© P. Pongcharoen CCSI/1 Scheduling Complex Products using Genetic Algorithms with Alternative Fitness Functions P. Pongcharoen, C. Hicks, P.M. Braiden and D.J. Stewardson. University of Newcastle upon Tyne Slides:

© P. Pongcharoen CCSI/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)

© P. Pongcharoen CCSI/3 Scheduling Problems Involve complex combinatorial optimisation For n jobs on m machines there are potentially (n!) m sequences, 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

© P. Pongcharoen CCSI/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.

© P. Pongcharoen CCSI/5 Product Structure 2 Products, 118 machining, 17 assembly operations and 17 machines

© P. Pongcharoen CCSI/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.

© P. Pongcharoen CCSI/7

© P. Pongcharoen CCSI/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

© P. Pongcharoen CCSI/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.

© P. Pongcharoen CCSI/10 GA developed for production scheduling

© P. Pongcharoen CCSI/11 Chromosome representation

© P. Pongcharoen CCSI/12 Example problem Product 1 st Operation Assembly Component Time

© P. Pongcharoen CCSI/13 Resource profile Resource overload

© P. Pongcharoen CCSI/14 New schedule from GA

© P. Pongcharoen CCSI/15 Resource profile of new schedule

© P. Pongcharoen CCSI/16 Crossover Operations

© P. Pongcharoen CCSI/17 Mutation Operations

© P. Pongcharoen CCSI/18 Fitness function Minimise :  P e (E c +E p ) +  P t (T p ) Where E c = max (0, D c - F c ) E p = max (0, D p - F p ) T p = max (0, F p - D p )

© P. Pongcharoen CCSI/19 An Example of Production Plan

© P. Pongcharoen CCSI/20 Industrial Scheduling Problems

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

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

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

© P. Pongcharoen CCSI/24 Experimental Factors

© P. Pongcharoen CCSI/25 Analysis of Variance

© P. Pongcharoen CCSI/26 Interaction Diagram for FF and P/G

© P. Pongcharoen CCSI/27 Interaction Diagram for FF and MOP

© P. Pongcharoen CCSI/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

© P. Pongcharoen CCSI/29 Any questions Please