Taming the Long Tail of Inventory: Gambler's Fallacy in Intermittent Demand Management

Abstract

Items with intermittent or demand often tie up valuable warehouse space and capital investment of manufacturers and retailers. Traditional inventory solutions were not designed for items with these demand characteristics. In the case of long tail products, the paucity of demand data poses additional challenges for model estimation and performance evaluation. Furthermore, while most inventory policies in the OR literature were conceived to maximize long run average cost per time period or expected total cost over a finite horizon, in reality, practitioners are more concerned with KPIs such as inventory turnover ratio or gross margin return on investment, metrics that often normalize the profit or cost performance with the number of sales generated in a finite horizon. The nature of intermittent demand product further accentuates the impact of these effects on the performance of inventory policies under these KPIs. We analyze the average cost per unit of goods sold for inventory policies over a finite horizon with intermittent demand product. Our analysis is motivated by the recent surprising observation that the gambler's fallacy phenomenon holds actually in a random sequence of independent events, due to the finite horizon effect. We use this to analyze the performance of stationary policies in finite horizon, and provide justification for the use of replenishment-delay policies for very slow-moving parts, even if the demand distribution is stationary and independent across time. This is surprising as the constant base stock policy is known to be optimal for items with these demand characteristics in the classical settings. More generally, we propose a class of stationary staggered base stock policy to minimize the average inventory cost per unit of goods sold for slow-moving items over a finite horizon. We call this the HBR (histogram-based robust) policy, obtained using a distributionally robust inventory control model with the Wasserstein uncertainty set on the nominal interarrival-demand distribution. Interestingly, to deal with the finite horizon effect, we need to bias the true interarrival and demand distribution to account for the gambler's fallacy phenomenon. We implement our policy and other benchmark methods on real data and find that our robust policy can reduce inventory cost compared to the benchmarks in all scenarios with varying cost parameters.