Evaluating Strategic Workforce Decisions in Aggregate Production Planning under Demand Uncertainty: A Two-Stage Stochastic MILP with Out-of-Sample Assessment

Abstract

Aggregate production planning (APP) requires balancing workforce and operational decisions over a medium-term horizon. This study formulates and applies a two-stage stochastic mixed integer linear program (MILP) for APP with the primary objective of evaluating strategic workforce planning decisions under demand uncertainty. Workforce decisions are modeled as here-and-now commitments, while operational decisions are optimized as recourse actions in response to realized demand. The framework is demonstrated in an illustrative furniture manufacturing setting over a 12-month horizon with seasonally varying cost parameters. Demand scenarios are generated by combining Holt–Winters point forecasts with forecast-error scenarios obtained through a rolling-origin procedure and a moment-matching approach, yielding demand trajectories that reflect the statistical properties and temporal dependence of forecast uncertainty. Using these scenarios, the model quantifies cost–service trade-offs under alternative backorder penalty severities. To assess the robustness of the resulting workforce plans, this study conducts an out-of-sample evaluation based on observed demand from a holdout year and a wait-and-see benchmark, a validation perspective that has received limited attention in the APP literature. The out-of-sample results indicate that the stochastic model produces feasible and cost-effective workforce decisions that remain near-optimal under observed demand. Overall, the proposed framework serves as an effective decision-support tool for APP under demand uncertainty, supporting the evaluation of workforce and operational decisions within a unified stochastic framework.