A Local Search for Solving the Multi-item Capacitated Lot Sizing Problem and Vehicle Routing: A Case Study

Our research focuses on the development of two algorithms based on the mathematical programming and local search procedures for resolution the Multi-Item Capacitated Lot Sizing Problem and Vehicle Routing Problem (MICLSP-VRP). It concerns so a particularly important and difficult problem in the strong sense for solving. In particular, our study is motivated by a real case study in a butcher’s shop firm whose meat processing. Several production lines are considered of (turkey and chicken) items and a fleet of vehicles that is used to deliver. In this study, an effective approach based on the local search and accurate mixed integer programming model is presented to solve multi-item capacitated lot sizing problem and vehicle routing problem with delivery time windows. This consists of determining the production quantities at each site by minimizing the cost of transport and solving the sub problem. By considering an integrated approach, the computational results of a case study show a 25.33% percent decrease in the total cost production.