Group-constrained assortment optimization under the multinomial logit model

Abstract

We study an assortment problem under the multinomial logit model with two new types of group constraints that are motivated by a joint project with the German car manufacturer BMW. Under group constraints, products are either attributed to exactly one group or to several groups at once and there is either a bound on the number of products offered per group or on the number of groups from which products are offered. We formulate both optimization problems as binary fractional linear program and provide reformulations that can be solved using state-of-the-art solvers. Finally, we conduct a numerical study and find that all instances of the products-per-group constrained problem as well as small to medium size instances of the number-of-offered-groups constrained problem can be solved within fractions of a second, whereas large instances of the latter problem might take some seconds to be solved.