Flowshop Machine Scheduling: Markov Modeling, Optimal Schedules and Heuristics

Abstract

Flowshop machine scheduling has been of main interest in several applications where the timing of its processes plays a fundamental role in the utilization of system resources. Addressing the optimal sequencing of the jobs when equivalent failures across machines exist is a decision of particular relevance to the general scheduling problem. Such failures allow for unpredictable time consumption and improper utilization of the machines. Therefore, it is of particular relevance to address the problem with new modeling approaches considering the parallel and sequential components of the manufacturing process under equivalent failure in the jobs at each machine. In this paper, we propose a novel Markov chain to model the N/ M/P/F permutation flowshop. We analyze the time cost encountered due to M consecutive machine equivalent failures in processing N jobs. We derive new closed form expressions of the completion time under such setup. We extend the Markov model into its underlying components, providing another new Markov model with processes that dont encounter failures and compare both systems. We provide new insights on job ordering decision rules and new approaches in a set of proposed algorithms that provide novel optimal and heuristic methods that provides optimal or near optimal schedules. We derive closed form expressions that divide per machine CT and per machine processing and waiting times. Further, we provide a novel scheme that proves intimate connections between such time components and the maximum number of rounds per machine that allows optimal utilization of the machines in one CT.