaches more than 100 million downloads
\n\t
Publishing milestone: IntechOpen publishes its 3,000th Open Access book, making it the largest Open Access book collection in the world
\n
\n"}]},successStories:{items:[]},authorsAndEditors:{filterParams:{sort:"featured,name"},profiles:[{id:"6700",title:"Dr.",name:"Abbass A.",middleName:null,surname:"Hashim",slug:"abbass-a.-hashim",fullName:"Abbass A. Hashim",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/6700/images/1864_n.jpg",biography:"Currently I am carrying out research in several areas of interest, mainly covering work on chemical and bio-sensors, semiconductor thin film device fabrication and characterisation.\nAt the moment I have very strong interest in radiation environmental pollution and bacteriology treatment. The teams of researchers are working very hard to bring novel results in this field. I am also a member of the team in charge for the supervision of Ph.D. students in the fields of development of silicon based planar waveguide sensor devices, study of inelastic electron tunnelling in planar tunnelling nanostructures for sensing applications and development of organotellurium(IV) compounds for semiconductor applications. I am a specialist in data analysis techniques and nanosurface structure. I have served as the editor for many books, been a member of the editorial board in science journals, have published many papers and hold many patents.",institutionString:null,institution:{name:"Sheffield Hallam University",country:{name:"United Kingdom"}}},{id:"54525",title:"Prof.",name:"Abdul Latif",middleName:null,surname:"Ahmad",slug:"abdul-latif-ahmad",fullName:"Abdul Latif Ahmad",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"20567",title:"Prof.",name:"Ado",middleName:null,surname:"Jorio",slug:"ado-jorio",fullName:"Ado Jorio",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Universidade Federal de Minas Gerais",country:{name:"Brazil"}}},{id:"47940",title:"Dr.",name:"Alberto",middleName:null,surname:"Mantovani",slug:"alberto-mantovani",fullName:"Alberto Mantovani",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"12392",title:"Mr.",name:"Alex",middleName:null,surname:"Lazinica",slug:"alex-lazinica",fullName:"Alex Lazinica",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/12392/images/7282_n.png",biography:"Alex Lazinica is the founder and CEO of IntechOpen. After obtaining a Master's degree in Mechanical Engineering, he continued his PhD studies in Robotics at the Vienna University of Technology. Here he worked as a robotic researcher with the university's Intelligent Manufacturing Systems Group as well as a guest researcher at various European universities, including the Swiss Federal Institute of Technology Lausanne (EPFL). During this time he published more than 20 scientific papers, gave presentations, served as a reviewer for major robotic journals and conferences and most importantly he co-founded and built the International Journal of Advanced Robotic Systems- world's first Open Access journal in the field of robotics. Starting this journal was a pivotal point in his career, since it was a pathway to founding IntechOpen - Open Access publisher focused on addressing academic researchers needs. Alex is a personification of IntechOpen key values being trusted, open and entrepreneurial. Today his focus is on defining the growth and development strategy for the company.",institutionString:null,institution:{name:"TU Wien",country:{name:"Austria"}}},{id:"19816",title:"Prof.",name:"Alexander",middleName:null,surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/19816/images/1607_n.jpg",biography:"Alexander I. Kokorin: born: 1947, Moscow; DSc., PhD; Principal Research Fellow (Research Professor) of Department of Kinetics and Catalysis, N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow.\r\nArea of research interests: physical chemistry of complex-organized molecular and nanosized systems, including polymer-metal complexes; the surface of doped oxide semiconductors. He is an expert in structural, absorptive, catalytic and photocatalytic properties, in structural organization and dynamic features of ionic liquids, in magnetic interactions between paramagnetic centers. The author or co-author of 3 books, over 200 articles and reviews in scientific journals and books. He is an actual member of the International EPR/ESR Society, European Society on Quantum Solar Energy Conversion, Moscow House of Scientists, of the Board of Moscow Physical Society.",institutionString:null,institution:{name:"Semenov Institute of Chemical Physics",country:{name:"Russia"}}},{id:"62389",title:"PhD.",name:"Ali Demir",middleName:null,surname:"Sezer",slug:"ali-demir-sezer",fullName:"Ali Demir Sezer",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/62389/images/3413_n.jpg",biography:"Dr. Ali Demir Sezer has a Ph.D. from Pharmaceutical Biotechnology at the Faculty of Pharmacy, University of Marmara (Turkey). He is the member of many Pharmaceutical Associations and acts as a reviewer of scientific journals and European projects under different research areas such as: drug delivery systems, nanotechnology and pharmaceutical biotechnology. Dr. Sezer is the author of many scientific publications in peer-reviewed journals and poster communications. Focus of his research activity is drug delivery, physico-chemical characterization and biological evaluation of biopolymers micro and nanoparticles as modified drug delivery system, and colloidal drug carriers (liposomes, nanoparticles etc.).",institutionString:null,institution:{name:"Marmara University",country:{name:"Turkey"}}},{id:"61051",title:"Prof.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"100762",title:"Prof.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"St David's Medical Center",country:{name:"United States of America"}}},{id:"107416",title:"Dr.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Texas Cardiac Arrhythmia",country:{name:"United States of America"}}},{id:"64434",title:"Dr.",name:"Angkoon",middleName:null,surname:"Phinyomark",slug:"angkoon-phinyomark",fullName:"Angkoon Phinyomark",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/64434/images/2619_n.jpg",biography:"My name is Angkoon Phinyomark. I received a B.Eng. degree in Computer Engineering with First Class Honors in 2008 from Prince of Songkla University, Songkhla, Thailand, where I received a Ph.D. degree in Electrical Engineering. My research interests are primarily in the area of biomedical signal processing and classification notably EMG (electromyography signal), EOG (electrooculography signal), and EEG (electroencephalography signal), image analysis notably breast cancer analysis and optical coherence tomography, and rehabilitation engineering. I became a student member of IEEE in 2008. During October 2011-March 2012, I had worked at School of Computer Science and Electronic Engineering, University of Essex, Colchester, Essex, United Kingdom. In addition, during a B.Eng. I had been a visiting research student at Faculty of Computer Science, University of Murcia, Murcia, Spain for three months.\n\nI have published over 40 papers during 5 years in refereed journals, books, and conference proceedings in the areas of electro-physiological signals processing and classification, notably EMG and EOG signals, fractal analysis, wavelet analysis, texture analysis, feature extraction and machine learning algorithms, and assistive and rehabilitative devices. I have several computer programming language certificates, i.e. Sun Certified Programmer for the Java 2 Platform 1.4 (SCJP), Microsoft Certified Professional Developer, Web Developer (MCPD), Microsoft Certified Technology Specialist, .NET Framework 2.0 Web (MCTS). 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