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 ò ò Background and literature review ò ò Characteristics of production scheduling problem ò ò Optimisation algorithms ò ò Genetic Algorithms(GAs) applied to production scheduling ò ò Experimental Program ò ò Results ò ò Discussions and conclusions

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

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

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

Literature review

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

Product structure from company

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

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

Production Scheduling with multiple levels of product structure

Example of Gantt Chart

Fitness function Minimise :  P e (E c +E p ) +  P t (T p ) Where E c = max (0, D c - F c ) E p = man (0, D p - F p ) T p = max (0, F p - D p )

Genetic Algorithms

Crossover Operation

Mutation Operation

Demonstration of Genetic Algorithm Program ò Genetic Algorithms for scheduling problems was written by using Tcl/Tk programming language. ò 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 ò ò When the problem size increases the execution times increase exponentially. ò ò Next step is to break “large” problems down into smaller independent problems that can be solved in a “reasonable” amount of time. ò ò The solutions to the small problems will be integrated to give an overall solution.

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

Further Research ò ò Bicriteria scheduling problems. ò ò Multiple criteria scheduling problems.

Any questions please ?