Variable neighborhood search-based algorithms for the parallel machine capacitated lot-sizing and scheduling problem

This paper addresses the capacitated lot-sizing and scheduling problem on parallel machines with eligibility constraints, sequence-dependent setup times, and costs. The objective is to find a production plan that minimizes production, setup, and inventory holding costs while meeting the demands of products for each period without delay for a given planning horizon. Since the studied problem is NP-hard, we proposed metaheuristic approaches, Variable Neighborhood Search, Variable Neighborhood Descent, and Reduced Variable Neighborhood Search algorithms to analyze their performance on the problem. Initially, we presented an initial solution generation method to satisfy each period's demand. Then, we defined insert, swap, and fractional insert moves for generating neighborhood solutions. We employed an adaptive constraint handling technique to enlarge the search space by accepting infeasible solutions during the search. Lastly, we performed computational experiments over the benchmark instances. The computational results show the effectiveness of the proposed solution approaches, compared to existing solution techniques in the literature, and the improvements in various problem instances compared to the best-known results