Single-period assortment and stock-level decisions for dual sales channels with capacity limits and uncertain demand

This paper addresses a dual channel, clicks-and-mortar retailer's problem of determining which among a set of products with seasonal demand will occupy limited retail shelf space, which products will be offered via an online channel, and which items will be available through both channels. Using a consumer choice model in which the set of products offered influences each product's demand in each channel, we consider stocking and price decisions under uncertain demand in a single-period setting with a constraint on the probability of stocking out. The resulting model is a large-scale, chance-constrained, two-stage stochastic programme. We propose a sample average approximation (SAA) method that permits quickly arriving at near-optimal solutions for this complex problem class. We also exercise the proposed model to gain insights on the problem's key tradeoffs and properties of optimal solutions.