Optimal Robust Inventory Management with Volume Flexibility: Matching Capacity and Demand with the Lookahead Peak-Shaving Policy

Abstract

We study inventory control with volume flexibility: A firm can replenish using period-dependent base capacity at regular sourcing costs and access additional supply at a premium. The optimal replenishment policy is characterized by two period-dependent base-stock levels but determining their values is not trivial, especially for non-stationary and correlated demand. We propose the Lookahead Peak-Shaving policy that anticipates or peak shaves orders from future peak-demand periods to the current period, thereby matching capacity and demand. Peak shaving anticipates future order peaks and partially shifts them forward. This contrasts with conventional smoothing, which recovers the inventory deficit resulting from demand peaks by increasing later orders. Our contribution is three-fold. Firstly, we use a novel iterative approach to prove the robust optimality of the Lookahead Peak-Shaving policy. Secondly, we provide explicit expressions of the period-dependent base-stock levels and analyze the amount of peak shaving. Finally, we demonstrate how our policy outperforms other heuristics in stochastic systems. Most cost savings occur when demand is non-stationary and negatively correlated, and base capacities fluctuate around the mean demand. Our insights apply to several practical settings, including production systems with overtime, sourcing from multiple capacitated suppliers, or transportation planning with a spot market. Applying our model to data from a manufacturer reduces inventory and sourcing costs by 6.7%, compared to the manufacturer's policy without peak shaving.

Keywords: Robust Optimization, Inventory, Peak Shaving, Flexibility