Cost optimization in production planning under demand uncertainty: a stochastic programming approach

Abstract

Production planning under demand uncertainty poses significant cost risks when decisions rely on deterministic point forecasts. This paper presents a two-stage stochastic programming model for multi-period production planning that explicitly incorporates demand uncertainty through discrete scenario analysis. In the first stage, production levels are set before actual demand is known. The second stage introduces recourse decisions inventory adjustments and backlog management once demand is realized. The model minimizes expected total costs across production, holding, and backlog penalties over all scenarios. Scenarios are generated from historical demand data, capturing seasonal patterns, trends, and inherent variability through a probability-weighted scenario tree. To solve the resulting large-scale program efficiently, an L-shaped decomposition algorithm is employed, enabling tractable computation across hundreds of scenarios. A realistic six-period, 500-scenario industrial case study demonstrates that the stochastic model reduces expected total cost by 9.1% compared to a deterministic benchmark. The Value of Stochastic Solution (VSS) is $4,150, quantifying the financial benefit of accounting for uncertainty. The Expected Value of Perfect Information (EVPI) stands at $1,870, representing the maximum value of acquiring perfect demand forecasts. Compared to robust optimization, the stochastic approach yields higher worst-case costs but substantially better average performance across demand scenarios. Sensitivity analysis further confirms that cost advantages over deterministic planning grow as demand variability increases. This framework offers manufacturers in volatile markets a practical, scalable tool for smarter production decisions turning demand uncertainty from a liability into a manageable, cost-optimized planning input.