Joint Assortment Optimization and Marketing Mix Allocation

Abstract

Problem definition: Assortment selection and marketing mix allocation are critical decisions for retailers, directly influencing consumer choices. In this paper, we propose a multinomial logit (MNL) choice model in which consumer utility is influenced by marketing decisions such as advertising and promotions – a model widely utilized in empirical marketing literature. We then study the joint assortment and marketing mix allocation problem subject to either cardinality constraints or knapsack constraints. Methodologies/results: We prove that the problem under cardinality constraints is already strongly NP-hard and does not admit constant ratio approximation. For the model with cardinality constraints, we provide an optimal ratio approximation algorithm and polynomial-time algorithms for special cases. With a constant number of marketing mix decisions, the problem can be solved using a linear program of polynomial size. Under knapsack constraints, we also provide an optimal ratio approximation algorithm and a fully polynomial-time approximation scheme (FPTAS) for special cases. With a constant number of marketing mixes, the problem admits an optimal polynomial-time approximation scheme (PTAS). Computational experiments with real-world NielsenIQ retail data show significant 2.05% revenue increases using our method over a two-stage “assortment-then-marketing mix allocation” heuristic approach. Managerial implications: Our comprehensive numerical experiments across various scenarios demonstrate that neglecting the impact of marketing decisions in assortment selection can lead to a significant decline in profitability. 

Keywords: Assortment Optimization, Marketing Mix Allocation, Approximation Algorithm