Dept. of MMME, University of Newcastle upon Tyne Genetic Algorithms for multiple resource constraints Production 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

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

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

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

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)

Literature review

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

Product structure from company

Type of scheduling environment Machine environment Þ Single or Multiple machines Product environment Þ Single or Multiple products Capacity planning Þ Infinite or Finite resources constraints Research methodology Þ Analytical or Simulation methodology

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

Production Scheduling with multiple levels of product structure

Example of Gantt Chart

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)

Genetic Algorithms

Crossover Operation

Mutation Operation

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.

Case study (data from Parsons)

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

Results from 240 runs on each problem sizes

Analysis of Variance

The best performance of GAs on the problems

Mean and standard deviation for each population

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.

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.

Further Research Bicriteria scheduling problems. Multiple criteria scheduling problems.

Any questions please ?