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This study addresses the Single-Product Capacitated Lot Sizing Problem (SP-CLSP) in conjunction with the Single-Row Facility Layout Problem (SRFLP) by proposing a mathematical model. To minimize total costs associated with a single product across all periods (including setup, inventory holding, production, and material handling), this model will determine optimal production quantities (lot sizes) for each period. Furthermore, it will identify an optimal facilities layout that minimizes material handling costs specifically based on those lot sizes. The model incorporates constraints for production capacity, single-product inventory balance, setup times, and machine-position assignments. Binary variables represent machines setup, machine assignments to specific positions in the layout, and potentially machine orientation if relevant. The model is illustrated with several example problems. CPLEX software is used to solve the Mixed-Integer Programming formulation, determining the optimal production quantities for each period and the machine layout that best suits these quantities. This integrated model allows for the simultaneous optimization of lot sizes and machine layouts for a single product, aiming to reduce total costs and improve production efficiency.
