Solving a stochastic hierarchical scheduling problem by VNS-based metaheuristic with locally assisted algorithms

Abstract

High-end equipment manufacture has features of intensive technology, uncertain process, and large scale. Hence, the scheduling of the High-end equipment manufacture is challenging. Large ships are a type of High-end equipment that is tied to national maritime security. In this paper, we study a stochastic hierarchical scheduling problem with serial-batch processing machines and the deterioration effect in ship manufacture. In the studied problem, the job processing time is uncertain and follows a normal probability distribution. Under the deterioration effect, the actual processing time of jobs is formulated as a function of the start time. The first objective is to maximize the robustness of the manufacturing system. The second objective is to minimize the total inventory cost subjected to the optimization of the first objective. The robustness of the manufacturing system is measured by the worst level of completion probability. The total inventory cost is measured by the difference between the job delivery time and the job completion time. The mathematical model for the studied problem is formulated. Some structural properties are derived to solve the problem. Based on the properties, the optimal sequence for the first objective can be obtained and a heuristic algorithm is designed to optimize the second objective. The considered problem is NP-hard involving several non-linearities. Hence, a variable neighborhood search (VNS) algorithm is developed to solve the problem in a reasonable time, which is integrated with three local search strategies and a heuristic algorithm. Various problem instances are generated and extensive computational experiments verify that the proposed VNS algorithm outperforms other compared algorithms and has strong robustness.