Sensitivity analysis of a fuzzy multiobjective scheduling problem

Abstract

This paper concerns sensitivity analysis of a class of complex job shop scheduling problems which are characterized by: (1) a large number of jobs and machines, (2) uncertain jobs processing times, and (3) multiple measures of schedule performance including average weighted tardiness, the number of tardy jobs, the total setup times, the total idle time of machines, and the total flow times of jobs. The base schedule is generated by applying a new fuzzy multiobjective genetic algorithm which takes into consideration batching of the jobs of a similar type, jobs’ lots sizing and load balancing of the machines. The aim of the proposed sensitivity analysis of a generated schedule is to investigate the consequences of prolongations of job processing times on the measures of schedule performance. The processing times are described by triangular fuzzy numbers and their prolongation is done by expanding the supports of fuzzy numbers. The sensitivity analysis is performed through a series of numerical experiments. The effects of prolongations of job processing times on the measures of performance of a generated schedule are recorded and analysed. It is shown that the sensitivity analysis is among the primaries in evaluating the quality of a generated schedule. The sensitivity analysis is used in identifying the critical jobs and the critical machines which have the properties that the prolongations of their processing times produce the largest deteriorations of the performance measures and the overall quality of a generated schedule.

Keywords:

• Sensitivity analysis
• Production scheduling
• Job shop scheduling
• Fuzzy sets
• Multiobjective decision making
• Genetic algorithm

Acknowledgments

The authors would like to thank the Engineering and Physics Sciences Research Council (EPSRC), UK, for supporting this research (Grant Nos. GR/R95319/01 and GR/R95326/01). We would also like to acknowledge the support of our industrial collaborator Sherwood Press Ltd, Nottingham.