Sustainable and Resilient Production–Distribution Planning Under Stochastic Demand: A Carbon-Aware MILP Framework with Lost Sales and Rolling Horizon Replanning

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.