Constrained Assortment Optimization Under the Mixed Logit Model with Design Options

Abstract

We present the constrained assortment optimization problem under the mixed logit model (MXL) with design options and deterministic customer segments. The rationale is to select a subset of products of a given size and decide on the attributes of each product such that a function of market share is maximized. The customer demand is modeled by MXL. We develop a novel mixed-integer non-linear program and solve it by state-of-the-art generic solvers. To reduce variance in sample average approximation systematic numbers are applied instead of pseudo-random numbers. Our numerical results demonstrate that systematic numbers reduce computational effort by 70%. We solve instances up to 20 customer segments, 100 products each with 50 design options yielding 5,000 product-design combinations, and 500 random realizations in under two minutes. Our approach studies the impact of market position, willingness-to-pay, and bundling strategies on the optimal assortment.