Parallel Identical Machines Scheduling to Minimize the Maximum Inter-completion Time with Uncertain Processing Time

Abstract

Motivated by parallel machines scheduling in practice that receive unplanned urgent job under uncertain environment, and it usually requires a response as soon as possible since its high-priority. This paper considers the response time to urgent job in a worst-case as an evaluation indicator. To the best of our knowledge, this paper is the first to study a parallel identical machine scheduling problem, which is to minimize the largest waiting time of an urgent job with the uncertain processing time of regular jobs. The objective of this problem is depicted to minimize the inter-completion time, that is, the maximum difference of the completion times between any two consecutively completed jobs. We first establish a stochastic programming model, and propose a scenario-reduction based sample average approximation method to solve this uncertain problem.