A robust modelling and optimisation framework for a batch processing flow shop production system in the presence of uncertainties

Abstract

This research aims to adopt two robust optimisation approaches for a real-world flow shop manufacturing system with batch processing machines, where the processing time and size of job are non-deterministic and uncertain. Each machine can process multiple jobs simultaneously as long as the machine capacity is not exceeded. Two important decisions are required: (1) grouping jobs into batches and (2) scheduling the established batches on machines. A mathematical optimisation model is presented, and then two famous robust optimisation approaches are adopted for the purpose of converting the deterministic model to the robust one. An efficient particle swarm optimisation (PSO) algorithm is developed to solve the problem in a reasonable time. In order to verify the developed model and evaluate the performance of our proposed algorithm, a set of small to large test problems are generated, and a simulation approach and a commercial optimisation solver are used to solve these problems. Analysis of the implementation of two independent robust optimisation methods is performed by the paired t-test on all of the test problems. Furthermore, the Taguchi method, as a statistical optimisation technique, is employed to investigate the appropriate level of PSO parameters.

Keywords:

• flow shop
• batch processing machine
• particle swarm optimisation
• robust optimisation
• Taguchi technique