Risk level-driven bi-objective stochastic parallel machine scheduling problem

摘要

In recent years, Industry 4.0 has emerged and received substantial attention. Industry 4.0 integrate physical and decisional aspects of manufacturing processes, to improve the ability to cope with unpredictable and negative events. Production scheduling has always been a common problem faced by manufacturing systems, stochastic scheduling is thus a hot research topic. It is usually assumed in the literature that job processing times are stochastic. Due to the inadequate or unrepresentative historical data, the probability distribution of processing times may not be well estimated. This work investigate a bi-objective stochastic parallel machine scheduling problem, to minimize the capital budget and risk level simultaneously. Only partial distributional information on uncertain job processing times, i. E., the mean and covariance matrix, is known. Especially, the risk level is measured by the probability of existing tardy jobs. For the problem, a distributionally robust bi-objective formulation is first proposed. Then a popular approximation method is applied for the probabilistic objective function, and ε-constraint method is further developed. A case study is conducted and analyzed, and some managerial insights are drawn.