## Pricing and Revenue Management in Supply Chain Networks and Service Systems

##### Abstract

This thesis comprises four topics focusing on pricing and revenue management, a powerful technique to enhance firm profitability through demand and supply management. Because of its efficacy, it has been adopted by small and big companies in a broad range of industries.
The first part of the thesis, we consider a canonical quantity-based network revenue management problem, where a firm accepts or rejects incoming customer requests irrevocably in order to maximize expected revenue given limited resources. Due to the curse of dimensionality, the exact solution to this problem by dynamic programming is intractable when the number of resources is large. We study a family of re-solving heuristics that periodically re-optimize an approximation to the original problem known as the deterministic linear program (DLP), where random customer arrivals are replaced by their expectations. We find that, in general, frequently re-solving the DLP produces the same order of revenue loss as one would get without re-solving, which scales as the square root of the time horizon length and resource capacities. By re-solving the DLP at a few selected points in time and applying thresholds to the customer acceptance probabilities, we design a new re-solving heuristic whose revenue loss is uniformly bounded by a constant that is independent of the time horizon and resource capacities.
An integrated pricing and routing problem on a network is considered in the second part of the thesis. The problem is motivated by applications in freight transportation such as package delivery and less-than-truckload shipping services. The decision maker sets a price for each origin-destination pair of the network, which determines the demand flow that needs to be served. The flows are then routed through the network given fixed arc capacities and costs. Demand for the same origin-destination pair can be routed along multiple paths in the network if desirable. The objective is to maximize the revenues from serving demand minus the transportation costs incurred given the capacity constraints. We propose two algorithms for the solution of this problem: (1) a Frank-Wolfe type algorithm, which requires the objective function to be smooth, and (2) a primal-dual algorithm using an online learning technique, which allows non-smooth objective functions. We prove that the first algorithm has a convergence rate of O(1/T) and the second algorithm has a convergence rate of O(log T/T), where T is the number of iterations. Numerical experiments on randomly generated instances show that coordinating pricing and routing decisions can improve profits significantly compared to independent pricing or routing strategies.
Motivated by applications in gig economy and online marketplaces, we study a two-sided queueing system under joint pricing and matching controls in the third part of the thesis. The queueing system is modeled by a bipartite graph, where the vertices represent customer or server types and the edges represent compatible customer-server matches.
Customers and servers sequentially arrive to the system and enter separate queues according to their types. The arrival rates of different types depend on the prices set by the system operator and the expected waiting time. At any point in time, the system operator can choose certain customers to match with compatible servers. The objective is to maximize the long-run average profit for the system. We first propose a fluid approximation based pricing and max-weight matching policy, which achieves an O(√η) optimality rate when all the arrival rates are scaled by η. We further show that a two-price and max-weight matching policy achieves an improved O(∛η) optimality rate.
Under a broad class of pricing policies, we prove that any matching policy has an optimality rate that is lower bounded by Ω(∛η). Thus, the two-price and max-weight matching policy achieves the optimal rate with respect to η. We also demonstrate the advantage of max-weight matching over a randomized matching policy. Under the complete resource pooling condition, we show that max-weight matching achieves O(√n) and O(∛n) optimality rates for static and two-price policies, respectively, where n is the number of customer and server types. In comparison, the randomized matching policy may have an Ω(n) optimality rate.
A neural network choice model is considered in the last part of this thesis. We study a discrete choice problem, where a customer chooses an option from a finite set of alternatives. The majority of discrete choice models are derived from the random utility maximization (RUM) principle. This assumption implies regularity property, i.e., adding an option to a choice set cannot increase the choice probability for any of the original choice options. However, many empirical evidences suggest that the regularity property may be violated. There are also several efforts to model choice behavior beyond the RUM class, but their predicting performances generally tie with the nature of dataset. We propose a more general choice model, which can explain any choice phenomenon. The model is based upon a neural network framework. Our numerical results show that using the proposed neural network choice model consistently outperforms other choice models, either RUM or non-RUM models, in both synthetic and real datasets.