Parallel machine scheduling with position-dependent processing times and deteriorating maintenance activities

Maintenance and production exert reciprocal influence in practical manufacturing applications. However, decisions regarding production scheduling and maintenance planning are often made separately, leading to frequent conflicts between production and maintenance plans. This paper investigates an integrated production scheduling and maintenance planning problem for a parallel machine system, considering both deteriorating jobs and deteriorating maintenance activities. Additionally, the problem features constraints on the number of available maintenance activities due to maintenance budget limitations. The objective is to determine the optimal scheduling and maintenance plan that minimizes the makespan. To tackle this complex problem, we initially delve into the special case where jobs and maintenance activities are already assigned to machines. In our endeavor to minimize the makespan for each machine, we uncover some crucial structural properties and present a polynomial-time algorithm. Subsequently, we develop a hybrid algorithm that combines Whale Optimization Algorithm and Variable Neighborhood Search (WOA–VNS) to address the assignment challenge encompassing jobs and maintenance activities within the parallel machine environment. A series of rigorous comparative experiments are conducted to assess the effectiveness of the proposed algorithm. The results conclusively demonstrate the superior performance of the WOA–VNS algorithm over the WOA, VNS, ABC, and ACO algorithms in addressing the presented problem.