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 optimization approaches for a real word 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 optimization model is presented, and then two famous robust optimization approaches are adopted for the purpose of convert deterministic model to robust one. An efficient particle swarm optimization (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 optimization solver is used to solve these problems. Analysis of the implementation of two independent robust optimization methods is performed by Paired t-test on all of test problems. Furthermore, Taguchi, as a statistical optimization technique, is employed to investigate the appropriate level of PSO parameters.