A dynamic programming approach to solving the assortment planning problem with multiple quality levels

While the assortment planning problem, in which a firm selects a set of products to offer, has been widely studied, several problem instances exist which have not yet been solved to optimality. In particular, we consider an assortment planning problem under a locational choice model for consumer choice with both vertical and horizontal differentiation. We present a combined dynamic programming/line search approach which finds an optimal solution when customer preference for the horizontal attributes are distributed according to a unimodal distribution. The dynamic program makes use of new analytical results, which show that high quality products will be distributed near the mode. This enables significant state reduction and therefore efficient solution times. Efficient computation times allow us to study the solution for a wide range of system parameters and thereby draw several managerial conclusions.