Emergency Material Dispatching Model Based on Particle Swarm Optimization

赵伟川2010.5.29

2

Outline

• Introduction• Literature Review• Model Formulations• PSO-Based Solution Algorithm• Numerical Analysis• Conclusions

3

Introduction

• The emergency material dispatching problem is a complicated process.

• It involves many factors: objective selection way of transportation transportation routing selection and so on.

4

Literature Review 1

author Literature review

Kemball C. and Stephenson (1984)

pointed out that material logistics management is vital to raise transportation effectiveness in emergency material dispatching.

Ray J. (1987)Eldessouki W.M. (1998)

research the emergency material transportation problem considering the minimum transportation costs as objective.

Merkle D., Middendorf M. and Schmeck H. (2002)

state the resource-constrained scheduling problem is a problem about how to schedule the activities of scheduling between the resource requirements and the resource capacity limit

Groothedde B. et al. (2005)

states collaborative intermodal hub networks are able to reduce logistics costs and maintain logistic serve level

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Literature Review 2author Literature review

Wei Y. (2007) study the FLP and VRP problems in emergency logistics, and the collaborative relationship between the emergency material dispatching and evacuation

Sun Y., Chi H. and Jia C.L. (2007)

analyze the logical resource dispatching mechanism considering the demand of emergency sites and the happening probability of potential emergency sites, using a nonlinear mixed-integer programming model

Weiqin Tang, Zhang M. and Zhang Y. (2009)

analyze the characteristics of material dispatching in large-scale emergencies, design the process model.

Song X.Y., Liu F. and Chang C.G. (2010)

establish a generalized rough set based multi-object scheduling model for emergency disaster-relief commodity scheduling

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Literature Review 3author Literature review

Jalilvand, K. and Shabaninia (2005)

use branch-and-bound method solving a scheduling problem.

Pan Y., Yu J. and Da Q.L. (2007)

establish a multi-objective emergency-resource scheduling model based on the continuous consumption emergency system, and solve this model using PSO

Lin H. and Xu W.S.(2008)

use ideal point method to convert a multi-objective material scheduling model to a single-objective model; then use discrete PSO to resolve the model

Sheu J.B.(2007) (2010)

studies emergency logistics distribution based on relief- demand, establish a dynamic relief-demand management model for emergency logistics operations under imperfect information conditions in large-scale natural disasters

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Model Formulationsscene

• Take continuous consumption of material as background

• m disaster areas:• n emergency material warehouses:• How to dispatch the material from the n

warehouses to make the emergency costs smallest .

mAAA ,,, 21

nWWW ,, 21

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Assumptions

Assumptions (1)We only consider one cycle of the material dispatching during the whole rescue process;

(2)On a practical side, we consider the cost element of dispatching and loss of lacking material as the objective and ignore other factors;

(3)In order to simply the model, suppose the times of transporting material to from every warehouse are equal.

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Notations 1• vj(t):material consume speech in Aj at time t

• Qij: maximum supply quantity of material from Wi to Aj

• T: the whole time of rescuing cycle• rj(t): requirement in Aj at time t

• Tj: transport time of material to Aj

• Ij(t):shortage quantity of material in Aj at time t

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Notations 2• Cij: unit cost of material dispatched from Wi to

Aj

• αj:unit loss cost of lacking material in Aj

• Bj(Ij(t)):the loss cost of material lacked quantity Ij(t) in Aj

• xij: quantity of material dispatched from Wi to Aj

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Mathematical Model 1

• Requirement

• TC :the total emergency cost

t

jjj Ttmjdssvrtr0

0,,,2,1,)()0()(

m

jjj

n

i

m

jjiij tIBxcTC

11 1

))((min

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Mathematical Model 2

• Subject to:

mjTtTxr

mjTtr

tIj

n

iijj

jj

j,,2,1,,

,,2,1,0,

)(

1

)())(( tItIB jjjj

mjniQx ijij ,,2,1,,,2,1,0

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PSO-Based Solution Algorithm

• PSO is a population based on stochastic optimization technique developed by Kennedy and Eberhart in 1995. PSO is an optimized search method on account of swarm intelligence produced by cooperation and competition among swarms in colony.

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Steps of PSO• Step 1: set the scope of the partial swarm; preset the

accuracy of solutions and the max iteration time;• Step 2: generate the initial partial swarm random based on

the constraints ,let t=1;• Step 3: calculate the fitness of each partial according to the

objective function;• Step 4: compare the current fitness value of the partial with

the local optimal value and the globally optimal value , and update and ;

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Steps of PSO• Step 5: according to the functions below, update the moving

speed and position of partial i;

• Step 6: judge if the optimal solution reaches the accuracy error or the iteration time reaches the max time, if yes, stop, and output the result; else , t=t+1 , turn to step 3.

))()((

))()(()()1(

22

11

tXtGbestrc

tXtPbestrctvtv

iit

iit

ii

)1()()1( tvtXtX iii

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Numerical AnalysisThe information of Aj

A1 A2 A3

Tj 6 5 8

vj(t) 1 2 1.5

rj(0) 232 324 523

αj 1 3 1

The maximum supply quantity Qij of material from Wi to Aj

W1 42 53 64

W2 35 33 45

W3 96 46 23

W4 24 57 53

W5 32 20 36

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Numerical Analysis

the unit cost Cij of the material transported from Wi to Aj

W1 2 5 2

W2 3 2 4

W3 2 1 9

W4 4 6 3

W5 3 4 4

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Numerical Analysis

• ω=0.5,c1=1.3,c2=1.1

• Through 50 iterative operations, we obtain the optimal solution:

xij W1 W2 W3 W4 W5

A1 42 35 30.7 13 10

A2 15 33 46 16 18

A3 7 5 15 20 20

TC 2338

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Numerical Analysis

0 5 10 15 20 25 30 35 40 45 502300

2350

2400

2450

2500

2550

2600

Iteration times

Fitness v

alu

e

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Conclusions

• In our study, a multi-regional emergency material dispatching problem with multi-reserve spots on continuous consumption of emergency material resource is considered, and a nonlinear programming model is developed for this problem.

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References• Kemball-Cook D, Stephenson R.: Lesson in logistics from Somalia. J.

Disaster. 8, 57--66(1984)• Eldessouki W.M.: Some development in transportation network analysis

and design with application to emergency management problem. Partial: North Carolina State University (1998)

• Merkle D. Middendorf M. Schmeck H.: Ant colony optimization for resource-constrained project scheduling. J. IEEE transactions on Evol.Comput. 4, 333-346(2002)

• Groothedde B., Ruijgrok C., Tavasszy L.: Towards collaborative intermodal hub networks a case study in the fast moving consumer goods market. J. Transportation Research Part E: Logistics Transportation Review. 6, 56--583(2005)

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• Wei Y., Özdamar L.: A dynamic logistics coordination model for evacuation and support in disaster response activities. J. European Journal of Operational Research. 3, 1177-1193(2007)

• Wei Y., Kumar A.: Ant colony optimization for disaster relief operations. J. Transportation Research Part E: Logistics Transportation Review. 6, 660--672(2007)

• Sun Y., Chi H., Jia Ch.L.: Nonlinear Mixed-integer Programming Model for Emergency Resource Dispatching With Multi-path. J. Operations Research and Management Science. 5, 5--8(2007)(in Chinese)

• Tang W.Q., Zhang M., Zhang Y.: Process model for materials dispatching in large-scale emergencies. J. China Safety Science Journal. 1, 33--37(2009)(in Chinese)

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• Song X.Y., Liu F., Chang Ch.G.: A disaster-relief commodity transport schedule model based on generalized rough sets. J. Control Engineering of China. 1, 120--122(2010)(in Chinese)

• Jalilvand A., Khanmohammadi S., Shabaninia F.: Scheduling of sequence-dependant jobs on parallel multiprocessor systems using a branch and bound based Petri net. J. Emerging technologies, Proceedings of the IEEE symposium. PP. 334-339(2005)

• Pan Y., Yu J., Da Q.L.: Emergency resources scheduling on continuous consumption system based on particle swarm optimization. Journal of Systems Engineering. 5, 556—560(2007)(in Chinese)

• Lin H., Xu W.S.: Research of emergency materials’ scheduling solved by binary PSO. J. Computer Knowledge and Technology. 7, 1503--1505, 1511(2008) (in Chinese)

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• Sheu J.B.: An emergency logistics distribution approach for quick response to urgent relief demand in disasters. J. Transportation Research Part E: Logistics Transportation Review. 6, 687--709(2007)

• Sheu J.B.: Dynamic relief-demand management for emergency logistics operations under large-scale disasters. J. Transportation Research Part E: Logistics Transportation Review. 1, 1--17(2010)

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