Modified Johnson rule for two-stage flowshop scheduling with random breakdowns

Abstract

The two-stage flowshop assembly scheduling problem where there are m machines at the first stage and an assembly machine at the second stage is considered in this paper. In several real world service and production systems, there is more than one parallel machine at stage one and an assembly machine to assemble job components at stage two. The machines at stage one will be subjected to unsystematic breakdowns. The jobs order sequence into the flowshop will be based on three jobs ranking rules, Johnson rule, and two modified Johnson rule, namely Johnson largest rule and Johnson smallest rule. A simulation model of the two-machine flowshop then will be constructed in which both machines at stage one are subject to random failures. Three simulation experiments will be conducted to examine the effect of the job ranking rules on the makespan. The result showed that Johnson largest ranking rule gave the minimum makespan over the others.