Scheduling identical serial-batching machines in the engine manufacturing supply chain by an integrated variable neighborhood search algorithm

The optimization of the high-end equipment manufacturing process is becoming progressively more difficult, which brings a big challenge for high-end equipment manufacturers. Numerous variables, such as equipment wear and tear, the service level of the supply chain, etc., may have a significant impact on the efficiency of highend equipment manufacturing. In this paper, motivated by the need to improve the productivity of engines, we study a scheduling problem considering the deterioration effect, component parts supply, and parallel serialbatch processing machines. The job processing time is sum-of-actual-processing-time-dependent and the set-up time of a batch is time-dependent. The objective is to minimize the makespan. Firstly, we analyze the structural properties of the problem under two special cases. Then, a dynamic programming (DP) algorithm is proposed to group the jobs into batches, and two heuristic algorithms are designed to improve the job sequence based on the structural properties. Algorithm 3 is proposed to provide a lower bound for the investigated problem. Next, we develop a variable neighborhood search algorithm (VNS-H) which integrates the DP algorithm, heuristic algorithms, and four local search strategies. Extensive computational experiments are conducted to validate the performance of the proposed algorithm. The results show that the VNS-H algorithm solves the proposed problem effectively and outperforms other involved metaheuristics. The proposed methods in this work can provide manufacturers with useful decision-making support that improves production efficiency and reduces operational costs.