Pricing and Assortment Planning Problems with Network Effects under Mixed Multinomial Logit Choice Models

Abstract

A product displays non-negative network effects if each individual customer’s valuation for the product increases in its overall sales. In the first portion of this thesis, we consider a pricing problem for a product that exhibits network effects. The primary objective in the pricing problem is to find a revenue-maximizing pricefor the seller of the product. We will focus on a setting in which demand and sales are built on a variation of the mixed multinomial logit (MMNL) choice model in which each customer picks between just two options: (a) buy the product or (b) do not buy the product. In an MMNL model, demand is composed of multiple segments of customers. Within any individual segment, each customer’s utility for the product is comprised of a segment-specific expected-utility term and a random term. We incorporate network effects by modifying the segment-specific expected-utility term to depend upon overall sales to all segments. Purchase probabilities and sales quantities arise as a solution to a set of fixed-point equations. We present a detailed analysis of cases with two segments. Here, we describe an algorithm that computes the optimal revenue within any desired level of accuracy, and analyze how the complexity of the algorithm depends upon the desired level of accuracy. The algorithm involves searching over a discretized space of sales quantities for just one of the two segments. We also discuss problems with an arbitrary number of segments and describe the results of a numerical study. When there are multiple products, a strategic firm should decide what subset of its products to make available when a customer arrives to maximize the firm's revenue. The problem of finding the best assortment of products is called the assortment planning or assortment optimization problem. In the second portion of this thesis, we attempt to find the best assortment of products when products exhibit network effects and when there are multiple segments of customers. To formulate the assortment planning problem, we introduce a mixed multinomial logit choice model with network effects to obtain purchase probabilities and sales quantities as a solution to a set of fixed-point equations. We identify conditions under which the solution to the fixed-point equations is unique. This demand modeling approach is the same as that used in the first part of the thesis. After describing the assortment planning problem, we show numerically that the policies existing in the literature such as revenue-ordered and quasi-revenue-ordered assortments are not always optimal for the MMNL model with network effects. We introduce another type of policy which we refer to as a k-quasi-revenue-ordered assortment. Our numerical experiments suggest we can often find an optimal policy within this class. Since our problem is NP-hard, we provide a method to construct upper bounds on the optimal value of the assortment planning problem. Our numerical experiments show that the upper bounds perform well. When there are a large number of products, it is not possible to compute the revenue of all possible subsets of products, and therefore, we cannot compute an optimal policy by enumeration. In our numerical experiments, we show that upper bounds can be computed quickly. In addition, we evaluate the gap between the upper bounds and the best revenue-ordered assortments, the best quasi-revenue-ordered assortments, and k-quasi-revenue-ordered assortments.