Surrogate Measures for the Robust Scheduling of Stochastic Job Shop Scheduling Problems

Abstract

This study focuses on surrogate measures (SMs) of robustness for the stochastic job shop scheduling problems (SJSSP) with uncertain processing times. The objective is to provide the robust predictive schedule to the decision makers. The mathematical model of SJSSP is formulated by considering the railway execution strategy, which defined that the starting time of each operation cannot be earlier than its predictive starting time. Robustness is defined as the expected relative deviation between the realized makespan and the predictive makespan. In view of the time-consuming characteristic of simulation-based robustness measure (RMsim), this paper puts forward new SMs and investigates their performance through simulations. By utilizing the structure of schedule and the available information of stochastic processing times, two SMs on the basis of minimizing the robustness degradation on the critical path and the non-critical path are suggested. For this purpose, a hybrid estimation of distribution algorithm (HEDA) is adopted to conduct the simulations. To analyze the performance of the presented SMs, two computational experiments are carried out. Specifically, the correlation analysis is firstly conducted by comparing the coefficient of determination between the presented SMs and the corresponding simulation-based robustness values with those of the existing SMs. Secondly, the effectiveness and the performance of the presented SMs are further validated by comparing with the simulation-based robustness measure under different uncertainty levels. The experimental results demonstrate that the presented SMs are not only effective for assessing the robustness of SJSSP no matter the uncertainty levels, but also require a tremendously lower computational burden than the simulation-based robustness measure.