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.

Background: Manufacturing supply chains must increasingly coordinate cost, environmental impact, and service continuity under demand uncertainty and limited capacity. Methods: This study develops a stochastic mixed-integer linear programming framework for carbon-aware production–distribution planning in an automotive supply chain. The model jointly optimizes production quantities, inventory levels, shipments, truck usage, and lost sales over a multi-period horizon. Demand uncertainty is represented through scenarios, while production- and transportation-related emissions are monetized using an internal carbon price. Lost-sales penalties capture service degradation when demand cannot be fulfilled by the focal plant, and a rolling-horizon analysis evaluates planning responsiveness as demand information is updated. The framework is applied to an industrially inspired, capacity-constrained automotive case with multiple products, production lines, destinations, and demand scenarios. Computational experiments assess carbon pricing, lost-sales penalties, demand volatility, deterministic versus stochastic planning, and rolling-horizon replanning. Results: Results show that carbon pricing mainly acts as an economic valuation mechanism under the studied fixed-structure configuration, whereas lost-sales penalties strongly influence service performance. Demand volatility increases unmet demand, and lower emissions may reflect lower fulfilled demand rather than improved efficiency. Conclusions: The study provides a decision-support framework for evaluating cost–carbon–service trade-offs under stochastic demand while acknowledging single-plant and fixed-routing limitations.