978-1-4244-7330-4/10/$26.00 ©2010 IEEE 1532

Study on Multi-destination Emergency Scheduling Model under Dynamic Continuous Consumption

Chang Chunguang1,Chen Dongwen1,Wang Lijie2, Kong Fanwen 1 1. School of Management, Shenyang Jianzhu University, Shenyang 110168

E-mail: ccg7788@sohu.com

2. Product Innovation Support Center, China United Network Communications Corporation Limited Liaoning Branch, Shenyang 110016, China E-mail: ccg777@sohu.com

Abstract: With the purpose to enhance efficiency and accurate of emergency dispatch, realize reasonable distribution material quantity, reduce life and property loss caused by paroxysmal emergency events, a dynamic continuous consumption emergency scheduling model is established. Some features of emergency scheduling goals are analyzed. The objective function includes minimizing earliest emergency start time and the least disaster relief participated places. Simultaneously, satisfactory degree of disaster area is also considered in the objective function. Two main categories of constraints, namely, continuous consumption, supply and demand quantity are considered. GA is employed to solve the model, and the basic implement step of GA is given in detail. To employ GA easily, the constraints are disposed with penalty function idea so that they are introduced to the fitness value. To validate the validity of GA, the multi disaster places emergency scheduling problem for dynamic and continuous consumption is abstracted. The experiment shows that by multi running, GA can get multi efficient typical solutions so as to provide significant support for decision-making of emergency scheduling. The global search capacity of GA is strong, and it is suitable to solve complex optimization problems such as emergency scheduling problem under dynamic and continuous consumption condition. Key Words: Emergent Events, Multi-destination, Scheduling, Optimization Model

I. INTRODUCTION

Emergency schedule is an important logistics scheduling type to reduce the social influence when the emergency incidents happen. With the development of society, the social problem become more and more obvious day after day, the correlation of some things are higher. Thus, the happening frequency, dimension and the kinds of the emergent incidents become bigger. The emergent incidents appear multi disaster place trend, namely, in a short time even almost the same time, the incident happens in several different places. In recent years, the happening frequently of incidents in our country such as the May 12th earthquake can be the typical multi disaster places emergent incidents. So rely on the advanced technology and method of emergency management to enhance the city emergency management efficiency and horizontal is the guaranty of the social development. Emergency scheduling is the key technology and the most important part of emergency management, it builds close links to the life and property of the human, and the stabilization of our society. There has been a large amount of research work in home and abroad on emergency scheduling. A smallest cost or largest amount logistics scheduling model is put forward in [1]. An emergency scheduling model with the objective of minimizing the task completed time is studied in [2]. A multi-destination emergency scheduling model after earthquake disasters is established in [3]. Considering the potential incidents happening possibility, an optimization model which takes the shortest time as the goal is given out in [4]. A model taking least disaster relief

The work is supported by the National Key Technology R&D Program under Grant 2006BAJ06B08-03, Humanities and Social Sciences Project from Ministry of Education of the People’s Republic of China under Grant 2009-340.

participated places within limited time as the objective is used, and the corresponding solving algorithm is given out in [5]. Selection of optimal scheme for multi-depot emergency systems is studied in [6]. In [7], the particle swarm algorithm is employed to solve the multi-objective model, the smallest cost is taken as objective, and the cost includes not only the cost but also the loss due to be not in time emergency response. A multi-mode resource constrained project scheduling problem based on genetic algorithm is studied in [8]. Today, most research on emergency scheduling are static and one emergent incidents place in optimal resources schedule or the shortest emergency response time. Resource optimization is to cause the limited resources be used efficiently. Shortest emergency response time means to make emergency scheduling in time. So far, research on emergency scheduling model which are dynamic and continuous consumption, multi-destination, multi-objective is still quite rarely.

II. PROBLEM DESCRIPTION On the basis of continuous consumption, the earliest emergency start time and least disaster relief participated places emergency scheduling model is established, and cost is not considered. Multi disaster places and demands of the disaster places are known, the initial status of the whole system is known. Suppose A1, A2,……,Am are m emergency suppliers, B1, B2,……,Bn are n emergency disaster places, si is the quantity of the emergency supplier place Ai (the amount can be scheduled), dj is the demand quantity of the disaster place Bj , the quantity xij is the scheduled resources from Ai to Bj.

A. The Objective of the Model

(1)Non-cost and least disaster relief participated places

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Emergent incidents happened emergently must be controlled in time. According the characteristic of emergency, the schedule cost at the beginning of the incident during the emergent management is not considered. At the beginning of the incident, the later emergency response time is, the bigger destroy by the incident will appear. So the earliest emergency start time is one of the most important factors in emergency management. Thus, in objectives, the earliest emergency start time and the least disaster relief participated places are both should be considered. We describe the objective functions as follows.

'1

1Min (M in )

n

ijj

Z t=

= ∑ (1)

2Min Z g= (2) Suppose that tij is the time from the supply place Ai to the demand place Bj, t’ij is the time from the supply place A’i to the demand place B’j, t’1j<t’2j<……<t’mj is turn of tij from smallest to biggest. Formula (1) denotes to minimize the earliest start time from A’ to Bj. In formula (2), g is the amount of supply places during the emergency scheduling process. (2) Un-equality emergency disaster places When multi disaster places incident happens, the damage scale and degree are different among varied disaster places. The scope and population of varied disaster places are different too, thus, the important degrees for varied disaster places are different. Thus, the important degrees for varied disaster places should be considered. Use the coefficient iλ to measure the different important degrees among the different disaster places. If the places are more important, iλ is smaller. 1ϕ and 2ϕ are the coefficients of the objective, based on above discussed, the objective function can be adapted as follows.

'1 i 2

1(min )

n

ijj

MinZ t gϕ λ ϕ=

= +∑ (3)

(3)Satisfactory degree of resource supply During the process of emergent management, dj is the lowest demand in disaster place Bj. The supply quantity should be reach some standard value, larger quantity does not means

better solution,1

/m

ij j ji

x d β=

=∑ is the coefficient of the

satisfactory of the resource supplies. When the supply and the demand have the proportion of α , demand have the optimal supply. So have the objective function:

'1 2

1

| |(min )

nj

i ijj

MinZ t gβ α

ϕ λ ϕα=

−= +∑ (4)

B. Constraints Description

(1)Supply and demand The model must subject to the basic supply and demand constraints.

s.t.1

, 1, 2,n

ij ij

x s i m=

≤ =∑ (5)

1, 1, 2,

m

ij ji

x d j n=

≥ =∑ (6)

During the emergency scheduling process, formula (5) means that all disaster places get the resource from every disaster relief participated places must be smaller than the inventory quantity. Formula (6) means that the sum of the resource from every disaster relief participated places must be more than the demand quantities of every disaster places. (2)Continuous consumption Continuous consumption means that once the emergency rescue begins, the resource consumption must be continuous. Sometimes, once the rescue is interrupt, what we have done at the earlier stage will lost, and we have do everything from the beginning even made the condition much more terrible. So the consumption must be continuous. We have the restrictions of (7), vj is the consumption speed of Bj: ;,2,1 mi = x’ij is

the corresponding emergency resource quantity to t’ij, 0' jx is

the initial resource quantity of disaster place:

1,1

( ' ' ) 0m

i j j iji

x v t−=

− >∑ ， =1 2j n，…… (7)

III. GENETIC ALGORITHM DESIGN GA was firstly put forward by Holland. It is based on the biology evolution theory and genetics, and it is a self-adaptive global optimization probability search algorithm which imitates biology evolutional process and shows strong robust. It start from a group of potential solutions, In population, chromosomes selection, crossover and mutation give rise to a new population, use the fitness to measure the individual, evolution by population.

A. Encoding System

The encoding of GA is a process to change a feasible solution of a problem to a search space can be handled by GA. The population evolve at the basis of encoding, the selection, crossover and mutation operator are also based on encoding system. The encoding system will support searching high fitness individual, and finally finding the optimum solution or approximately optimum solution. There are two important principles during encoding, namely, building block encoding principle and minimal character set principle. According to the first principle, the encoding scheme by which related problem is easily to be generated, the encoding scheme is low rank and short definition length mode; according to the second principle, the problem should be represented or described naturally, and the encoding scheme with minimal encoding character set should be selected.

B. Fitness Evaluation

In GA, the population evolves according to individual fitness iteration so as to obtain optimum solution or approximate optimum solution. By certain decoding mode, the individual encoding cluster is disposed so that the individual manifestative form is obtained. The value of objective function can be

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calculated by the individual manifestative form, then, the value of the objective function can be transformed to individual fitness by certain rules according to the problem optimization condition. The higher the fitness is, the larger the genetic probability for next generation is. For GA, the design of fitness will influence the performance of algorithm. For constraints, the penalty function method is employed. For the individual which is not feasible solution within solution space, the penalty factor function is set when calculating fitness, thus, its fitness will be reduced so that its genetic probability to the next generation is reduced. Considering that the objective function is minimization one, the fitness F and objective function value Z can be transformed as follows:

{ max,

0,

C ZF

else

−=

constraint(5),(6) and (7) are all met (8)

C. Genetic Operators

Some operators including selection operator, crossover operator, mutation operator are employed to implement population evolution. Natural selection of population of population is implemented by selection operator. The individual with high fitness will be genetically transmitted to the next generation with high probability. By crossover operator and mutation operator, the diversity of population can be assured. By crossover operator, it is implemented that the individual with high fitness will be genetically transmitted to the next generation with high probability. However, new individual can not be generated so that the search process will run into the local optimal search. By employing crossover operator and mutation operator, the diversity can be assured, simultaneously, the probability of running into local optimization is reduced. However, the values of crossover rate and mutation rate should be determined according practical application, it the value of crossover is too large, the individuals with high fitness will be destroyed, contrarily, if the value of crossover is too small, the search of optimization will become difficult. In the same way, if the value of mutation rate is too large, the algorithm will run into single random search process, contrarily, if it is too small, the diversity of population will be influenced.

D. Implement Steps of GA

To make clear the foundation parameter of population M, the highest evolution generation T, crossover rate Pc, mutation rate Pm, use GA to find optimal solution. To improve the complexity of calculation and enhance the efficiency, we use float-encoded, mechasim. The individual have attribute as xij, value, fitness, mount, respectively means the gene, function value, fitness and the amount of disaster relief participated places. xij is the quantity of source from disaster relief participated places i to disaster places j, generate the gene which is the random number among 0 and surplus of resource to be the supply from place Ai to Bj. Step1: Initiate. Set up the highest evolution generation T, population M, crossover rate and mutation rate Pc, Pm, Step2: Generate M individuals randomly as the initial population P(0); Step3: Evaluate the fitness of the individuals, judge whether the individual is better or not; Step4: Slection. According to the individual fitness, use proportional model to choose individual whether to retain to the new population. The rate of the old individual to be retained

is:1

/M

i i ii

p F F=

= ∑ ；

Step5: Crossover. According to the Pc, two individuals are crossover. With the purpose of reducing destruction of effective model, we choose one-point crossover; Step6: Mutation. Choose the gene of individual according to Pm to guaranty population diversity; Step7: Judge the termination. If t≤T, t→t+1 turn to step2, else t >T stop.

IV. RUNNING RESULT AND ANALYSIS

There are 11 disaster relief participated places A1, A2……A11，

three disaster places B1,B2……B3, demand of the disaster places dj are 6, 3 and 3. The coefficient iλ to measure the different disaster places are respectively 1, 1.4 and 1.2. The quantity of supply si, and the other detail listed in the table I and table II.

TABLEⅠ SUPPLY QUANTITY

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11

si 1 11 2 2 2 1 1 1 2 1 1

TABLE Ⅱ EMERGENCY REQUIRED TIME

tij A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11

B1 1.2 5 1 4 2.5 2.7 1 2.5 1 6 4

B2 2.5 4 3 5 1.5 3.6 0.2 1.5 2.5 8 3.5

B3 4 6 4 7 3 2.2 3.2 1 3.5 2.4 0.5

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In Microsoft Visual C++ 6.00, GA is compiled to solve the problem. As the parameter of the algorithms plays a key role in algorithm capability. A large quantity of experiment when population is among 50 ～ 500, and the highest evolution generation among 100～300, crossover rate is 0.4～0.99, mutation rate 0.0001～0.1 is carried on. Then, a group of approximately optimal solutions are obtained as follows. {(06000000200),(01101010000),(00001101001)}, {(05000000100),(00201000100),(01001100001)}, {(06000000100),(020100010000),(01101001000)}, {(06000000000),(00001010200),(01100101001)}. The amount of disaster relief participated places and the satisfactory of the resource supplies and so on are considered, some quality factors are hardly changed into quantity factors. Under real environment, a group of typical solutions can be obtained by GA. We can choose the optimum solution among them according to practical condition.

V. CONCLUSION Emergency scheduling is one the most important cycles of emergency management. The characteristic of emergency incidents made the emergency scheduling are different from commercial scheduling, namely, it will not consider the cost as the objective. Multi-disaster places emergency incident happened frequently during recent years, research on emergency scheduling in which several disaster places need to be rescued is an important theory and practical problem. When emergent incidents happen, the model for multi-destination emergency scheduling model under dynamic continuous

consumption is established in this paper, and it will benefit for the emergency scheduling work within limited time. By GA, the above can be solved effectively, and several typical effective solutions can be obtained.

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