Distributionally robust scheduling on parallel machines under moment uncertainty
Distributionally robust scheduling on parallel machines under moment uncertainty
复制标题
矩不确定性下并行机的分布式鲁棒调度
DOI：
10.1016/j.ejor.2018.07.007
复制
发表时间：
2019-02-01
影响因子：
6.4
通讯作者：
Song, Shiji
中科院分区：
文献类型：
--
作者：
Chang, Zhiqi;Ding, Jian-Ya;Song, Shiji
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. (C) 2018 Elsevier B.V. All rights reserved.
