Emerging Inventory Planning

Abstract

In the last decade, the industry has been driven by the fifth industrial revolution, but it has also had to face unforeseen challenges in the economic, political, and international conflict arenas. These factors have generated difficulties that impact the efficient operation of global supply chains. In response to this uncertainty, many organizations have chosen to stockpile large quantities of inventory, increasing working capital while reducing their Return on Assets (ROA). This crisis has brought about swift changes in markets, with shifts in purchasing behavior and increasing competition in terms of prices and offers. Organizations need to use knowledge and technology more intelligently in this dynamic context to design strategies that enhance inventory planning and management. This chapter will explore the significance of logistical conditions, planning, and several strategies to achieve a responsive inventory in an ever-evolving market, where inefficiency and poor service are no longer tolerated.

1. Introduction

Over the past decade, the global economy has been characterized by unpredictable behavior, fueled by a multi-crisis driven by the post-pandemic era, the Ukraine conflict, and now the turmoil in the Arabian region. These situations have brought to light subsequent difficulties such as an energy crisis, inflation, food insecurity, and security concerns. These effects translate into present risks in the medium term, in which economic slowdown, high living costs, societal divisions, and misinformation through digital channels can destabilize the performance of global supply chains [1, 2].

The interconnectivity of these supply chains is determined by economies of scale and the flows represented in geography. Countries with limited maritime connections face specific constraints as they must frequently engage in container or loose cargo transshipments. This has led to temporal dispersion, less reliable connections, and, consequently, a lower logistical performance, resulting in high operating costs for various organizations [1].

In light of the recent risks and disruptions in supply chains, it becomes important not only to quantify costs but also to focus on planning the length, the network’s specific characteristics, and the sector’s resilience in all logistical processes. To achieve the improved logistical performance, it is crucial to revise certain organizational policies. Additionally, the academic community plays a constructive role in enhancing tools, technology, and, consequently, decision-making to gain an ever-increasing competitive advantage in economic sectors [2].

In addition to the risks experienced in the performance of supply chains, competition and the quality of logistical services are crucial factors for organizations. According to the World Bank’s Logistics Performance Index, which covers 139 countries, these elements significantly impact overall performance.

This report assesses six variables, including customs, infrastructure, international shipments, logistics competence, traceability, and shipping times. Figure 1 displays the scores of key representative countries for each variable. For instance, in logistics competence, Singapore achieved the highest score with 4.4, Mexico fell around the average with a score of 3.0, and Somalia had the lowest score at 1.8 out of 5.0.

Figure 1.

Logistics performance index variables 2023.

For the countries under study, the objective of this research is to compare their logistical performance, identify key challenges in their international logistics, gain visibility into global trends, and discover the improvement opportunities to enhance productivity in supply chains [3].

In light of this study, 75 out of the 139 countries do not exhibit high logistics competence, meaning their indicators are close to 3.0. Countries such as Benin, Mexico, Panama, Rwanda, Chile, Colombia, Hungary, and Uruguay have made efforts to enhance their logistical conditions, achieving modest progress. However, when it comes to knowledge and the application of models in logistics, they still have room for improvement [3].

Upon reviewing the data provided by the World Bank since 2007, the Colombian government has shown a commitment to enhancing the logistical conditions within the country. Through the National Planning Department (DNP), national surveys have been conducted to identify the characteristics and improvement opportunities that entrepreneurs can explore within their supply chains.

The latest edition of this survey was conducted in 2020, with a probabilistic sample of 3383 companies. It evaluated five key areas:

• Logistical Performance: This assesses operational costs, service quality, and the utilization of technology in logistics.

• Outsourcing of Logistical Services: This determines the extent to which companies contract out logistical services (involving 3, 4, or 5 logistical parties) within their logistics processes, aiming for efficiency in time and costs.

• International Logistics: It evaluates foreign trade processes, including cost, customs regulatory compliance, and ease of international trade.

• Regional Logistics: This aims to highlight challenges and issues in different regions, assessing the availability of logistical services in these areas.

The Future of Logistics in the Country: The objective here is to identify challenges in operations aligned with the needs, such as road, river, rail, port, and airport infrastructure, that the government can address through the design and implementation of public policies [4].

One of the most relevant indicators in this study is logistical performance. Colombia’s economic openness and tariff negotiations with other countries have turned logistical costs into a key variable for organizational competitiveness in this country. Measuring the cost of logistics at the national level has enabled the government to design more effective policies to enhance the logistical conditions that various companies require for managing their supply chains at a competitive level [5].

In the case of this country, logistical costs are measured as a percentage of its sales. For the year 2020, the indicator had a value of 12.6% of sales, with a target of 13.3%, as shown in Figure 2. In this report, the highest costs were incurred in warehousing, accounting for 47%, and transportation, accounting for 35%. Due to the pandemic, consumers adapted to the digital market, grew accustomed to swift response times, and no longer wanted to wait. They assumed new roles within their families, transforming business and logistical practices for companies. This created the need for more competitive resources in the relevant areas. However, stock levels increased to keep up with this consumption pace. Unfortunately, organizations lacked a suitable transactional system to keep up with demand, resulting in high costs for warehousing and inventory [4].

Figure 2.

Logistics cost; percentage of sales in Colombia.

Globally, high inventory levels primarily affect the retail sector. Currently, this group is experiencing a decline in its sales. Among several challenges, companies are dealing with high inflation, supply chain issues, evolving consumer behaviors, labor shortages, global conflicts, climate change, and the pressing need for improved technology to meet the demands of a more demanding consumer base [6].

By the statement made by Juan Germán Osorio, Consumer Leader Partner at Deloitte Americas [7]:

“In the world, seven out of ten executives in the food and beverage, household goods, personal care, or clothing industries claim that their job is more stressful today than it was 5 years ago. This is attributed to factors such as record-high inflation, supply chain issues, evolving consumer behaviors, labor shortages, global conflicts, and climate change”.

These words are derived from a report released by Deloitte in 2023, titled “Consumer Products Industry Outlook to 2023.” This study conducted surveys with 150 global consumer product companies in the food and beverage, household goods, personal care, and clothing industries. The data sources are multinational industries with annual revenues exceeding $500 million. As mentioned earlier, Deloitte has confirmed that organizations are facing new challenges, as indicated in Figure 3. The market landscape has transformed into a dynamic scenario where organizational planning must be more attuned to demographic, political, environmental, technological, and cultural changes.

Figure 3.

Inventory’s effect on ROA.

Among the surveyed group, there are organizations with profitable growth that are implementing the following strategies [8]:

• 93% adapt to the changing consumer and align with their dynamics.

• 85% believe that the current environment provides an opportunity to increase market share.

• 68% view vertical integration as a strategic approach.

• 90% are investing in technology to have real-time information throughout their supply chains.

• 97% consider environmental issues a priority for organizations.

Of all these perceptions, technology is one of the most significant. In the survey, nine out of ten companies are investing in enhancing supply chain management and operational excellence. They are also investing in big data to share information with their suppliers and distribution channels, to coordinate and optimize logistics. Ultimately, all the strategies and tactics managed along this chain will be reflected in the price, determining whether or not a competitive advantage is achieved [8].

Organizations cannot move forward independently; they need to have a partner and invest in Artificial Intelligence (AI). Sales channels and the multitude of Stock Keeping Units (SKUs) can no longer be sustained solely by the workforce. They require assistance with predictive analytics and mathematical models that can optimize inventory and provide responses to customers, almost in real time [9].

In the face of an economic slowdown in 2023, organizations are beginning to encounter problems and more challenges, such as a lack of investment, limited working capital, and an increase in competitive rivalry [10]. This, coupled with a lack of visibility and synchronization from the sourcing of materials to the storage of finished products in retail channels, has led to the accumulation of high inventory levels in various supply networks, compromising profitability on assets (ROA) and return on investment (ROI). This, in turn, reduces inventory turnover and, therefore, the company’s profitability, especially in times of crisis.

2. Inventory as a strategic asset

Inventory, while basic to many, is an essential and strategic component in the operation of organizations. As a significant entity among current assets, inventories represent an organization’s ability to produce, store, and market goods and services. Likewise, their proper management has a significant impact on profitability, service levels, and the competitiveness of the business.

As Coyle mentions, “Inventory as an asset on the balance sheet and as a variable expense on the income statement has gained significant importance as organizations seek more effective ways to manage their assets and working capital” [11].

The ability of inventories to generate economic value through their sale or use in the production of goods or services for marketing makes them a primary asset for organizations seeking to improve their profitability. Managing variables related to their management is key to achieving cost savings in operations [12, 13].

Among the most important current assets on the balance sheet are cash, accounts receivable, and inventories, with the latter being the most valuable. However, the lack of assessment and calculation of inventory for each item can lead to unnecessary expenses in the income statement, posing a challenge for organizations [12]. The management of this asset determines the return on investment (ROI), and as Coyle and other authors mention, “reducing inventories leads to a short-term increase in ROI as assets decrease and available working capital increases, while an increase in inventories results in an increase in assets, causing a decrease in the same indicator and available working capital” [11]. In this sense, considering inventory as an asset, one must monitor the return on assets (ROA).

Similarly, the value of inventory influences the return on assets (ROA) of an organization when considered as an asset. Figure 3 illustrates how the inventory level affects each phase of the financial relationship until reaching this indicator.

Considering this relationship, if a company aims to increase its return on assets (ROA), it should redefine its procurement policy to control the quantities and frequencies of procurement. Similarly, it should review operational costs and their utilization, such as transportation frequency, storage costs, inventory, and maintenance. However, it is essential to ensure that the percentage variation of these variables is in line with the capacity and nature of the business to avoid compromising the quality of the delivery service.

Additionally, to maintain this level of service, it is important to consider the existing relationship between transportation and inventory. If there is a decrease in inventory, it will lead to an increase in transportation costs, and vice versa, all to fulfill the sales promise. For this reason, when redefining the procurement policy, it is crucial to always seek a balance or trade-off between these variables. The company’s policy will determine which strategy benefits the company more: reducing transportation costs or inventory costs while maintaining a high fill rate¹.

Another one of the main and most common challenges faced by some organizations is the proper management of inventories to the demand encountered. Well-managed inventory can help improve operational efficiency, reduce costs, and meet customer demand. However, poorly managed inventory can lead to unnecessary costs and product shortages. At this point, companies must present a solid planning strategy because, depending on the market type and corporate strategy, it is necessary to have enough inventory to meet demand and avoid losses due to stock-outs. However, it is not advisable to have too much inventory, as it poses a significant risk of increased operational costs [14].

Achieving the balance between maintaining sufficient stock without excess has a significant impact on various areas, and some of the main benefits that can be achieved include [15, 16]:

Cost Optimization: Avoiding storage costs due to excess inventory while also preventing additional costs from production delays or penalties for inventory shortages.

Customer Satisfaction: Maintaining sufficient stock ensures that the company can meet customer demand promptly, enhancing customer satisfaction.

Risk Minimization: Excess inventory increases the risk of product deterioration, which can result in financial losses. On the other hand, inventory shortages can reduce the level of service.

Adaptation to Demand Changes: A proper inventory balance allows the company to quickly adjust to changes in market demand. If demand suddenly increases, the company can meet it without delays or sales losses. If demand decreases, the company would not be burdened with excess unsold inventory.

Cash Flow Improvement: Excess inventory negatively impacts available cash flow, while insufficient inventory can lead to sales losses, also affecting cash flow.

On the other hand, the inventory value represents a significant influence in the study of the financial health of the company, with which some factors can be analyzed, such as [17, 18]:

• Solvency and Liquidity: The inventory level is related to financial obligations, where an appropriate level of inventory indicates that the company can meet its obligations and debts.

• Profitability: Efficient inventory management can enhance profitability by reducing purchasing and storage costs.

• Operational Efficiency: Excessive inventory suggests inefficiency and additional costs, while low inventory indicates service level issues.

In conclusion, inventory becomes a strategic asset that improves a company’s profitability and success. Proper management has a significant impact on the financial health of the organization and its ability to meet market demand. Next, we will present some methods and practices for achieving proper and optimal inventory planning.

3. Aggregate inventory horizon

An effective methodology for comprehensive planning across all three inventory levels is the aggregate plan. This technique allows for the determination of optimal levels of capacity, production, and inventory over a specific period to meet demand and maximize profits.

This planning over the horizon emerges as an essential strategy in the management of operations and assets in the supply chain of any organization. Its primary goal is to achieve an optimal balance between demand, production capacity, and inventory turnover, thereby facilitating effective resource planning and decision-making [19].

This planning focuses on medium-term decision-making, aiming to optimize plant capacity utilization and the strategic use of inventories. It should not be regarded as a predictive tool because it involves decisions at the level of aggregated units and families, rather than specific decisions for individual stock-keeping units (SKU) [20].

To achieve effectiveness and reliability in the model, data from each of the operations in the process being evaluated are required. This requirement poses one of the greatest challenges for some companies that either have not collected the data or choose not to share it with their suppliers or customers. Without these data, which serve as a fundamental input in planning, whether they are related to costs or constraint conditions, it will be difficult to achieve the expected outcome of this planning.

This planning model provides a valuable tool for the production management and control process, as well as for strategic control. It facilitates effective communication among different departments and areas to achieve the company’s strategic objectives. However, some of the challenges that arise in the application of this method include:

• Market Demand Variability: Companies must understand how to reduce or mitigate the effects of market demand variability through flexibility and adaptability.

• Collaboration with suppliers and distributors is essential for achieving successful aggregate planning. Establishing strong relationships and sharing information is key to this collaboration.

By the suggestions resulting from the model, the supply chain management should be aware of which tactics to employ to align the strategy within the organization. Defining inventory policies for raw materials, work-in-progress, and finished products in terms of inventory days is crucial for the tactical level, meaning leveraging inventories to respond to the market when capacity is limited. Flexible scheduling is related to using time as a lever, where capacity remains constant, but the number of hours worked is adjusted in response to changes in demand. Finally, capacity acts as a lever that allows for the synchronization of production based on demand fluctuations, involving capacity adjustments through machinery modifications or hiring and firing employees [19].

3.1 Study case

Steel Wire, a company in the steel industry, is facing the challenge of optimizing its production and inventory planning due to inadequate plant capacity to meet the growing demand for its primary product, the 80-kg Link Mesh. To address this situation, a specific aggregate planning model is being developed for this product.

This aggregate planning model will be a valuable tool to help Steel Wire balance demand and production capacity, enabling it to make strategic decisions regarding resource allocation and inventory management. Additionally, the company can consider options such as production flexibility, collaboration with suppliers and distributors, and inventory policy optimization to ensure an effective approach in this situation.

The production of the 80-kg Link Mesh involves three fundamental stages: wire drawing, galvanizing, and transformation. The process begins with the supply of material, which consists of an SAE 1006 steel wire rod with an initial diameter of 5.5 mm. This type of wire rod is purchased in 2-ton coils supplied by Paz del Río, a steel company located in Boyacá, Colombia.

These wire rod coils are transported from the raw materials warehouse to the two wire drawing machines of each drawing bench using forklifts. During the wire drawing phase, an operator is responsible for supervising and operating two semi-automatic wire drawing machines: The Kock 3 and the Kock 4.

The wire drawing operation involves the plastic deformation of steel through continuous tensile stresses, where the wire passes through a set of dies [21]. For this particular product, a diameter of 3.28 mm is required. The resulting wire is wound into coils, which can weigh up to 900 kg each. These coils are then transported by the forklift to the hot-dip galvanizing area. On each trip, the vehicle can transport up to four coils at a time.

The galvanizing process has a capacity of 50 wires, of which five are programmed to supply the mesh production line. This process begins with the degreasing stage, where organic contaminants are removed, pickling is continued to eliminate the oxide scale on the wire’s surface, and then, fluxing is done. Fluxing uses a saline solution of ammonium chloride and zinc to remove any remaining oxide, providing a protective layer to the steel. Finally, the galvanizing process is carried out by immersing the 50 wire lines in a bath of molten zinc, the conditions of which comply with the specifications of the American standard ASTM B6. This process requires a minimum of 98% pure zinc and a heating temperature within the range of 435–455°C [22, 23].

Once the material has passed through the galvanizing process, its diameter is adjusted to 3.30 mm as the wire is coated with a 0.2-mm-thick layer of zinc. After zinc immersion, the wire is wound into 900 kg coils, which are then transported to the production area of the link mesh. In this section, there are 8 Waffios machines programmed to transform the wire into rolls of link mesh, each weighing 80 kg.

Each machine requires two coils to interlace the link mesh, as shown in Figure 4. The operator of each machine is responsible for threading the wires and adjusting the machine’s settings, which operate semi-automatically. Once the manufacturing process of a roll is completed, the operator places cardboard and labels at the ends, wraps the roll with stretch paper, and stacks it on a pallet (Figure 5).

Figure 4.

Chain link mesh detail.

Figure 5.

Chain link mesh process.

The data associated with this process are indicated in Table 1.

Operation	Equipment	Production speed (Ton/Shift)	Efficiency (%)	Real production (Ton/shift)
Drawing	Kock 3	8	66	5.3
	Kock 4	8	66	5.3
Hot dip galvanized	5 lines	14	70	9.8
	wafios 1	1.28	75	0.96
	wafios 2	1.28	75	0.96
	wafios 3	1.28	75	0.96
	wafios 4	1.28	75	0.96
Transformation	wafios 5	1.28	75	0.96
	wafios 6	1.28	75	0.96
	wafios 7	1.28	75	0.96
	wafios 8	1.28	75	0.96

Table 1.

Standard data of the chain link mesh process x 80 kg.

The aggregate plan is a model designed to maximize profitability over a specific time horizon within a given process. In the case of an organization in the steel industry, its primary focus is to provide maximum value to customers by committing to meet all projected demand, even if this entails certain delays. The key to maximizing profitability lies in operational efficiency, with the additional consideration of pricing and promotion policies. By effectively minimizing operating costs, a significant contribution is made to profit maximization, always in line with the company’s strategy.

In this regard, this company aims to optimize the planning of the 80-kg Link Mesh, one of its high-demand products in the market.

The process operates for 25 days a month, with each worker putting in 8 hours per day in regular time. However, they can work overtime, but according to the country’s legislation, they cannot exceed more than 15 hours of overtime per month. The production operation’s capacity is primarily determined by the total hours of work employed. Therefore, the machine capacity is not a limiting factor for the production operation.

The monthly subcontracting capacity is set at 50 tons, while the inventory has a capacity of 80 tons per month, with a shortage limit of no more than 0.5 tons per month. At the end of the semester, the company will ensure the maintenance of 5 days of available inventory and avoid the generation of orders in a state of shortage.

The design of this plan aims to maximize profitability over the semester while ensuring an adequate level of service for the market. This will be achieved by assuming that prices will remain constant during this period and that the task of reducing costs will be determined by the model, allowing us to optimize profitability. The forecast for the upcoming months is illustrated in Table 2.

Month	Demand (Kg.)
July	320,000
August	290,000
September	260,000
October	210,000
November	240,000
December	300,000

Table 2.

Estimated demand for chain-link mesh.

At the end of June, the following figures were recorded: 8 workers in the Link Mesh production line, 2 tons of work-in-progress in the wire drawing stage, 4 tons of work-in-progress in the galvanizing stage, 7 tons of finished product, and 6.2 tons in a shortage state. The costs associated with this process are detailed in Table 3.

Process	Cost	Unity
Material	4,500	$ / kg
Inventory holding cost	500	$ / kg/ month
Cost of stock-outs	1,500	$ / kg/ month
Hiring + training cost	1,150,000	$ / worker
Layoff cost	1,400,000	$ / worker
Hours MOD transformation (1 Operator - 1 Machine)	120	Kg. / hour
Cost of overtime MOD transformation	15,500	$ / hour
Drawing cost + operator	9,500	$ / hour
Galvanizing cost + operator	11,500	$ / hour
Transformation cost (Only machine)	6,500	$ / hour
Outsourcing cost	15,000	$ / kg

Table 3.

Costs associated with the production process of chain link mesh.

To calculate the cost per kilogram of operations like wire drawing, galvanizing, and transformation, the actual production per hour (Table 1) is divided by the hourly cost for each area or line (Table 2). The result is presented in Table 4. In the case of the mesh area, the cost of employed workers is added to this calculation, which is subject to market demand and the established inventory policy.

Operation cost	Standard production (Kg. / hour)	Cost ($ / hour)	Cost/kg.
Drawing	1,320	9,500	7.20
Galvanizing	1,225	11,500	9.39
Transformation	960	6,500	6.77

Table 4.

Costs per kg. Of production process of chain link mesh.

Additionally, the organization needs to establish its work-in-progress inventory policy. The number of inventory days defines the availability period for this inventory. For example, if there is a 5-day work-in-progress inventory, it means there is availability to cover 5 days of operation.

The purpose of this policy is to control working capital and ensure a buffer throughout the entire process. This policy is defined for all three operations, as well as for finished product inventory and the allowed delay in each month, as shown in Table 5.

Product in process		Finish product - 5 days of inventory)	Backlog (Kg.)
Drawing - 3 days of inventory (Kg.)	Galvanizing - 4 days of inventory
32,000	42,667	53,333	500
29,000	38,667	48,333	500
26,000	34,667	43,333	500
21,000	28,000	35,000	500
24,000	32,000	40,000	500
30,000	40,000	50,000	0

Table 5.

Inventory policies.

3.2 Case solution

In order to find a reliable and time-efficient solution, the case study is solved using an algorithm implemented in the Python programming language. The resolution process consists of several steps:

3.2.1 First steep

In this phase, the “pulp,” “pandas,” and “numpy” libraries are imported to leverage the linear and integer programming problem-solving capabilities provided by “pulp.” Additionally, the data manipulation and numerical operation functionalities provided by “pandas” and “numpy” are used.

3.2.2 Second steep

At this point, we start defining a linear programming model. This begins by creating a list that maps the defined decision variables, whose values will be determined by the aggregate plan. Twelve variables are defined over a range of six periods (Table 6).

Variable	Description
Hire t	Number of workers hired in month t.
Fire t	Number of workers laid off in month t.
Workforce t	Number of active operators in month t.
Overtime	Number of overtime hours in month t
Prod_draw_out t	Number of kilograms produced in the drawing mill in month t.
Prod_GVZ t	Number of kilograms produced on the galvanizing line in month t.
Prod_mesh t	Number of kilograms produced on the processing line in month t.
Inv_draw_out t	Inventory of drawn material in kilograms in month t.
Inv_GVZ t	Inventory of galvanized material in kilograms in month t.
Inv_FP t	Inventory of 80-kg chain-link mesh in kilograms in month t.
Stock_out t	Kilograms of product overdue for delivery to the customer in month t.
Outsourcing t	Number of kilograms produced by subcontracting in month t.

Table 6.

Model decision variables.

Next, a cost matrix is created to represent the costs associated with various variables and activities. Demand is defined for each period, and initial variables such as workforce, stock-out, inventory, and others are initialized. Additionally, four lists are created that contain the monthly inventory values for drawing, galvanizing, finished product, and stock-out.

3.2.3 Third steep

In this stage, the linear programming model is created by defining the objective function of the problem, which aims to minimize the total cost incurred during the planning horizon. The total cost is defined by the following components:

• Regular labor time cost

  $$\sum _{t=1}^6\mathit{\text{Workforc}}{e}_t·6500$$E1

• Overtime labor cost

  $$\sum _{t=1}^6\mathit{\text{Overtim}}{e}_t·15500$$E2

• Hiring and firing costs

  $$\sum _{t=1}^6\mathit{Hir}{e}_t·1150000+\sum _{t=1}^6\mathit{Fir}{e}_t·1400000+$$E3

• Inventory and stock-out costs

  $$\sum _{t=1}^6\mathit{Inv}F{P}_t·500+\sum _{t=1}^6\mathit{Inv}\mathit{\text{draw}}\mathit{ou}{t}_t·500+\sum _{t=1}^6\mathit{Inf}\mathit{GV}{Z}_t·500+\sum _{t=1}^6\mathit{\text{Stock}}\mathit{ou}{t}_t·1500$$E4

• Outsourcing cost

  $$\sum _{t=1}^6\mathit{\text{Outsourcin}}{g}_t·15000$$E5

• Production cost

  $$\sum _{t=1}^{6}Pr\mathit{od}\mathit{\text{draw}}\mathit{ou}{t}_t·4507+\sum _{t=1}^{6}Pr\mathit{od}\mathit{GV}{Z}_t·9.4+\sum _{t=1}^{6}Pr\mathit{od}\mathit{mes}{h}_t·6.8$$E6

The sum of the mentioned costs results in the total cost, thus defining the following objective function denoted by Z:

$$\begin{array}{ll}\mathit{Min}Z=& \sum _{t=1}^6\mathit{\text{Workforc}}{e}_t·6500+\sum _{t=1}^6\mathit{\text{Overtim}}{e}_t·15500+\sum _{t=1}^6\mathit{Hir}{e}_t·1150000+\sum _{t=1}^6\mathit{Fir}{e}_t·1400000\\ & +\sum _{t=1}^6\mathit{Inv}F{P}_t·500+\sum _{t=1}^6\mathit{Inv}\mathit{\text{draw}}\mathit{ou}{t}_t·500+\sum _{t=1}^6\mathit{Inv}\mathit{GV}{Z}_t·500\\ & +\sum _{t=1}^6\mathit{\text{Stock}}\mathit{ou}{t}_t·1500+\sum _{t=1}^6\mathit{\text{Oursourcin}}{g}_t·15000+\sum _{t=1}^{6}Pr\mathit{od}\mathit{\text{draw}}\mathit{ou}{t}_t·4507\\ & +\sum _{t=1}^{6}Pr\mathit{od}\mathit{GV}{Z}_t·9.4+\sum _{t=1}^{6}Pr\mathit{od}\mathit{mes}{h}_t·6.8\end{array}$$E7

The “LpProblem” object from the “pulp” library is used to define the minimization problem. A list is created to store variable names composed of the numeric value of the period (from 1 to 6) and the variable number (from 1 to 12), along with their respective descriptions.

Next, a matrix is defined to organize the decision variables. The objective function is calculated as the weighted sum of the decision variables and their corresponding costs. The model is set up to minimize the objective function.

3.2.4 Fourth step

In this step, constraints are introduced into the linear programming model:

3.2.4.1 Labor force restriction

It is established that the workforce must not exceed the number of available machines, as each machine should be operated by a single worker, and it ensures that the sum of the workforce from the previous month, minus the workforce allocated in the current month, plus the number of workers hired and minus the number of workers fired in the same month, equals zero.

$$\mathit{\text{Workforc}}{e}_t=\mathit{\text{Workforc}}{e}_{t-1}+\mathit{Hir}{e}_t-\mathit{Fir}{e}_t$$E8

3.2.4.2 Constraint on overtime hours

A loop is created that iterates through each period, setting the overtime hours to be less than or equal to 15, as stipulated in the case study.

$$\mathit{\text{Overtim}}{e}_t\le 15·\mathit{\text{Workforc}}{e}_t$$E9

3.2.4.3 Drawing, galvanizing, and transformation capacity constraint

A loop is set up in which, in each iteration, it is determined that the amount of material produced in each process must be less than or equal to the available monthly capacity of both workers and machines.

$$\mathit{\text{prod\hspace{0.17em}draw}}\mathit{ou}{t}_t\le 3\mathit{\text{turn}}·8\frac{\mathit{\text{hours}}}{\mathit{\text{turn}}}·25\frac{\mathit{\text{days}}}{\mathit{\text{month}}}·1320\frac{\mathit{Kg}}{\mathit{\text{hour}}}$$E10

$$\mathit{\text{prod}}\mathit{GV}{Z}_t\le 3\mathit{\text{turn}}·8\frac{\mathit{\text{hours}}}{\mathit{\text{turn}}}·25\frac{\mathit{\text{days}}}{\mathit{\text{month}}}·1225\frac{\mathit{Kg}}{\mathit{\text{hour}}}$$E11

$$\mathit{\text{prod}}\mathit{mes}{h}_t\le 3\mathit{\text{turn}}·8\frac{\mathit{\text{hours}}}{\mathit{\text{turn}}}·25\frac{\mathit{\text{days}}}{\mathit{\text{month}}}·960\frac{\mathit{kg}}{\mathit{\text{hour}}}·\mathit{\text{Workforc}}{e}_t+960\frac{\mathit{kg}}{\mathit{\text{hour}}}·\mathit{\text{overtim}}{e}_t$$E12

3.2.4.4 Drawing, galvanizing, and finished product inventory balance constraint

To balance inventory and production, a loop is created in which, in each period, it is ensured that the inventory of the corresponding process in a month “i” is equal to the inventory of finished products and the stock-out from the previous month, plus the total production and outsourcing of month “i” minus the stock-out from the previous month and the demand of month “i.”

$$\mathit{Inv}{\mathit{GVZ}}_t=\mathit{Inv}\mathit{GV}{Z}_{t-1}+Pr\mathit{od}\mathit{GV}{Z}_t-Pr\mathit{od}\mathit{mes}{h}_t$$E13

$$\mathit{Inv}{\mathit{\text{Draw\hspace{0.17em}out}}}_t=\mathit{Inv}\mathit{\text{Draw}}\mathit{ou}{t}_{t-1}+Pr\mathit{od}\mathit{\text{Draw}}\mathit{ou}{t}_t-Pr\mathit{od}\mathit{GV}{Z}_t$$E14

$$\mathit{Inv}{\mathit{FP}}_t=\mathit{Inv}F{P}_{t-1}+Pr\mathit{od}\mathit{mes}{h}_t+\mathit{\text{Outsourcin}}{g}_t-\mathit{\text{Stockou}}{t}_{t-1}+\mathit{\text{Stockou}}{t}_t-\mathit{\text{deman}}{d}_t$$E15

3.2.4.5 Inventory policy constraints for drawing, galvanizing, and transformation

To adhere to the defined inventory policies and prevent stock-outs or excess inventory, a loop is created where, for each period, it is established that the inventory of the respective process should be equal to the predefined amount of inventory on the initial list. A similar process is carried out for the “stock-out” variable.

$$\mathit{Inv}{\mathit{\text{Draw\hspace{0.17em}out}}}_t={\mathit{\text{Draw\hspace{0.17em}out\hspace{0.17em}inventory\hspace{0.17em}policy}}}_t$$E16

$$\mathit{Inv}{\mathit{GVZ}}_t=\mathit{GVZ}{\mathit{\text{inventory\hspace{0.17em}policy}}}_t$$E17

$$\mathit{Inv}{\mathit{FP}}_t=\mathit{FP}{\mathit{\text{out\hspace{0.17em}inventory\hspace{0.17em}policy}}}_t$$E18

$${\mathit{\text{Stock\hspace{0.17em}out}}}_t\le \mathit{\text{Inventory\hspace{0.17em}Back}}{log}_t$$E19

3.2.4.6 Non-negativity constraint

It is specified that the value of each of the variables in each period cannot be negative.

$${\mathit{\text{Hire}}}_t,{\mathit{\text{Fire}}}_t,{\mathit{\text{Workforce}}}_t,\mathit{\text{Overtim}}{e}_t,Pr\mathit{od}{\mathit{\text{draw\hspace{0.17em}out}}}_t,Pr\mathit{od}\mathit{GV}{Z}_t,Pr\mathit{od}\mathit{mes}{h}_t,$$E20

$$\mathit{Inv}\mathit{\text{draw}}\mathit{ou}{t}_t,\mathit{Inv}\mathit{GV}{Z}_t,\mathit{Inv}F{P}_t,\mathit{\text{Stock}}\mathit{ou}{t}_t,{\mathit{\text{Outsourcing}}}_t\ge 0$$E21

3.2.5 Fifth step

Finally, the linear programming model is solved using the “solve()” function, which searches for the optimal solution to the problem, considering all previously defined constraints and objectives. The results are organized in a Dataframe that displays the model’s solution, which means the values that each defined variable should take. Additionally, the total cost associated with the optimal solution is printed.

3.3 Results

After formulating the problem and subsequently optimizing it to minimize costs, the following aggregate plan has been established.

Total cost over the planning horizon: €1,880,655.

According to the obtained solution, there is no need for layoffs or additional hires. In other words, a constant workforce of eight employees will be maintained during the 6 months of planning, without the need for overtime, as shown in Table 7.

Month	Workforce	Workers to be hired	Workers to be fired	Overtime
July	8	0	0	0
August	8	0	0	0
September	8	0	0	0
October	8	0	0	0
November	8	0	0	0
December	8	0	0	0

Table 7.

Workforce and overtime required.

Similarly, with this workforce, there is no need to implement overtime or subcontracting. Throughout all the months, an inventory of both work-in-progress and finished products is maintained, which is why there are no shortages.

Additionally, as shown in Table 8, the following monthly production plan has been established for each of the processes involved.

Month	Stock out (kg)	Outsourcing (kg)	Drawn inventory (kg)	Galvanized inventory (kg)	Finished product inventory (kg)
July	0	0	32,000	42,667	53,333
August	0	0	29,000	38,667	48,333
September	0	0	26,000	34,667	43,333
October	0	0	21,000	28,000	35,000
November	0	0	24,000	32,000	40,000
December	0	0	30,000	40,000	50,000

Table 8.

Stock-out, outsourcing policies, and inventories.

As shown in Table 9, it is evident that the main cost component in the company’s cost structure is related to material acquisition, characterized by a unit cost of €1 per kilogram. During the six-month planning period, it is anticipated that a total quantity of 1,733,200 kilograms of material will need to be acquired. This expenditure results in a total material cost reaching €1.8 million, representing 95% of the total planning cost.

Month	Wire drawing production (Kg)	Galvanized production (Kg)	Mesh production (kg)
July	441,200	411,200	372,533
August	278,000	281,000	285,000
September	248,000	251,000	255,000
October	190,000	195,000	201,667
November	252,000	249,000	245,000
December	324,000	318,000	310,000

Table 9.

Production during the planning horizon.

Therefore, it is suggested that the company explore and make modifications to its supply strategies, considering possible alternatives such as evaluating new suppliers, initiating negotiation processes, or redesigning procurement policies and lead times for material.

This plan leads not only to the determination of optimal solutions but also to the achievement of more efficient resource management and effective planning. Furthermore, it provides organizations with the ability to make strategic decisions that enable them to thrive and reach their goals, effectively addressing the changing dynamics of the market.

4. Strategic sourcing

In today’s business landscape, organizations face two significant challenges: increased volatility in demand variability and growing pressure to enhance their competitive advantage in the market. These sudden and unforeseen changes have given rise to conflicts throughout the supply chain.

High levels of shortages occur during periods of high demand, while excess inventory accumulates during periods of low demand. This lack of synchronization between supply and demand has led to increased costs, underutilized working capital, reduced responsiveness of companies, and dissatisfied customers.

In the face of this scenario, organizations must work toward finding a balance between supply and demand through effective coordination between the sales and operations/logistics departments. This is essential for increasing the company’s profitability.

Firstly, on the sales side, strategies such as cross-selling, discounts, promotions, or more detailed pricing and revenue management can be explored.

Secondly, on the operations and logistics side, achieving supply smoothing can be accomplished through optimal inventory management, in terms of both sourcing and delivery frequency.

The fill rate, or service level, is a metric that relates to the attributes of reliability and responsiveness. Its main indicators focus on timely delivery, the right quantity, and appropriate quality [24].

Inventory availability plays a crucial role in demonstrating competitive service. This metric represents the probability of having sufficient stock to meet demand, thus minimizing the likelihood of running out of products during a specific period.

Availability is subject to constant evaluation, measured about a pre-established monthly target. However, this availability comes with a series of costs that can also impact competitive advantage. These costs include opportunity cost, which represents the investment in inventory instead of other activities; variable costs associated with storage; fixed costs related to storage; the cost of tied-up capital; costs associated with risk; and costs related to external services [25].

Therefore, a supply chain manager must ensure a balance between inventory availability and cost. This involves seeking the optimization of availability and frequency to maximize the profitability of the chain. This goal can be achieved through the implementation of procurement policies. Four tactics have been adapted from well-known inventory management models to respond to various demand behaviors.

Taking into account the variables T (lead time), Q (optimal order quantity), S (safety stock), and R (inventory roof), four procurement policies are adapted to address four different demand behaviors, as seen in Figure 6 [26, 27, 28, 29].

Figure 6.

Supply policies proposed.

4.1 TQ policy

This model is based on the well-known concept of Economic Order Quantity (EOQ), which involves placing orders for a fixed quantity at a calculated frequency. The optimal order quantity, denoted as “Q,” is requested at time intervals “T,” which are calculated based on demand [26, 27, 28, 29].

The demand exhibits a constant and predictable behavior, which enables the supplier to commit to a frequent delivery schedule. This strategy not only optimizes efficiency in transportation but also allows for more effective management of the quantity supplied.

Figure 7 provides a visual representation of this policy. The red line reflects the inventory behavior, where the sloping lines indicate consumption levels, and the vertical lines represent inventory replenishment points. By calculating the optimal time “T” for replenishment, it is possible to deduce the reorder point, which is indicated by the yellow markers.

Figure 7.

TQ policy.

With this information in mind, inventory consumption begins from time zero. As consumption reaches the green point, or the reorder point, an order is placed for a quantity “Q.” This quantity is selected as the optimal balance between order costs and storage costs and will arrive in a period of “T,” in this case, 6 days. Then, consumption occurs again, and the process repeats continuously as it touches the new reorder point. To perform the necessary calculations, the formulas are shown in Table 10.

Abbreviations	formulas
T: Optimal supply time	T = Square root ((2*Cp)/(Cs*d)) T = Q´/d
Q’: Optimal supply quantity
Cp: Ordering cost
Cs: Sustaining cost
d: Average demand

Table 10.

TQ formulas.

4.2 SQ policy

This model aims to prevent inventory depletion situations by calculating a safety stock that should cushion the conditions of uncertainty that arise when demand shows variability and volatility [26, 27, 28, 29].

Due to this nature, predicting and optimizing it is a challenging task. While it is possible to calculate the optimal quantity “Q,” this model adapts to the supplier’s lead times due to its condition.

Both demand and lead times are subject to variability, so the safety stock “S” will be determined by the variability of demand, lead times, and the level of service required by customers.

As illustrated in Figure 8, the inventory consumption process begins at time zero. When this consumption reaches the safety stock level, the order is triggered, as indicated in point 1. According to the agreement on the lead time with the supplier, the optimal quantity “Q” of the order arrives, as indicated in point 2, and inventory consumption continues. It is important to note that, due to demand variability, the slopes of the red lines representing consumption may be more or less steep.

Figure 8.

SQ policy.

Although this model is reactive and provides a quick response, sudden and aggressive demands can be challenging to cushion. As seen in point 3, this can lead to an inventory depletion situation, that is, a “stock-out,” which is quickly resolved thanks to the prompt response of the supplier, as the order was placed in advance. To calculate the data, it is necessary to review the formulas in Table 11.

Abbreviations	formulas
Q´: Optimal supply quantity; Cp: Ordering cost; Cs: Sustaining cost; d: Average demand; Sq: Safety stock for q; k: Safety factor; ϭ: Standard deviation of demand; t: Current supply time	Q´= (Square root ((2*Cp)/(Cs*d)))*d; Sq = k * ϭ * (Square root (t)); k= NORM.S.INV1 (P); P = Probability that they will not show up out of stock (Stock-out); ϭ = STDEV^4 (Demand)

Table 11.

SQ formulas.

¹

Excel functions.

4.3 SR policy

This combination aims to balance the inventory behavior, in both decrease and increase. In addition to demand volatility, it exhibits a trend toward growth or decrease. Although the lead time is not ideal, its high variability makes it difficult to calculate an optimal “Q.” Instead, the order calculation is based on a maximum level “R” and the inventory level at period “n.” [26, 27, 28, 29].

Concerning Figure 9, inventory consumption starts in period zero with a total of 270 units, sufficient to cover a 15-day demand. When inventory consumption reaches the safety stock level, an order “Q₁” is generated, which is equal to the difference between the maximum level “R” and the inventory level at period “n₁,” as indicated in point 1. The lead time is governed by the negotiated agreements with the supplier and is taken into account when calculating the safety stock.

Figure 9.

SR policy.

At point 2, the requested quantity “Q’₁” is received, and consumption continues until the safety stock level is reached again, as shown in point 3. At this moment, a new order “Q’₂″ is generated, and as agreed with the supplier, the material is delivered.

The inventory decreases again due to consumption, but at a specific point, a more significant consumption is observed in a single period. This can be interpreted as an unanticipated or special request, as shown in point 4.

This consumption causes the inventory to drop below the safety level, leading to placing an order for the quantity “Q’₃,” which is the difference between the maximum level and the inventory at period “n₃.”

After this significant consumption, the normal demand continues to deplete the remaining inventory, anticipating a stock-out. However, the supplier responds promptly with their delivery, which is reflected in the increase in inventory, as seen in point 5.

Since it is not possible to calculate an optimal order quantity “Q” or an optimal lead time “T” in this model, a quantity “Q’_n” must be calculated for each replenishment period “n.” As a result, it is necessary to create a plan based on the maximum level “R,” taking into account the formulas in Table 12.

Abbreviations	Formulas
SR: Safety stock for R; d: Average demand; k: Safety factor; ϭ: Standard deviation of demand; t: Current provisioning time; R: Roof; Q: Supply quantity; i: Inventory; n: Period	SR = d*t + k * ϭ * (Square root (t)); d = Average D; k = NORM.S.INV1 (P); P = Probability that they will not show up out of stock (Stock-out); ϭ = STDEV^5 (Demand); RSR = d * t + SR; Q’n = R - in; in = in-1- dn + Qn

Table 12.

SR formulas.

¹

Excel functions.

As shown in Table 13, during the first period, there is a demand “d₁” along with an organization-set ceiling “R” and an initial inventory level “i₀.” To determine the order quantity “Q’_n” for this period, the process begins by calculating the current inventory “i₁,” which is obtained by adding the initial inventory to the received supply quantity “Q₁” in that period and then subtracting the demand for that same period “d₁.” Next, the order quantity “Q’_n” is calculated, which is obtained by subtracting the upper limit “R” from the previously calculated initial inventory “i₁.” This scheduled quantity will arrive as supply “Q₂” in the next period, following the agreed-upon lead times with the supplier.

n	1	2	3	4	5
d	d1	d2	d3	d4	d5
RSR	R	R	R	R	R
Q´ (Place order)	Q´1 = R – i1	Q´2 = R – i2	Q´3 = R – i3	Q´4 = R – i4	Q´5 =R – i5
Q (Order arrival)	Q1 = Q´0	Q2 = Q´1	Q3 = Q´2	Q4 = Q´3	Q5 = Q´4
in-1	i0	i1	i2	i3	i4
in	i1= i0+Q1−d1	I2= i1+Q2−d2	I3= i1+Q3−d3	I4= i2+Q4−d4	I5= i3+Q5−d5

Table 13.

Quantity SR planning.

4.4 TR policy

This model is designed to address seasonal demands by gradually adapting to smooth market fluctuations in a cyclical manner. It effectively cushions these changes using expected optimal lead times, thus avoiding the accumulation of unnecessary inventory. In this context, responsiveness is not as critical, although we should consider that there are peak demand moments that can impact product availability. The optimization of this model focuses on lead time and is accompanied by an upper limit to prevent inventory excesses [26, 27, 28, 29].

As represented in Figure 10, inventory consumption begins at time zero. When consumption reaches half of the inventory, the order “Q₁´” is generated, as indicated in point 1. When the optimal time “T” is reached, the quantity “Q₁” from the order is received, as indicated in point 2, and the inventory consumption cycle continues. Because demand is seasonal, variations in demand rates are not as abrupt.

Figure 10.

TR policy.

In this model, it is not feasible to calculate an optimal order quantity “Q,” which leads to calculating a quantity “Q” for each period “T,” but it is possible to achieve an optimum in the lead time “T.” Consequently, it is necessary to develop a plan based on the maximum level “R,” taking into account the formulas in Table 14.

Abbreviations	Formulas
T: Optimal supply time; Cp: Ordering cost; Cs: Sustaining cost; dTR: Average plus deviation demand for TR; R: Roof; Q: Supply quantity; i: Inventory; t: Current supply time	T = Square root ((2*Cp) / (Cs*d)); dTR = Average D + Desvest D RTR = (d + ϭ) * t; Q’T = R - iT; iT = iT-1 + QT - dTR

Table 14.

TR formulas.

As seen in Table 11, in the first period, there is a demand for “T₁,” a calculated ceiling for “TR” (R_TR), and an initial inventory level of “i₀.” To determine the order quantity “Q’_T1” for this period “T,” the process begins by calculating the current inventory “i₁.” This is obtained by adding the initial inventory to the received supply quantity “Q₁” in the same period and then subtracting the demand for that period “d₁.”

Next, the order quantity “Q’_T1” is calculated. This quantity is obtained by subtracting the upper limit “R_TR” from the previously calculated initial inventory “i₁.” The planned quantity “Q’_T1” will be delivered as supply “Q₂” in the next period (Table 15).

T	1	2	3	4	5
dTR	d1	d2	d3	d4	d5
RTR	R	R	R	R	R
Q´ (Place order)	Q´1 = R – i1	Q´2 = R – i2	Q´3 = R – i3	Q´4 = R – i4	Q´5 = R – i5
Q (Order arrival)	Q1 = Q´0	Q2 = Q´1	Q3 = Q´2	Q4 = Q´3	Q5 = Q´4
iT-1	i0	i1	i2	i3	i4
iT	i1= i0+Q1−d1	I2= i1+Q2−d2	I3= i1+Q3−d3	I4= i2+Q4−d4	I5= i3+Q5−d5

Table 15.

Quantity TR planning.

“T,” which is the optimal time for replenishment.

The implementation of these four supply policies originates from the need to provide a strategic focus to the supply and inventory operation, as suggested by Michael Porter regarding the bargaining power of suppliers. In many instances, suppliers gain a greater share of the value and, consequently, pass on the costs to other players in the chain. Powerful suppliers can exert pressure on an industry, especially if it cannot effectively control costs related to raw materials, particularly in terms of supply logistics. This largely depends on the concentration of suppliers in a particular sector [30].

The degree of supplier bargaining power determines how skillful the industry must be to avoid excessive dependence. In situations where the supply source is highly competitive, meaning that several suppliers are offering attractive prices, the industry has greater bargaining power. However, in cases where the source is oligopolistic, the industry loses its bargaining power and becomes increasingly dependent due to the scarcity of suppliers. Lastly, when the source is monopolistic, the industry becomes entirely dependent on that single supplier. In such a scenario, a supplier serving multiple industries will not hesitate to maximize its profits at the expense of the companies [31].

In situations where the number of industries requiring the services of a supplier is limited or when one of these industries represents a significant portion of the purchase volume, the supplier will seek to protect it by offering competitive prices, and discounts, and collaborating in training and promotional activities.

Summarily, it can be concluded that suppliers can exert a significant influence on the market, especially when the cost of materials and inputs represents a substantial percentage of the cost of the final product. Therefore, companies must be strategic and insightful in their planning, procurement, and storage processes.

5. Conclusions

Inventory planning will continue to evolve into new models and strategies, largely influenced by a country’s conditions and its structural capacity to coordinate logistical activities, as well as the emerging way in which markets evolve. However, it is essential to keep in mind that inventory remains a significant asset and, therefore, a crucial part of an organization’s working capital. As such, it must be managed strategically, especially in the procurement process.

Given the current evolution of the industry into its fifth generation, the information era becomes even more crucial in its management. In the realm of procurement, this aspect takes on particular relevance. Inventory planning supported by artificial intelligence has become an imperative necessity, as it establishes an essential link between demand behavior and efficient industry responsiveness.

Inventory management becomes an essential strategic resource for organizations, as it plays a critical role in optimizing operations and a company’s profitability, as well as customer satisfaction. A thorough understanding of the influence of inventory in all areas of a company, from operations to finance, enables organizations to appreciate the value it represents as an asset. This, in turn, empowers them to develop various strategies aimed at generating benefits, maximizing operational efficiency, and achieving greater profitability.

It is essential to recognize that while inventories are an asset for companies, they also represent a capital investment. Inadequate inventory management can trigger financial problems or reduce service quality. Therefore, it is crucial to achieve a balance between inventory levels, their associated costs, and productive capacity.

Currently, the market is characterized by constant dynamism and uncertainty, representing significant challenges for organizations in their planning strategies. Therefore, aggregate planning emerges as a fundamental tool that allows for strategic decision-making, considering both demand volatility and the organization’s production capacity. However, companies must understand that to achieve effective results when implementing this model, it is necessary to foster collaboration throughout the supply chain.

An aggregate plan, the integration of all supply chain actors, and effective inventory management not only ensure flexibility and adaptability to market changes but also enable agile and flexible operation. This becomes even more crucial in highly competitive and volatile markets. Strategic strengthening in operations management is no longer a choice; it becomes imperative if an organization aspires to enhance its competitive advantage.

For any professional working in logistics or supply chain areas, mastering mathematical models and the ability to program algorithms become essential. Success in decision-making lies in the quality of information and, consequently, in the precise modeling of logistical or planning problems. This allows for accurately predicting operational behavior at a competitive cost and anticipating demand, ensuring adequate service levels at a competitive cost.

Inventory management is a fundamental part of an organization’s operations and has a significant impact on its profitability and efficiency. As the industry evolves into fifth-generation models and the information era becomes more crucial, inventory planning supported by artificial intelligence becomes a necessity to stay competitive and adaptable to market changes.