Emergency Material Dispatching Model Based on Particle Swarm Optimization

1. 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

5. Literature Review 2

6. Literature Review 3

7. 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 .

8. Assumptions

9. Notations 1 • vj(t):material consume speech in Ajat 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

10. 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 Wito Aj

11. Mathematical Model 1 • Requirement • TC :the total emergency cost

12. Mathematical Model 2 • Subject to:

13. 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.

14. 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 ;

15. 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.

16. Numerical Analysis

17. Numerical Analysis

18. Numerical Analysis • ω=0.5,c1=1.3,c2=1.1 • Through 50 iterative operations, we obtain the optimal solution:

19. Numerical Analysis

20. 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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25. Thank You! http://log.seu.edu.cn 2014/10/10