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Scheduling Stochastic Jobs on a Single Machine to Minimize Weighted Number of Tardy Jobs

Auther : H. M. SOROUSH

ABSTRACT
An important scheduling problem in manufacturing and service organizations is the on-time deliveries of products and services. This paper addresses a single machine scheduling problem wherein processing times or due-dates are random variables and fixed weights (penalties) are imposed on late jobs. The objective is to derive the schedule that minimizes the expected weighted number of tardy jobs. The problem is NP-hard; however, we prove that, under some agreeable conditions, special cases of various problem scenarios are solvable optimally in polynomial time. We also introduce heuristic methods for the general cases of these scenarios. Our computational results demonstrate that the heuristics perform well in providing either the optimal sequence or a near optimal solution. The illustrative examples and computational results also show that the stochasticity of processing times or due-dates can affect scheduling decisions. In addition, special cases of the problem reduce to some new stochastic and some existing single machine models.
Keywords: Scheduling; single machine; stochastic; number of tardy jobs
 

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