Revenue management is the study of models and algorithms that address inventory allocation and pricing decisions in the face of uncertainty and limited capacities. Out of many models studied in revenue management, fluid approximations have been an effective tool to deal with large-scale inventory allocation and pricing problems and develop efficient algorithms; while inventory placement, which determines how to place on-hand products into different fulfillment centers, is an important decision that has a significant impact on subsequent inventory allocation and pricing power; lastly, discrete choice models are widely used to model customer choice behaviour and capture the fact that customers substitute among the offered products, which ultimately help in making better inventory allocation and pricing decisions. In this dissertation, we investigate one new model in each of these areas and develop efficient algorithms with performance guarantees. These new models represent various approaches from different angles we take to aid in improving inventory allocation and pricing decisions.First, based on the fact that high-variance demand occurs in many applications but is not fully addressed by traditional revenue management models, we explore a new revenue management model that incorporates general mean and variance for the number of customer arrivals, with the goal of developing a policy to determine which product to make available to each arriving customer in order to maximize total expected revenue. We devise a fluid approximation corresponding to this model and use it to develop an asymptotically optimal policy.Second, we consider inventory placement, delivery promise and fulfillment decisions faced by an online retailer jointly. We study a two-stage model where in the first stage, we place a set of products with given numbers of units into different fulfillment centers with capacity constraints. Once we make the placement decisions, we enter the second stage where we face random demand for the products from different demand regions. In response to each demand, we pick a delivery promise to offer and choose a fulfillment center to use to serve the demand. The goal is to determine where to place the units in order to maximize the total expected profit from sales over a finite selling horizon. For this problem, we provide a general approximation framework, which leads us to a set of policies. The best policy provides 1/(4 + ϵ)-approximation for any ϵ > 0, and the policy can be computed in polynomial time for each fixed ϵ.Lastly, we study a natural variant of the multinomial logit model by incorporating rank cutoffs, which characterizes the number of products customers will focus on during the choice process. To be more specific, after associating random utilities with all the products and the no-purchase option, a customer with rank cutoff k would ignore all alternatives whose utilities are not within the k largest utilities and choose among the remaining alternatives. We show that the assortment optimization problem under this choice model is NP-hard and propose a polynomial-time approximation scheme. We also run numerical experiments to show that incorporating rank cutoffs can result in better predictions of customer choices and more profitable assortment recommendations.
