Choice Modeling and Assortment Optimization in the Presence of Context Effects

Abstract

In the presence of context effects, the perceived attractiveness of individual items is not fixed and depends on other items that are offered beside them. While context effects are well explored in the marketing and psychology literature, very little work has been done on incorporating these effects in discrete choice and investigating revenue management problems in their presence. In this paper, we introduce a new Random Utility Maximization choice model, the Contextual MNL model, that incorporates these effects. In our model, the utility of a presented item to the customer depends on what other items are offered beside it in an assortment. We compare the prediction power of our choice model and some of the other widely used choice models in the literature on a real data set and show that incorporating the context effects may significantly enhance the prediction scores and our understanding of the patterns of choice selection. We show the NP-hardness of the assortment optimization problem and the click through rate optimization problem, under our choice model. Several polynomially solvable special cases of the model are identified that also perform well in our empirical validation for our data set. In addition, to derive approximation results, we obtain some conditions for monotonicity and submodularity of the objective function of the assortment optimization and click through rate maximization problems. We also develop fast heuristics for solving the assortment optimization problem which provide near-optimal solutions according to our test results.