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.
