Dynamic stochastic lot sizing with forecast evolution in rolling‐horizon planning

Alexandre Forel and Martin Grunow

Production and Operations Management, 2023, vol. 32, issue 2, 449-468

Abstract: Academic approaches considering demand uncertainty in lot sizing are seldom used in practice. Industry typically implements deterministic models and accounts for uncertainties by using a rolling‐horizon planning framework with frequent forecast updates. This paper bridges this gap by proposing a stochastic lot‐sizing methodology adapted to rolling‐horizon processes. Using the martingale model of forecast evolution (MMFE), we are able to anticipate the forecast updates from rolling‐horizon planning in stochastic lot sizing. Our formulation is extended with production recourse to reflect the replanning flexibility of rolling‐horizon planning. Extensive simulations on both synthetic and real‐world data show the value of forecast evolution models. Forecast evolution models reduce actual costs by 14% on average compared to traditional deterministic planning. The advantage of the extended model with production recourse depends on several factors including capacity, correlation, and uncertainty. Sensitivity analyses show that recourse can reduce costs by an additional 3% on average and up to 10% in specific settings. Using real‐world and synthetic data, we provide the first analysis of the value of additive and multiplicative MMFE‐based planning models when the true forecast evolution process is unknown. We show that, contrary to the existing consensus, the additive model performs more robustly than the multiplicative model on a wide array of problem settings.

Date: 2023
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