Estimating Demand in the Absence of Sales and Inventory Information

Abstract

Nanostores, the backbone of the retail sector in many emerging economies, face unique operational challenges. These include liquidity and shelf-space constraints, and lack of IT infrastructure such as point-of-sale devices. Consequently, upstream partners responsible for replenishment (such as a manufacturer or its agent) do not have access to sales data and must rely on historical replenishment data to estimate customer demand for replenishment planning. However, replenishment data are subject to two distortions: (i) demand-to-sales distortion due to stockouts, i.e., censoring, and (ii) sales-to-replenishment distortion caused by the retailer's inventory policy. The latter is amplified because nanostores operate at a small scale, while inventory is replenished in relatively large batch sizes. We develop a parsimonious model of the nanostore's inventory dynamics using a modified base-stock policy: the nanostore receives replenishments in batches to reach a target inventory level. Using this model as the data generating process for the replenishment data, we construct a distribution of the unobserved inventory and sales data. We employ the Expectation-Maximization (EM) algorithm to jointly estimate the parameters of the demand distribution and the target inventory level. We find that the EM algorithm misattributes stockouts in some periods involving the maximum observed replenishment quantity and therefore systematically underestimates the target inventory level and correspondingly overestimates the demand. We further show that augmenting the replenishment data with a binary stockout indicator can almost eliminate the upward bias in the demand estimate. Finally, we show that this bias correction can help the upstream partners significantly reduce their visit frequency to the nanostore without adversely impacting the cycle service levels. Our results suggest that manufacturers and distributors can significantly reduce the cost of replenishment to nanostores by more accurately estimating the retail demand with little additional information (i.e., stockout indicators) without making heavy investments in digitization of nanostores with sophisticated POS or inventory management tools.

Keywords: Demand Estimation, Nanostores, Expectation-Maximization