Scheduling Complex Products using Genetic Algorithms with Alternative Fitness Functions

1. Scheduling Complex Productsusing Genetic Algorithmswith Alternative Fitness Functions P. Pongcharoen, C. Hicks, P.M. Braiden and D.J. Stewardson. University of Newcastle upon Tyne Slides: http://www.staff.ncl.ac.uk/chris.hicks

2. Scheduling • “The allocation of resources over time to perform a collection of tasks” (Baker 1974) • “Scheduling problems in their static and deterministic forms are extremely simple to describe and formulate, but are difficult to solve” (King and Spakis 1980)

3. Scheduling Problems • Involve complex combinatorial optimisation • For n jobs on m machines there are potentially (n!)msequences, e.g. n=5 m=3 => 1.7 million sequences. • Most problems can only be solved by inefficient non-deterministic polynomial (NP) algorithms. • Even a computer can take large amounts of time to solve only moderately large problems

4. Production Scheduling of Capital Goods • Deep and complex product structures • Long routings with many types of operations on multiple machines • Multiple constraints such as assembly, operation precedence and resource constraints.

5. Product Structure 2 Products, 118 machining, 17 assembly operations and 17 machines

6. Kinds of Due Dates • External due date is quoted to the customer by the company and should be achieved with high probability. • Internal due date, which may include contingency, is used to design the production plan to meet the external due date. • Component due date.

8. Conventional Optimisation Algorithms • Integer Linear Programming • Dynamic Programming • Branch and Bound These methods rely on enumerative search and are therefore only suitable for small problems

9. More Recent Approaches • Simulated Annealing • Taboo Search • Genetic Algorithms Characteristics : • Stochastic search. • Suitable for combinatorial optimisation problems. • Due to combinatorial explosion, they may not search the whole problem space. Thus, an optimal solution is not guaranteed.

10. GA developed for production scheduling

11. Chromosome representation

12. Example problem Component Product 1st Operation Assembly Time

13. Resource profile Resource overload

14. New schedule from GA

15. Resource profile of new schedule

16. Crossover Operations

17. Mutation Operations

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

19. An Example of Production Plan

20. Industrial Scheduling Problems

21. Factors Considered by Pongcharoen et al. (1999, 2000a, 2000b, 2000c)

22. Penalty Cost (£) of the Best Schedule Obtained by Pongcharoen et al. (1999, 2000a, 2000b, 2000c)

23. Appropriate GA Configuration (Pongcharoen et al. 1999, 2000a, 2000b, 2000c)

24. Experimental Factors

25. Analysis of Variance

26. Interaction Diagram for FF and P/G

27. Interaction Diagram for FF and MOP

28. Conclusion • BCGA scheduling tool was developed for scheduling complex products. • The schedules produced are dependent upon the fitness function used. • The appropriate GA configuration is case specific. Independent fitness function : high population and low generations Dependent fitness function : low population and high generations

29. Any questionsPlease