Tractable Models and Algorithms for Assortment Planning with Product Costs

Assortment planning under a logit demand model is a difficult problem when there are product-specific fixed costs. We develop a new continuous relaxation of the problem that is based on the parametrization of the problem on the total assortment attractiveness. This relaxation provides an upper bound and a heuristic integer solution, for which we develop performance guarantees. We analytically prove that it provides a close-to-optimal solution when products are homogeneous in terms of preference weights. Moreover, our formulation can be easily extended to incorporate additional constraints on the assortment, or multiple customer segments. Finally, we provide numerical experiments that show that our method yields tight upper bounds and performs competitively with respect to other approaches found in the literature.