Emergency Material Dispatching Model Based on Particle Swarm Optimization

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Emergency Material Dispatching Model Based on
Particle Swarm Optimization

• ???
• 2010.5.29

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Outline

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

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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.

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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 2
author 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 3
author 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 Formulations

• scene
• 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 .

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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
• ajunit 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

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Mathematical Model 2

• Subject to

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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 t1
• 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 , tt1 , turn to step 3.

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Numerical Analysis
The information of Aj The information of Aj The information of Aj The information of Aj
A1 A2 A3
Tj 6 5 8
vj(t) 1 2 1.5
rj(0) 232 324 523
aj 1 3 1
The maximum supply quantity Qij of material from Wi to Aj The maximum supply quantity Qij of material from Wi to Aj The maximum supply quantity Qij of material from Wi to Aj 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 the unit cost Cij of the material transported from Wi to Aj the unit cost Cij of the material transported from Wi to Aj 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

• ?0.5,c11.3,c21.1
• 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 2338 2338 2338 2338
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Numerical Analysis
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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

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• Groothedde B., Ruijgrok C., Tavasszy L. Towards
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  J. Transportation Research Part E Logistics
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• Wei Y., Özdamar L. A dynamic logistics
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• Song X.Y., Liu F., Chang Ch.G. A disaster-relief
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• Sheu J.B. An emergency logistics distribution
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• Sheu J.B. Dynamic relief-demand management for
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Thank You!
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