Distributionally robust scheduling on parallel machines under moment uncertainty

• Published in: European journal of operational research Vol. 272; no. 3; pp. 832 - 846
• Main Authors: Chang, Zhiqi, Ding, Jian-Ya, Song, Shiji
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2019
• Subjects: Distributionally robust optimization; Integer second-order cone programming; Robustness and sensitivity analysis; Scheduling; Scheduling; Robustness and sensitivity analysis; Integer second-order cone programming; Distributionally robust optimization
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2018.07.007

•A distributionally robust model is built for parallel machine scheduling.•The uncertainty of estimated moments is considered in the formulation.•The min-max formulation is reduced to an integer second-order cone program.•An exact algorithm is designed to solve the problem efficiently.•Our model withstands the estimation bias and enhances the robustness of schedules. This paper investigates a distributionally robust scheduling problem on identical parallel machines, where job processing times are stochastic without any exact distributional form. Based on a distributional set specified by the support and estimated moments information, we present a min-max distributionally robust model, which minimizes the worst-case expected total flow time out of all probability distributions in this set. Our model doesn’t require exact probability distributions which are the basis for many stochastic programming models, and utilizes more information compared to the interval-based robust optimization models. Although this problem originates from the manufacturing environment, it can be applied to many other fields when the machines and jobs are endowed with different meanings. By optimizing the inner maximization subproblem, the min-max formulation is reduced to an integer second-order cone program. We propose an exact algorithm to solve this problem via exploring all the solutions that satisfy the necessary optimality conditions. Computational experiments demonstrate the high efficiency of this algorithm since problem instances with 100 jobs are optimized in a few seconds. In addition, simulation results convincingly show that the proposed distributionally robust model can hedge against the bias of estimated moments and enhance the robustness of production systems.