A new and general stochastic parallel machine ScheLoc problem with limited location capacity and customer credit risk

Abstract

Scheduling-Location (ScheLoc) problem considering machine location and job scheduling simultaneously is a relatively new and hot topic. The existing works assume that only one machine can be placed at a location, which may not be suitable for some practical applications. Besides, the customer credit risk which largely impacts the manufacturer-s profit has not been addressed in the ScheLoc problem. Therefore, in this work, we study a new and general stochastic parallel machine ScheLoc problem with limited location capacity and customer credit risk. The problem consists of determining the machine-to-location assignment, job acceptance, job-to-machine assignment, and scheduling of accepted jobs on each machine. The objective is to maximize the worst-case probability of manufacturer-s profit being greater than or equal to a given profit (referred to as the profit likelihood). For the problem, a distributionally robust chance-constrained (DRCC) programming model is proposed. Then, we develop two model-based approaches: (1) a sample average approximation (SAA) method; (2) a model-based constructive heuristic. Numerical results of 300 instances adapted from the literature show the average profit likelihood proposed by the constructive heuristic is 9.43% higher than that provided by the SAA, while the average computation time of the constructive heuristic is only 4.24% of that needed by the SAA.