Distributionally robust parallel machine ScheLoc problem under service level constraints

Abstract

Abstract Scheduling-Location (ScheLoc) problem is relatively new and has received a lot attention. Such a problem focuses on integrating the tactical-level decision (i.e., selecting locations for machines) and the operational-level decision (i.e., schedule of the jobs). Especially, the release time depends on the distance between the job storage location and its processing machine, as each job should be transported to the machine location for processing. The existing researches considering the ScheLoc problem are limited, and most of them focus on the deterministic settings. In practice, job processing times are usually uncertain, and the probability distribution of the uncertain processing times may not be exactly estimated, due to various factors. This work investigates a parallel machine ScheLoc problem under stochastic processing times with only partial distributional information (i.e., the mean and covariance matrix), to minimize the cost for operating machines and control the service level at the same time. The service level in this work is measured by the probability of ensuring no tardy job. For the problem, a distributionally robust formulation is first proposed, in which the service level is restricted with a joint chance constraint. By applying a popular approximation method, an approximated mixed integer second-order cone programming (MI-SOCP) model is then developed. A case study is conducted and reported, to illustrate the applicability of the MI-SOCP model.