A probabilistic approach to the Stochastic Job-Shop Scheduling problem

Uncertainty exists in almost any manufacturing process, and its effect may be detrimental to the manufacturing outcomes. In the Stochastic Job Shop Scheduling Problem (SJSSP), some of the process parameters are random variables, in particular the processing time. This paper considers another facet of the SJSSP, which is the probability for success (or failure) of a manufacturing job and its effect on other jobs. The paper presents a mathematical model for determining the expected manufacturing cost, and proposes heuristics for reducing that cost. The fundamental model is based on a single resource (e.g. a single machine) and a set of manufacturing jobs, each characterized by a cost and a probabilistic distribution for success. A failure causes either a re-work of the failed job, or restarting the entire process from the first job. Since the problem is NH Hard, a set of heuristics for scheduling the jobs is proposed, and simulation results validate these heuristics.