Integrated Optimization of Multi-Product Capacitated Lot Sizing and Dynamic Single-Row Facility Layout Problem: Application in the Food Industry

This paper presents an integrated optimization approach for the Multi-Product Capacitated Lot Sizing (MPCLS) problem in conjunction with the Dynamic Single-Row Facility Layout Problem (DSRFLP). A mathematical model is proposed to minimize total costs associated with multiple products across all periods, including setup, inventory holding, production, and material handling costs. This model determines optimal production quantities (lot sizes) for each period and identifies an optimal facilities layout for each period that minimizes material handling costs based on those lot sizes. The model is illustrated with an example from the food industry. CPLEX software is used to solve the Mixed-Integer Programming formulation, determining the optimal production quantities for each period and the dynamic machine layout that best suits these quantities. This integrated model allows for the simultaneous optimization of lot sizes and machine layouts, aiming to reduce total costs and improve production efficiency.