Heuristics for the stochastic single-machine problem with E/T costs

Abstract

This paper addresses the problem of concurrent due-date assignment and sequencing of a set of jobs on a stochastic single-machine environment with distinct job earliness and tardiness penalty costs. It is assumed that the jobs processing times are statistically independent and follow a normal distribution whose mean and variance are provided. The objective is to determine the job sequence and the due dates which minimize the expected total earliness and tardiness costs. Previous theoretical results regarding normally distributed processing times and expected values of earliness and tardiness costs are reviewed. Two efficient insertion-based constructive heuristics with polynomial time complexity are proposed. It is shown that both heuristic solution methods include safety time and the obtained sequence remains the same regardless of disruptions, which means that the results are robust. A comparative study with known methods from the literature was conducted using a set of 1700 problems with up to 2000 jobs. The results indicated that the best performance was achieved by one of the developed heuristics. Furthermore, it was proven that the heuristics are asymptotically optimal. An extension of the problem with processing times modeled as lognormal random variables was also investigated and solved with good results.