A matheuristic approach to integrated multi-Range lot-sizing and vehicle routing problems with time windows for perishable products

Our starting point in this paper was based on the overview of recent developments in the field of modeling multi-range capacitated lot-Sizing problem and vehicle routing problem with time windows. However, the objective is to synchronize the two problems and to build a better overall solution applied to a real case study. We propose a mixed-integer linear programming (MILP) model that incorporates the new dimension of product range along with time windows, specifically applied to the distribution of perishable products. An iterative two-phase matheuristic, combining mathematical programming and a variable neighborhood search algorithm, is employed to solve these NP-hard problems. In this study, we assigned a product to each production range while respecting capacity constraints and minimizing the total costs of production, shortage, backlog, and storage. Additionally, we optimized vehicle routing to deliver the product ranges while accounting for vehicle capacity constraints and the time windows assigned to each customer. We demonstrate the efficiency of our mathematical formulation through numerical experiments conducted on real-world data.