Integrated production–distribution planning using a MILP optimization model and CPLEX solver

This paper presents an integrated mathematical model for optimizing production, inventory, and transportation planning in a multi-product, multi-period supply chain. The model aims to minimize total variable costs—including transportation, storage, backlog, overtime production, and vehicle usage—while satisfying customer demand and adhering to real-world operational constraints such as pallet-based shipping, trailer capacity, warehouse limits, and backlog penalties. Formulated as a Mixed-Integer Linear Programming (MILP) problem and solved using IBM ILOG CPLEX, the model considers a single factory, two warehouses, and a single customer across four planning periods and six finished products. Key logistical parameters include pallet sizes, trailer capacities, and a maximum number of vehicles available per week. The model integrates tactical and operational decisions such as the number of products transported (in pallets), vehicle use, extra vehicle penalties, warehouse inventory dynamics, and controlled backlog. The numerical results highlight the critical role of transportation capacity and backlog management in driving overall system cost. While production costs remain constant, backlog and transportation expenses, suggesting that limited vehicle capacity significantly affects service levels and cost-effectiveness, dominate variable costs. The results also demonstrate efficient warehouse utilization and minimal overtime, reflecting a lean operational strategy. This work contributes to the literature by addressing integrated supply chain decision-making with detailed and realistic transport-unit constraints. It offers a flexible decision-support tool that can be extended to multi-factory or multi-client contexts, and enhanced with stochastic demand or sustainability metrics for real-world deployment.