Constrained Assortment Optimization Under the Mixed Logit Model with Design Options
26 Pages Posted: 26 Jun 2020
Date Written: June 11, 2020
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.
Keywords: assortment optimization, mixed logit, mixed-integer non-linear prob- lem, pricing, design options, heterogeneous customers, sample average approxima- tion, simulation-based optimization, systematic sampling, variance reduction
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