Capacitated strategic assortment planning under explicit demand substitution

Buyers have easier access to a variety of products with the rise of multi-channel distribution strategies and the increase in new product introductions. On the other hand, firms experience greater pressure in offering the correct product variety given that the manufacturing infrastructure often imposes physical and financial constraints in attaining variety. This study examines a firm’s optimal assortment planning problem under an exogenous demand model, where each customer has a predetermined preference for each product from a potential set. Proportional demand substitutions are allowed from out-of-assortment products to those available. We show that the problem is NP-complete. We also show that an optimal assortment is composed of some number of the highest margin products, if one product having a higher margin than another implies that the former product has a lower demand rate than the latter. The firm’s assortment capacity is fully utilized at the optimum if the customers’ substitution ratio does not exceed a particular threshold. We also introduce several approximate assortment policies that can be easily implemented, and test these policies through extensive numerical analyses. The results reveal that some of the policies can provide less than a 1% profit gap with an optimal solution for a 20-product set. The policy’s performance highly depends on the firm’s assortment capacity-to-product set size ratio. Moreover, we provide performance bounds for two of these well-performing approximate policies.