Optimal Merchandise Testing with Limited Inventory

Abstract

We consider the allocation of inventory to stores in a \merchandise test, whereby a fashion retailer deploys a new product to stores in limited quantities in order to learn about demand prior to the main selling season. Our problem formulation includes practical considerations like fixed costs and multiperiod inventory considerations but is challenging to analyze directly. Instead, we take a bounding approach that isolates the novel aspect of our problem: the impact of test inventory allocation on demand learning. We specifically examine a tradeoff between the quantity of stores tested and the quality of observations, which can be impacted by demand censoring due to inventory stockouts. We find that the visibility into the timing of each sales transaction has a pivotal impact on the allocation decisions that optimize learning. When such timing information is unobservable, the retailer may need to consolidate inventory in few stores to increase service levels during the test and thereby to minimize the negative impacts of demand censoring. When sales timing information is observable, the retailer optimizes learning by maximizing the number of sales during the test period without regard to stockouts in individual stores. In a numerical study, we show that heuristics motivated by our analyses are near-optimal and that inefficient allocations can considerably reduce the learning value of the merchandise test. We also examine the interplay between the retailer's learning incentive and the natural incentives brought by fixed costs and profits earned during the test itself. We find that that it is sufficient for the retailer to consider only the learning incentive when the main selling period is relatively long compared with the testing period.