1. IGLS/1 © P. Pongcharoen Using Genetic Algorithms for Scheduling the Production of Capital Goods P. Pongcharoen, C. Hicks, P.M. Braiden, A.V. Metcalfe, D.J. Stewardson University of Newcastle upon Tyne

2. IGLS/2 © P. Pongcharoen 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. IGLS/3 © P. Pongcharoen Scheduling Problems Involve complex combinatorial optimisation For n jobs on m machines there are potentially (n!) m sequences, e.g. n=10 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. IGLS/4 © P. Pongcharoen Scheduling the Production of Capital Goods Deep and complex product structures Long routings with many types of machine and process Multiple constraints such as assembly, precedence operation and resource constraints.

5. IGLS/5 © P. Pongcharoen 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

6. IGLS/6 © P. Pongcharoen 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.

7. IGLS/7 © P. Pongcharoen Melting substance Too fast cooling Heating up Slowly cooling Simulated Annealing Substance Equilibrium state with resulting crystal Out of equilibrium state with resulting defecting crystal

8. IGLS/8 © P. Pongcharoen Taboo Search

9. IGLS/9 © P. Pongcharoen Evaluation criteria Determination coefficient (R 2 ) Adjusted determination coefficient (R a 2 ) Mean square error (MS E ) Mallows statistic (C p )

10. IGLS/10 © P. Pongcharoen Conclusion (1) BGA has been developed for the scheduling of complex products with deep product structure and multiple resource constraints. Within a given execution time, large population (fewer generations) produced lower penalty costs and spread than small populations (many generations).

11. IGLS/11 © P. Pongcharoen Conclusion (2) BGA produced lower penalty costs than corresponding plans produced by using simulation.

12. IGLS/12 © P. Pongcharoen Any questions Please