By : Pupong Pongcharoen (Ph.D. Research Student) Supervisors : Prof. Paul Braiden

1. Genetic Algorithmsfor multiple resource constraintsProduction Scheduling with multiple levels of product structure By : Pupong Pongcharoen (Ph.D. Research Student) Supervisors : Prof. Paul Braiden Dr. Chris Hicks 26 April 1999 Dept. of MMME, University of Newcastle upon Tyne

2. Overview of this presentation • Background and literature review • Characteristics of production scheduling problem • Optimisation algorithms • Genetic Algorithms(GAs) applied to production scheduling • Experimental Program • Results • Discussions and conclusions

3. What is scheduling ? Baker(1974) “Scheduling problems in their simple static and deterministic forms are extremely simple to describe and formulate but difficult to solve” “The allocation of resources over time to perform a collection of tasks” King and Spackis(1980)

4. Scheduling problems n jobs & m machines = (n!)m possible solutions e.g. 20 x 10 problem => 7.2651x10183 solutions

5. Type of scheduling problems in literature • Job shop problem (JSP) different routing of jobs Þ machines • Flow shop problem (FSP) same routing of jobs Þ machines • Permutation scheduling problem (PSP) same job sequence Þ machines King and Spackis (1980)

6. Literature review

7. Conventionaloptimisation algorithms Example Branch & Bound, Integer Linear Programming and Dynamic Programming. works well with small problems slow can’t solve “big” problems Approximationoptimisation algorithms Example Dispatching rules, Simulated Annealing, Taboo Search and Genetic Algorithms. fast can be applied with big or small problems approximate “optimal” solutions. Optimisation algorithms Jain et.al. (1999)

8. Product structure from company

9. Type of scheduling environment • Machine environment ÞSingle or Multiplemachines • Product environment ÞSingle or Multipleproducts • Capacity planning ÞInfinite or Finiteresources constraints • Research methodology ÞAnalytical or Simulationmethodology

10. The objectives of this research • Apply Genetic Algorithms to complex capital goods production scheduling problems • Minimising penalty cost due to earliness and tardiness • Assume finite capacity • Using simulation methodology for testing plans

11. Production Scheduling with multiple levels of product structure

12. Example of Gantt Chart

13. Fitness function Minimise :å Pe(Ec+Ep) + å Pt(Tp) Where Ec = max (0, Dc - Fc) Ep = man (0, Dp - Fp) Tp = max (0, Fp - Dp)

14. Genetic Algorithms

15. Crossover Operation

16. Mutation Operation

17. Demonstration of Genetic Algorithm Program • Genetic Algorithms for scheduling problems was written by using Tcl/Tk programming language. • The program was runs on Unix system V release 4.0 on a Sun workstation.

18. Case study (data from Parsons)

19. Experimental program Full factorial experimental design was performed. Total number of runs = 3 x 2 x 2 x 4 x 5 = 240 (per replication)

20. Results from 240 runs on each problem sizes

21. Analysis of Variance

22. The best performance of GAs on the problems

23. Mean and standard deviation for each population

24. Discussions • When the problem size increases the execution times increase exponentially. • Next step is to break “large” problems down into smaller independent problems that can be solved in a “reasonable” amount of time. • The solutions to the small problems will be integrated to give an overall solution.

25. Conclusions • Genetic algorithms represents a powerful technique for solving scheduling problems. • Practical software produced for solving scheduling problems. • Solutions far better than original schedules obtained from Company • Appropriate levels for Genetic Algorithm parameters identified.

26. Further Research • Bicriteria scheduling problems. • Multiple criteria scheduling problems.

27. Any questions please ?