Theories and Methods for the Emergency Rescue System

According to the “China State Plan for Rapid Response to Public Emergencies” (hereinafter referred to as “Plan”), which was published by the Central Government of the People’s Republic of China, “public emergencies” refer to those emergencies that happened suddenly, and would (or might) cause heavy casualties and property loss, damage ecological environment, bring severe harms to our society and threat public safety. In the “Plan”, public emergencies were divided into four categories: natural disasters, accidental disasters, public emergencies and social security events.

in disaster-stricken areas. The disaster-stricken people didn't have enough emergency resources to make their living. Consequently, they ransacked shops for food and medicine and severely undermined the local social order.
These two examples have fully revealed the importance of designing a sophisticated emergency rescue system. The loss of public emergencies would be greatly reduced by understanding the distribution of disaster-stricken people and providing appropriate emergency resources to them. Otherwise, the public emergencies would be uncontrollable. To make things worse, the situation of disasters might be more serious, and even lead to the breakout of secondary disasters.

Problem statement
When we design an emergency rescue system, we need to coordinate the manpower with the financial, material resources. It is a complicated process to optimally allocate various elements within a system. It involves a wide range of contents. Repeated researches should be made on several theories and methods. Designing of an emergency rescue system covers the following four aspects (See Figure 1 These four aspects have been cross-linked each other essentially.

Demand Forecasting of Emergency Resources
In recent years, unconventional emergencies frequently broke out, severely endangered people's life and property. How to timely predict people's demand on resources after the disasters? This issue has become an important problem for us.
Here, a precise predictive method has been designed by combining the Fuzzy Set Theory with the Learning Rules of Hebb Neural Network, Multiple Linear Regression and Case Optimal dispatching of emergency resources Optimal allocation of emergency resources Site selection for the base station of emergency resources Demand forecasting of emergency resources www.intechopen.com Reasoning. By applying this method, we have solved the problems of information insufficiency and inaccuracy when we predict the resource demand after unconventional emergencies, and could correctly predict people's demand on resources.

Optimal Site Selection for the Base Station of Emergency Resources
If the resource demand has been determined, sufficient emergency resources need to be transported to the emergency base stations (Emergency rescue station). To achieve this goal, how many base stations for emergency resources should be established, and where should we establish these stations, these issues will be worth considering. In other words, we should optimally select the sites of base stations and find appropriate locations within a certain region as the base stations of emergency resources. The number of location should also be suitable. When disasters break out, we could allocate resources from these base stations to deal with the emergencies. By optimally selecting the sites of base stations, we could not only reduce costs, but could also ensure the timeliness of emergency resources, making these resources arrive at the emergency scenes quickly, safely and timely.
Here, a summarization has been made on relevant site selection knowledge, and the Operations Research theories have been applied based on the existing site selection methods. A multistage model of site selection has been designed to make an optimal planning on the number and location of base stations. Example analysis has also been made to verify the results of calculation. It has been proved that this model is simple, convenient for use, and could get results quickly. This model would be suitable for the site selection and planning of base stations of emergency resources.

Appropriate Allocation of Emergency Resources
The emergency resources deployment is a hardcore of emergency management. After the happening of the public emergency, it is important to study how to deliver the emergency resources to base stations quickly. When we've determined the location of base stations, we should optimally allocate emergency resources. More to this point, it should predetermine the number, type and quality of resources for each base station. Otherwise, there's an important constraint condition for us to consider: the costs.
This chapter proposed the dynamic optimal process of emergency resources deployment planning, making use of Markov decision processes, and discovered the optimal deployment planning to guarantee the timelines.

Optimal Dispatching of Emergency Resources
Aiming at solving the resource allocation problems in case of emergency events, this chapter presented an optimum mathematical simulation model based on the dynamic programming.
In accordance with the number of emergency base stations, the given model tries to divide the resource allocation procedure into the some stages. The stated variable stands for the amount of the emergency resource available for allocation can be used at the beginning of each stage. As is depicted in the dynamic programming theory, the remaining resource of the previous stage may have a strong influence on the succeeding stage. During each stage, three factors may restrict the object function, that is, the remaining resource, the decision, and the demand. The total function is the sum of the object function of each stage. In www.intechopen.com addition, the concrete case can be used to confirm the model's validity and practicability. The results of our repetitive experimental application of the model show that it works perfectly for its duty in improving the efficiency of emergency management and overcoming the problem of wasting emergency resource as well as low efficiency in emergency rescue.

Research background
Public emergencies usually bring great negative impacts on economy and society, cause damage on casualties and property, bring destructions on ecological environment and human living environments, have adverse impacts on social order and public safety, and even arise social and political instability. Moreover, due to the change and influence of multiple factors, the type, occurrence probability and influence degree of public emergencies are increasing.
The demand on emergency resources refers to the minimum guarantee requirements for effective response to public emergencies. The so-called effective response refers to that the response on public emergencies should be efficient, and it also refers to that the emergency resources should be used with high efficiency. While the minimum guarantee requirements refer to that the smallest demands are needed when public emergencies are successfully solved. Obviously, an optimized idea is involved in the determination of emergency resource demand, meaning that under some given parameters such as type, intensity and influencing range of Emergency response, the smallest resource demand required for the successful response to public emergencies.
Currently, there are few researches on this aspect, in most cases the emergency decision maker subjectively decides whether the quantity, quality and type of emergency resources are rational and can meet the requirements of emergency. Besides, due to the particularity of emergency process, the effect of cost is smaller than that of time effect, so that in many cases, no efforts are spared to conduct the emergency rescue. But the method is easily to cause the irrational demand of emergency resources, so that it is unscientific and will cause groundless waste of numerous resources, meaning that a scientific prediction method is sorely needed to achieve the prediction on the demand of emergency resources.
Case-based reasoning (CBR) is a relatively new problem solving technique that is attracting increasing attention. For a long time, expert systems or knowledge-based systems (KBS) are one of the success choices in Artificial Intelligence (AI) research. The first generation KBS, and today's systems, are based upon an explicit model of the knowledge required to solve a problem. When it comes to so called second generation systems, a deep causal model was adopted to enable a system to reason using first principles [1]. But whether the knowledge is shallow or deep an explicit model of the domain must still be elicited and implemented often in the form of rules or perhaps more recently as object models. However, knowledge elicitation is a difficult process, often being referred to as the knowledge elicitation bottleneck; implementing KBS is a difficult and slow process requiring special skills; and once implemented they are difficult to maintain [2][3][4][5][6].
Over the last few years an alternative reasoning paradigm and computational problem solving method has increasingly attracted more and more attention. Case-based reasoning (CBR) solves new problems by adapting previously successful solutions to similar problems. CBR is attracting attention because it seems to directly address the problems outlined above. CBR does not require an explicit domain model and so elicitation becomes a task of gathering case histories, implementation is reduced to identifying significant features that describe a case, an easier task than creating an explicit model, by applying database techniques largely volumes of information can be managed, and CBR systems can learn by acquiring new knowledge as cases thus making maintenance easier.
The work Schank and Abelson in 1977 is widely held to be the origins of CBR [7]. They proposed that our general knowledge about situations is recorded as scripts that allow us to set up expectations and perform inferences. Whilst the philosophical roots of CBR could perhaps be claimed by many what is not in doubt is that it was the work of Roger Schank's group at Yale University in the early eighties that produced both a cognitive model for CBR and the first CBR applications based upon this model [8]. Janet Kolodner developed the first CBR system called CYRUS [9][10][11]. An alternative approach came from Bruce Porter's work, at The University of Texas in Austin, into heuristic classification and machine learning resulting in the PROTOS system [12][13].
In the U.S., Edwina Rissland's group at the University of Massachusetts in Amherst developed HYPO [14]. This system was later combined with rule-based reasoning to produce CABARET [15].
In Europe, the first one is that of Derek Sleeman's group from Aberdeen in Scotland. They studied the uses of cases for knowledge acquisition, developing the REFINER system [16]. Mike Keane, from Trinity College Dublin, undertook cognitive science research into analogical reasoning [17]. Michael Richter and Klaus Althoff in the University of Kaiserslautern applied CBR to complex diagnosis [18]. This has given rise to the PATDEX system [19] and subsequently to the CBR tool S3-Case. In the University of Trondheim, Agnar Aamodt has investigated the learning facet of CBR and the combination of cases and general domain knowledge resulting in CREEK [20][21].
In the UK, CBR seemed to be particularly applied to civil engineering. A group at the University of Salford was applying CBR techniques to fault diagnosis, repair and refurbishment of buildings [22]. Yang & Robertson [23] in Edinburgh developed a CBR system for interpreting building regulations, a domain reliant upon the concept of precedence. Another group in Wales applied CBR to the design of motorway bridges [24].

Methods for emergency resource demand prediction
According to the characteristics of emergency resource demand prediction process, both the risk analysis and case-based reasoning method are introduced into the process, accordingly a case-based reasoning method for emergency resource demand prediction based on risk analysis is obtained, which improves the scientificity of emergency resource demand. The case-based reasoning flow for emergency resource demand prediction based on risk analysis is shown in Fig.2. www.intechopen.com  The case-based reasoning is a comprehensive form of three types of human thoughts including imaginal thinking, logical thinking and creative thinking. From the view of reasoning method, the case-based reasoning is an analogy reasoning from one case (old case) to another case (new problem), while from the view of knowledge, the case-based reasoning is a method based on memory in which old experiences are used to guide the problems. The CBR is generally composed of four main processes, including retrieve, reuse, revise and retain [29][30], so that CBR is also called 4R.
Therefore, in this paper, the case-based reasoning prediction method associated with risk analysis process is used to conduct demand prediction on the quantity, quality and type of emergency resources. After conducting risk analysis on target area, characteristic values of risk in these are can be obtained, including possible incident type, incident results, occurrence probability of incident, etc., accordingly the case-based reasoning process can be used for emergency resource demand prediction.

Expression of case
The case generally includes two parts, including case attribute description and case solution, of which the former one is the index structure of case and the latter one is the answer of case. While the emergency resource demand prediction is composed of three parts, including characteristic description of Emergency response, characteristic description of emergency rescue plan and description of emergency resource demand, all of which can be determined based on the results of risk analysis, namely risk probability and risk results.
 Characteristic description of Emergency response: it includes some characteristic information of Emergency response, including type, intensity, natural environment surround the occurrence site, population density, losses, duration time of hazard, etc., all of which depict and describe the characteristic attributes of Emergency response.  Characteristic description of emergency rescue plan: it includes the characteristic attributes of emergency object, emergency rescue method, emergency procedure, etc. If there is a difference in the emergency object, way, technique and process of Emergency response of the same type, the material demands will be different too.  Description of emergency resource demand: it includes the quantity, quality and type of emergency resources.
On the whole, in order to obtain complete data, the case should be described in detail as can as possible under the specific condition. Generally, one case can be composed of several attributes, all of which can be further divided, while the whole case library is composed of associated cases at different attribute levels. Therefore, in the emergency resource demand prediction, the case can be modeled as follows:

case (F, P, D)
In the formula: F=(f 1 , f 2 ,…, f n ), f n is a characteristic attribute of Emergency response, which can be obtained according to the results of risk analysis; P=( p 1 , p 2 , …, p n ), p n is a characteristic attribute of emergency rescue plan; D is the demand attribute of emergency resource.
2. Case-based reasoning process of emergency resource demand a. Characterization of emergency resource demand case www.intechopen.com Given that there are n cases in the case library, the case i is expressed as C i (i=1,2,…,n). Its characteristic factor set B={b 1 , b 2 ,…,b m }. Therefore, the membership function of case C i to the characteristic factor b j (j=1,2,…,m) is expressed as () i Cj nb, and the characteristic vector corresponding to the case C i in the case library is as follows: (1) Given that the characteristic vector set of prediction plan is T, which can be expressed as the formula below: (2) b. Emergency resource demand case retrieve-similarity calculation According to the organization form of case, the nearest neighbour method is used. The nearest neighbour method is a method in which the cumulative sum of characteristic weights of the input case that is matched with the existing case in the case library is used to retrieve the case, namely that: In the formula above: w is the important weight value of characteristic factor, sim is the similarity function, b I and b R is the input case value and retrieve case value of characteristic factor i.
In the similarity matching of cases using the characteristics of case, the effect of each characteristic is different, so that in the similarity calculation, it is necessary to assign different weights to each characteristic factor.
Given that the influencing weight set of the characteristic factor set B={b 1 , b 2 ,…,b m } is {w 1 , w 2 ,…,w m }, and the following condition is satisfied: Consequently, the similarity can be calculated by the formula below: In the formula (5), is the maximum lower limit, and is the minimum upper limit. Generally, under different decision-making environments, the same characteristic factor has different effects on the decision output. Given that represents the value of case when the characteristic factor is b. If there is a large difference in distribution of in the case library C (C ={c 1 , c 2 ,…,c n }), which indicates that the factor has great effect on classification identification, and it should be assigned a larger weight value. On the contrary, if there is a small difference in distribution of in the case library C (C ={c 1 , c 2 ,…,c n }), which indicates that the factor has little effect on classification identification, and it should be assigned a smaller weight value.
Therefore, each case in the case library can be classified into one type. Given the case C i takes the value of when the characteristic factor is b j , the membership function of the case to the characteristic factor b j can be expressed as , and the formula below can be obtained: Thus, the mean square deviation is expressed as the formula below: The weight w j of each characteristic factor can be obtained by the formula below: After the weight of characteristic factor is obtained, the similarity function is combined with the weight of characteristic factor, and the formula below can be obtained: In the formula above, the similarity between target case T and C i can be expressed as sim(T,C i ) (∈[0,1]), η is a threshold value, and the learning strategies of case are divided into following types: All cases in accordance with the similarity calculation formula are the similar cases, among which the one with the maximum sim (T, C i ) is the most similar case. Accordingly, the material demands of the most similar case are taken as the prediction results of material demand when the Emergency response occurs.

Research background
Urban Planning refers to the specific method or process of predicting urban development and managing various resources to adapt to its development, to guide the design and development of built environments. While modern urban planning is trying to study the impact which a variety of economic, social and environmental factors have on the change of land using patterns, and develop planning reflecting the continuous interaction. Currently, in the process of making urban planning, parties have paid more and more attention to urban safety planning, in which the optimization of location planning of emergency logistics base station is one of the very important contents [31][32][33].
Emergency Logistics refers to the special logistics activities through which the necessary emergency supplies are provided to minimize the loss caused by unforeseen accidents and disasters in the shortest time, while an important role of emergency logistics base station (also known as emergency resource base station) is to provide adequate and timely emergency response resources to potential unforeseen accident or disaster sites [34][35][36][37].
The optimization of location planning of emergency resource base station includes determining reasonable position and scale of emergency resource base station, and since the special construction of emergency logistics base station costs a lot due to its specialization, so the optimization of the location planning of emergency resource base station should mainly start with two aspects, one is to determine the appropriate scale or the reasonable amount of emergency resource base stations, the other is to solve the problem of spatial distribution, namely, location optimization [38][39][40]. Ninghe and Jixian. It has a total area of 11,919.7 square kilometers, and a resident population of 1023.67 million. Table 1 shows the statistics of accidents this year in City T.  Table 1. Statistics of accidents in recent years in City T*.
As can be seen from the table, City T is a metropolis with a good security situation, but in order to take preventive measures, it is very important and very necessary to carry out the optimization of location planning of emergency logistics base stations in City T. Therefore, in this paper, taking City T as the object, the author makes use of multi-stage location planning optimization model to study the location planning of emergency resource base stations in this city and seek a reasonable location planning program to provide a decision making basis for the future construction and development of City T.

Multi-stage location planning optimization model of emergency resource base station
An important role of emergency logistics base station is to provide adequate and timely emergency response resources to potential unforeseen accident or disaster sites. And the optimal planning of emergency logistics base station helps to make rational use and allocation of spaces and emergency resources, to reduce the risks the city, as well as conduce to the efficient, orderly and sustained operation of urban economy, social activities and construction activities.
The optimization of location planning of emergency resource base station includes determining reasonable position and scale of emergency resource base station. Therefore, the optimization of the location planning of emergency resource base station should mainly start with two aspects, one is to determine the appropriate scale of emergency resource base stations, and the other is to solve the problem of spatial distribution.
The first step is to use set covering model to determine the minimum number of emergency resource base stations which can meet the needs of all demand sites; and the second step is to use maximum coverage model to determine the optimal sites of the minimum number of emergency resource base stations among the options, to meet the needs of all demand sites to the maximum.
a. Scale optimization -set covering model Coverage model is one of the most basic models of optimal planning of emergency resource base stations. The meaning of coverage refers to that the services scope of emergency resource base stations set up should be able to cover all sites requiring service. And it is one of the common goals of optimal planning of emergency logistics base station to cover all demand sites with the minimum number of emergency logistics base stations.
Set covering model is simple, but highly practical. It can be used to determine the most efficient number the emergency resource base stations covering all demand sites. Since the investment in emergency resource base stations can be quite expensive, so decision-makers need to keep a minimum number of base stations at the same time of taking providing services of necessary level to each demand site into account, therefore, they need to determine the reasonable number of emergency logistics base station under the limitation of covering distance or covering time.
The binary decision variable x j is set as follows: When the candidate site j is selected, x j = 1; otherwise x j = 0. if the set of candidate sites which can cover all the demand sites i is , the minimum number of the necessary facilities which can cover all the demand sites may be decided by set covering model: In which the objective function can minimize the number of base stations, the constraint 1 can ensure that each demand site is covered by at least one emergency resource base station, and it is one of the basic objectives of optimal planning of emergency resource base station. The constraint 2 limits the decision variables x j as integer variables between (0, 1).
Set covering model is of integer linear programming model, mathematically, it is a typical NP-hard model. Generally, its solution can be obtained through relaxing integer limiting requirement against x j , using the procedure of general linear programming, and in most cases, integer solution of general problems can be directly obtained.
Maximum coverage model can be used to seek the best possible using method of available resources, but does not guarantee to cover all demand sites. Therefore, maximum coverage model can be used to determine the optimal solution of maximum coverage on the base of the optimal solution of set coverage.

Research background
At present, our country is in an important opportunity period for economic and social development, which is also the crucial period to implement the third-step strategic deployment of the modernization construction; therefore, the important task of our country is to maintain the long-term harmonious and stable social environment and stable and united situation. As the most important link in emergency handling, the contingency plan strengthens the research in respect of optimized resource allocation, which has very important significance for promoting the technological level of dealing with unexpected accidents and emergency management capacity of our country, guaranteeing public safety in our country and establishing reasonable and efficient contingency plans for national public safety.
The emergency resource management process of unexpected public events is in fact a set of decisions and decision implementation processes under a series of goal constraint conditions. These series of decisions and decision implementation processes mean "when and which resources at which place to allocate, and what to do". It is necessary to invest in enhancing urban comprehensive emergency capability, which proposes the problems of optimized allocation and dispatch of limited emergency resources, and the problem solving relates to whether the limited resources can exert the greatest effect, whether the emergency rescue system can achieve the desired goal and so on. At present, the researches related to emergency resource allocation practically aim at single resource optimization, such as the emergency service vehicle dispatch or vehicle relocation problems. When the emergency service vehicle system receives the service demand, it dispatches its emergency response unit (such as police car, fire engine, ambulance and so on) to the service demand zone. After  (2000) studied the problems of simultaneous resource allocation for different disaster relief tasks and so on through building a dynamic programming model [42]. At the present stage, there are fewer studies on optimized allocation of many resources under unexpected accident disasters, moreover the majority of studies only take shortest emergency time as the optimized objective of the system, and the optimized method is too simple, and lacks consideration of the complexity of the emergency process; in addition, static models are more widely used in the studies, which lack emergency resource allocation parameters reflecting the accident disaster development status.
The present research aims at enhancing the urban emergency management capacity, establishes the emergency resource allocation model in view of many accident disasters, so as to effectively integrate various emergency resources, and reduce the investment cost of emergency resource management.

Decision model based on dynamic programming
The emergency resource allocation process is divided into N corresponding stages in view of the accident disaster emergency management characteristics, using the dynamic programming method, and according to the number of emergency zones (the number is supposed as N), based on which, a mathematical model is built, so as to optimize the emergency resource allocation. In the emergency process, a certain amount of resources are allocated to meet the emergency demand, and various parameter variables are expressed as follows.
k is the emergency stage (k 1,2, ,N)   ; k x is the state variable in the dynamic programming model, representing the gross amount of allocated emergency resources at the k th stage; k u is the decision variable in the model, representing the alternative decision scheme; k w represents the emergency resource demand at the k th stage with given probability distribution. k D is the set of all decision variables from 1st stage to the k th stage.
Suppose that 12 N w, w, , w  are independent random variables depending on the disaster situation at emergency zones. The relationship between allocatable resource k x , emergency resource demand k w and emergency decision variables k u in the emergency process is shown in Figure 3.  For the ( k 1  ) th stage, the dynamic system has Where, N is the number of emergency zones in the emergency process.
The decision function sequence composed of the decision kk u( x) ( k 1 , 2 , , N )    at each stage is called the whole process strategy, strategy for short. Strategy refers to the set of all emergency resource allocation decisions established at any emergency stage, which is only related to the stage and state in that stage process, and is expressed as An appropriate u value (namely, appropriate decision sequence) is selected, so as to minimize J (or use other evaluation standards of J, such as the maximization of J), and optimize the objective function. Function J is called the criterion function.

Establishment of an optimized resource allocation model
The decision-making process at the N th stage is determined using the following factors.
, and x(0) is the known initial state, suppose that all x(k)(k 1 N ,2, , )   can be expressed as x(0) and u(k)(k 0, , 1, N 1)    , so the criterion function x(0) is the given initial state, decision u(k)(k 0 N ,1, , )   is free variables, so the simultaneous nonlinear equation To solve practical problems, it is necessary to analyze and calculate the form of limit criterion function J in multistage decision process. In the present model i.e., the existing decision is only the function of existing state and stochastic disturbance.
The criterion function of emergency resource allocation has Markov properties, i.e., the objective function has the following attributes Where, L(x(k), u(k), w(k)) is the objective function at each stage of the emergency process.
In this model, L is a nonnegative function depending on the state and sum of decision items at a single stage. J is the objective function of the whole emergency process, equivalent to the sum of objective functions at all stages.
In general, it is known that a group of states x(k) X  , and X is available emergency resources, then a new group of states x(k 1)  can be obtained according to x(k) with the computing formula as At the same time, J(x(k 1),k 1)   can also be calculated So the total cost function of the emergency process of any systematic sample can be expressed as

Research background
It is necessary for the emergency command department to make the emergency resource scheduling decisions after the occurrence of sudden public events. It is necessary for www.intechopen.com emergency decision-makers to determine future resource scheduling according to the emergency resource demand situation at the present stage, and multi-stage emergency resource scheduling with the event development and changes and according to the emergency effect at the last stage and present situation. Therefore, the emergency resource scheduling is a dynamic process. Under the situation that the emergency resource site layout and allocation is known, emergency managers are concerned about the problems of how to formulate optimized scheduling scheme, guarantee the timeliness of emergency resource scheduling, and minimize the resource arrival time [43][44]. As a result, it is necessary to formulate beforehand the optimized scheme of emergency resource scheduling in the light of the specific scene of sudden public events, so as to start the emergency resource scheduling scheme as early as possible and guarantee the timeliness of emergency rescue action.
The Markov decision process can select an action from the available action set to make a decision according to the observed state at each moment. Meanwhile, the decision makers can make another new decision according to the newly observed state, and repeat such process [45]. Therefore, this section plans to study the dynamic optimization of emergency resource scheduling of sudden public events using the Markov decision process, so as to provide a basis for optimized emergency resource scheduling under sudden public events

Dynamic Markov decision of emergency resource scheduling
Due to a series of characteristics of sudden public events, such as nonrepeatedness, uniqueness, gradual evolution and so on, the decision-making problems for emergency resource scheduling have three main characteristics: sudden public event is dynamically changing; information about the event development is from fuzziness to clearness and from incompleteness to completeness, namely the future state is uncertain; the scheme formulated under incomplete information can be easily adjusted in time under complete information.
The optimized emergency resource scheduling can be more scientifically and reasonably realized by referring to the Markov decision analysis method, but sudden public events are not evolved and developed according to the pre-established direction. Therefore, emergency measures can be only taken according to previous experience, emergency plan and real-time information at the scene of accident (usually incomplete), and be adjusted according to unceasing improvement of the information in the emergency process.
The application of Markov decision analysis method in the optimized emergency resource scheduling process of sudden public events is shown in Figure 4. The whole decisionmaking process is how to select a scheme to cope with the uncertainty development state of the sudden public event, until the sudden public event is completely under control.
Basic thought of the Markov process is to infer the future state distribution according to the probability distribution of current state, and make judgment and decisions accordingly. X(t) is used to express the system state, the state sequence {X(t);t T}  is a stochastic process, m (i) U is the decision set of the state i at the nth stage. Suppose that ij P is the one-step state transition probability, nn f( i , )  represents the expected total reward when the system state shifts from X(n) i  at the nth stage to the process end; ij r represents the  (24) This formula is the basic equation for Markov decision problems.
To research the transient state behavior the ergodic Markov chain, it is necessary to obtain its basic equations set using z transform analysis method. z transform can transform the difference equation to corresponding generalized equation. There is one-to-one correspondence between the function and its z transform, and meanwhile the primary function can be mutually converted with its z transform. Therefore, the following formulae can be obtained through z transform This is the basic equations set for Markov decision problems, which can be obtained through the following algorithms.
a. An initial strategy n  is selected, a decision regulation n  is selected for each state d. If the obtained strategy π n+1 is completely equal to the strategy π n obtained through the last iteration, namely π n+1= π n , then the iteration is stopped, and the optimized strategy is obtained. Otherwise, return to step 2 and let n = n+1.

Case study 4.1 Case study -Emergency resources demand prediction using case-based reasoning
The prediction process above can be applied not only in the prediction on emergency resource demand for the public emergencies that have not yet happen, but also in the prediction on emergency resource demand for occurred public emergencies.
Given that the city T plans to conduct a prediction on the demand of emergency resource when the earthquake occurs, and there are four cases for this type of Emergency response in the case library, expressing as C=(C 1 , C 2 , C 3 , C 4 ), and each case includes the demand information of quantity, quality and type of corresponding emergency resource, as shown in Table 2. Given that the emergency rescue plans for this type of Emergency response are the same. Through the risk analysis, five characteristic factors reflecting the characteristics of Emergency response are selected, meaning that the characteristic factor set B is composed of hazard intensity, disaster-affected population, direct economic losses, stricken area and duration time of disaster, and the membership function of four cases to five characteristic factors is as follows respectively: (27) Given that an Emergency response occurs now, and it needs to conduct a prediction on its emergency resource demands. Given that the emergency resource demand prediction plan for this Emergency response expressed as T, and its membership function can expressed as the formula below:

Case
.....    Table 2, and the similarity of each case is ordered as follows: It can be seen from the calculations above that this Emergency response is similar to the case C 3 in the case library, so that the emergency resource demand prediction results of this Emergency response are similar to that of the case C 3 . Consequently, the conclusions of prediction on this emergency resource demand can be drawn by correcting and adjusting the emergency resource demand analysis results of the case C 3 .  Table 3. Characteristic Factor Information of each Case.
Using WinQSB to find the solution of set covering model, the optimal solution of z = 4 is obtained, that is, to cover all demand sites, four emergency resource base stations are www.intechopen.com necessary. Then using MCLP model, and having the p-value increase continuously from 1 to 4, using WinQSB, solution of the model can be obtained as follows:  -min drive  A1  A2,A3,A4,A5,A6,A7,A8,A9,A12,A13  A2  A1,A3,A4,A5,A6,A7,A8,A12  A3  A1,A2,A5,A7,A8,A12  A4  A1,A2,A5,A6,A7,A8,A13  A5  A1,A2,A3,A4,A6,A7,A8,A9,A12,A13  A6  A1,A2,A4,A5,A7,A8,A9,A13  A7  A1,A2,A3,A4,A5,A6,A8,A9,A12,A13  A8  A1,A2,A3,A4,A5,A6,A7,A9,A10,A12,A13  A9  A1,A5,A6,A7,A8,A10,A13  A10  A8,A9,A11,A13  A11  A10  A12 A1,A2,A3,A5,A7,A8 Through the same calculation process as above, the optimal solution of z = 2 is obtained, that is, to cover all demand sites, two emergency resource base stations are necessary. Then using MCLP model and having the p-value increase continuously from 1 to 2, using WinQSB, solution of the model can be obtained as follows:  Through the same calculation process as above, the optimal solution of z = 2 is obtained, that is, to cover all demand sites, two emergency resource base stations are necessary. Then using MCLP model and having the p-value increase continuously from 1 to 2, using WinQSB, solution of the model can be obtained as follows: Comparing the above results under the three emergency response time standards, we can find that: 1. Though the solutions of set covering model and maximum coverage model, it is found that within the area of a 30-min drive response time standard , four emergency resource base stations are the most reasonable and can meet the demand, and when the number of base stations is less than 4, the emergency demand can not be met, and when the number is more than 4, unnecessary waste and redundant coverage will be made, and through MCLP model, the construction site of the four base stations can be determined as Tanggu, Dongli, Baodi and Jixian. 2. When the emergency response time standards are set as 45min and 60min, the result shows a maximum of two emergency resources is enough to cover all administrative regions of City T, but for different time standards, the base stations should be built in different districts, when the time standard is 45min, they should be built in Beichen and Baodi, and when the time standard is 60min, they should be built in Tanggu and Wuqing. 3. Because this result is obtained through simplifying the actual problems appropriately, can provide a reference for the actual decision-making, but there may be some errors, so the research of planning method more precise and close to the actual is required.

Case study -Appropriate allocation of emergency resources
It is supposed that there are 4 dangerous emergency zones in the emergency process, namely N 4  ; total available amount of emergency resources is 12, namely X1 2  , and X represents the total amount of available resources. Risk value when each scene is allocated with different amounts of emergency resources is listed in Table 10.
Emergency resources are dispatched according to the emergency resource allocation model, so as to achieve the optimization objective of minimizing the sum of risk values at various emergency zones in the following processing steps: 1. Suppose that the emergency response process can be divided into 4 stages, namely 4 emergency zones, i.e. k 1,2,3,4  ; 2. The emergency resource allocation objective at each stage is k L , and the total emergency objective is expressed as formula (7) The optimized emergency resource allocation is calculated under the supposed scene of accidents with the mathematical mode of optimized emergency resource allocation, so as to obtain the optimized allocation result.
For the risk zone A, alternative resource allocation decision is 2-4, corresponding total risk value is from 20 to 11, so risks can be minimized to 11 with the decision 4 in the risk zone A ( Table 11). The optimized decision scheme of zones B, C and D can be obtained with the same method (Table 12-14). Under 4 dangerous scenes, optimized allocation of limited resources is 4 in zone A, 4 in zone B, 2 in zone C and 2 in zone D, thus the total risk value is reduced to 97.
Corresponding risk value of zone A at the first stageof the resource allocation strategy u 1 min∑L 1  23  4  2  20+0  --20  3  20+0  16+0  -16  4  20+0  16+0  11+0  11 Note: x 1 is the corresponding amount of resource demand under each resource allocation decision at the first stage; min∑L 1 is the minimum risk value corresponding to different decisions at the first stage.

Case study -Optimal dispatching of emergency resources
In order to validate the dynamic optimization process of emergency resource scheduling of sudden public events with the Markov decision process, here the rationality and practicability of dynamic optimization method of emergency resource scheduling based on the Markov decision process is proved through analysis and explanation by examples.
Now it is supposed that an earthquake disaster takes place in a city, which is likely to cause two secondary disasters S 1 and S 2 , namely the state space of this earthquake disaster is 12 S { S, S}  . where, S 1 and S 2 represent the initial event S, namely secondary accidents are likely to be obtained from evolution of the earthquake disasters.
Then it is supposed that only one emergency resource R is required in emergency of this sudden public event, and the emergency time standard T is 2 time units. So long as enough amounts of emergency resources is transported to sudden public event sites within the standard time under the state of an event, then the sudden public event can be under control. If the amount of resource R transported to the scene of accident is insufficient, then the sudden public event can only be partially controlled (expressed as the availability of the emergency resources a), and the range of values of a is 0%~100%. It is also supposed that the relationship between the demand and the availability of the emergency resource R is shown in Table  It is supposed that 4 emergency resource sites around the sudden public events can cover this event site in 2 time units, as shown in Figure 7. As can be seen from the Figure 7, only the site A is in 1 time unit, while the site B is in the space of 1.5 time units, and both the site C and site D are in 2 time units. The amount of stored emergency resources at each site is also shown in the Figure 7.
Now it is stipulated that the emergency satisfaction is defined as the emergency success. Under the circumstances, the emergency resource site A is closest to the scene of accident X, therefore it is necessary to choose the site A, so as to satisfy the shortest emergency time.
When the accident is under the state of S 1 , 80 units of emergency resource R are transported from the emergency resource site A to the event site X, so the availability of the resources is only 80% under the state of S 1 , which is unable to completely satisfy the emergency demand. Under the circumstances, it is necessary to be supported by the sites B, C and D. When the sudden public event is under the state of S 1 , 40 units of emergency resources can be transported from the emergency resource sites B, C and D to the site X, so that the total www.intechopen.com accumulated amount achieves 120 units, and the amount of resources achieves the availability of 100%; but it is necessary to transport 120 units of resources from the sites B, C and D to the site X under the state of S 2 , so that the total accumulated amount achieves 200 units, and the availability achieves 100%. Therefore, the state space in this example is 12 S { S, S}  , the decision space can be expressed as the scheduling scheme, and the reward can be expressed as the cost or scheduling duration, as shown in Table 16. The state transition probability of sudden public events can be obtained using the Domino effect analysis method, as shown in Table 17. This process is complex, so it is unnecessary to go into details in this section.  The solution process is as follows: There are two states in this case, and two decisions under each state, namely the scheduling schemes. 1 (1) u represents selecting the scheduling scheme I when the event is under the state of S 1 ; 2 (1) u represents selecting the scheduling scheme II when the event is under the state of S 2 ; 1 (2) u represents selecting the scheduling scheme III when the event is under the state of S 2 ; 2 (2) u represents selecting the scheduling scheme IV when the event is under the state of q8 . 6  , 2 2 q4 . 5  .
In the first step, select the initial strategy 0  ; let f0  is obtained through solving the equations set.
The third step is the strategy improvement program, in which the improvement strategy 1  is obtained.
www.intechopen.com f0  is obtained through solving the equations set.
In the fifth step, seek the improvement strategy 2  .
For the state S 1 , there is (2) u  is obtained, which is exactly the same as the previous iteration results, so the optimized strategy is obtained as 1  . That is, take the scheduling scheme I when the sudden event is under the state of S 1 , and take the scheduling scheme IV when the sudden event is under the state of S 2 . www.intechopen.com

Conclusion and future researches
When we design an emergency rescue system, we need to coordinate the manpower with the financial, material resources. It is a complicated process to optimally allocate various elements within a system. It involves a wide range of contents. Repeated researches should be made on several theories and methods. Designing of an emergency rescue system covers the following four aspects which have been cross-linked each other essentially, that are 1) Demand Forecasting of Emergency Resources;2) Optimal Site Selection for the Base Station of Emergency Resources;3) Appropriate Allocation of Emergency Resources;4) Optimal Dispatching of Emergency Resources. Here, it proposed the overall and detailed methods to fulfill these four aspects.
In the future it is necessary to develop a computer system, so that these methods can adapt to the dynamic optimization process of emergency resource scheduling scheme under complex conditions such as many times of derivation and many kinds of resources etc., and it can more greatly satisfy the actual need.