A probabilistic model toward a permutation flowshop scheduling problem with imperfect jobs

Abstract

This article addresses a permutation flowshop scheduling problem with rework activities. The concept of a reworkable job here means that a job on a machine may need more than one operation to reach a predefined quality level, stochastically. Therefore in this configuration, processing times become random variables with a known probability distribution. The objective function is the minimization of the expected makespan. The solution mechanism is based on using mathematical expectations of processing times in order to find a job sequence by solving a mixed integer mathematical model, then assessing the makespan of the obtained sequence by running several simulated trials and reporting the mean value. In other words, a flowshop scheduling problem with stochastic processing times on machines is considered in this article, and the solution approach merges a mixed integer programming model and simulation. Finally a comprehensive, randomly generated example is presented for verifying the proposed problem. According to the results, the existence of reworkable jobs in a flowshop scheduling problem can change the optimum job sequence when minimization of the makespan is assumed.

Keywords::

• permutation flowshop scheduling problem
• rework
• makespan

Keywords::

• C16
• C44
• C61
• C63
• M11

Disclosure statement

No potential conflict of interest was reported by the authors.