Provably Near-Optimal LP-Based Policies for Revenue Management in Systems with Reusable Resources

Motivated by emerging applications in workforce management, we consider a class of revenue management problems in systems with reusable resources. The corresponding applications are modeled using the well-known loss network systems. We use an extremely simple linear program (LP) that provides an upper bound on the best achievable expected long-run revenue rate. The optimal solution of the LP is used to devise a conceptually simple control policy that we call the class selection policy (CSP). Moreover, the LP is used to analyze the performance of the CSP policy. We obtain the _rst control policy with uniform performance guarantees. In particular, for the model with single resource and uniform resource requirements, the CSP policy is guaranteed to have expected long-run revenue rate that is at least half of the best achievable. More generally, as the ratio between the capacity of the system and the maximum resource requirement grows to in_nity, the CSP policy is asymptotically optimal, regardless of any other parameter of the problem. The asymptotic performance analysis that we obtain is more general than existing results in several important dimensions. It is based on several novel ideas that we believe will be useful in other settings

Provably near-optimal algorithms for multi-stage stochastic optimization models in operations management

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 157-165).Many if not most of the core problems studied in operations management fall into the category of multi-stage stochastic optimization models, whereby one considers multiple, often correlated decisions to optimize a particular objective function under uncertainty on the system evolution over the future horizon. Unfortunately, computing the optimal policies is usually computationally intractable due to curse of dimensionality. This thesis is focused on providing provably near-optimal and tractable policies for some of these challenging models arising in the context of inventory control, capacity planning and revenue management; specifically, on the design of approximation algorithms that admit worst-case performance guarantees. In the first chapter, we develop new algorithmic approaches to compute provably near-optimal policies for multi-period stochastic lot-sizing inventory models with positive lead times, general demand distributions and dynamic forecast updates. The proposed policies have worst-case performance guarantees of 3 and typically perform very close to optimal in extensive computational experiments. We also describe a 6-approximation algorithm for the counterpart model under uniform capacity constraints. In the second chapter, we study a class of revenue management problems in systems with reusable resources and advanced reservations. A simple control policy called the class selection policy (CSP) is proposed based on solving a knapsack-type linear program (LP). We show that the CSP and its variants perform provably near-optimal in the Halfin- Whitt regime. The analysis is based on modeling the problem as loss network systems with advanced reservations. In particular, asymptotic upper bounds on the blocking probabilities are derived. In the third chapter, we examine the problem of capacity planning in joint ventures to meet stochastic demand in a newsvendor-type setting. When resources are heterogeneous, there exists a unique revenue-sharing contract such that the corresponding Nash Bargaining Solution, the Strong Nash Equilibrium, and the system optimal solution coincide. The optimal scheme rewards every participant proportionally to her marginal cost. When resources are homogeneous, there does not exist a revenue-sharing scheme which induces the system optimum. Nonetheless, we propose provably good revenue-sharing contracts which suggests that the reward should be inversely proportional to the marginal cost of each participant.by Cong Shi.Ph.D

Revenue Management of Reusable Resources with Advanced Reservations

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137568/1/poms12672_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137568/2/poms12672.pd

Efficient Real-time Policies for Revenue Management Problems

This dissertation studies the development of provably near-optimal real-time prescriptive analytics solutions that are easily implementable in a dynamic business environment. We consider several stochastic control problems that are motivated by different applications of the practice of pricing and revenue management. Due to high dimensionality and the need for real-time decision making, it is computationally prohibitive to characterize the optimal controls for these problems. Therefore, we develop heuristic controls with simple decision rules that can be deployed in real-time at large scale, and then show theirs good theoretical and empirical performances. In particular, the first chapter studies the joint dynamic pricing and order fulfillment problem in the context of online retail, where a retailer sells multiple products to customers from different locations and fulfills orders through multiple fulfillment centers. The objective is to maximize the total expected profits, defined as the revenue minus the shipping cost. We propose heuristics where the real-time computations of pricing and fulfillment decisions are partially decoupled, and show their good performances compared to reasonable benchmarks. The second chapter studies a dynamic pricing problem where a firm faces price-sensitive customers arriving stochastically over time. Each customer consumes one unit of resource for a deterministic amount of time, after which the resource can be immediately used to serve new customers. We develop two heuristic controls and show that both are asymptotically optimal in the regime with large demand and supply. We further generalize both of the heuristic controls to the settings with multiple service types requiring different service times and with advance reservation. Lastly, the third chapter considers a general class of single-product dynamic pricing problems with inventory constraints, where the price-dependent demand function is unknown to the firm. We develop nonparametric dynamic pricing algorithms that do not assume any functional form of the demand model and show that, for one of the algorithm, its revenue loss compared to a clairvoyant matches the theoretic lower bound in asymptotic regime. In particular, the proposed algorithms generalize the classic bisection search method to a constrained setting with noisy observations.PHDBusiness AdministrationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145995/1/leiyz_1.pd

The Power of Static Pricing for Reusable Resources

We consider the problem of pricing a reusable resource service system. Potential customers arrive according to a Poisson process and purchase the service if their valuation exceeds the current price. If no units are available, customers immediately leave without service. Serving a customer corresponds to using one unit of the reusable resource, where the service time has an exponential distribution. The objective is to maximize the steady-state revenue rate. This system is equivalent to the classical Erlang loss model with price-sensitive customers, which has applications in vehicle sharing, cloud computing, and spare parts management. Although an optimal pricing policy is dynamic, we provide two main results that show a simple static policy is universally near-optimal for any service rate, arrival rate, and number of units in the system. When there is one class of customers who have a monotone hazard rate (MHR) valuation distribution, we prove that a static pricing policy guarantees 90.4\% of the revenue from the optimal dynamic policy. When there are multiple classes of customers that each have their own regular valuation distribution and service rate, we prove that static pricing guarantees 78.9\% of the revenue of the optimal dynamic policy. In this case, the optimal pricing policy is exponentially large in the number of classes while the static policy requires only one price per class. Moreover, we prove that the optimal static policy can be easily computed, resulting in the first polynomial time approximation algorithm for this problem

Lp-Based Artificial Dependency for Probabilistic Etail Order Fulfillment

We consider an online multi-item retailer with multiple fulfillment facilities and finite inventory, with the objective of minimizing the expected shipping cost of fulfilling customer orders over a finite horizon. We approximate the stochastic dynamic programming formulation of the problem with an equivalent deterministic linear program, which we use to develop a probabilistic fulfillment heuristic that is provably optimal in the asymptotic sense. This first heuristic, however, relies on solving an LP that is exponential in the size of the input. Therefore, we subsequently provide another heuristic which solves an LP that is polynomial in the size of the input, and prove an upper bound on its asymptotic competitive ratio. This heuristic works by modifying the LP solution with artificial dependencies, with the resulting fractional variables used to probabilistically fulfill orders. A hardness result shows that asymptotically optimal policies that are computationally efficient cannot exist. Finally, we conduct numerical experiments that show that our heuristic's performance is very close to optimal for a range of parameters.http://deepblue.lib.umich.edu/bitstream/2027.42/108712/1/1250_ASinha.pd

Stochastic regret minimization for revenue management problems with nonstationary demands

We study an admission control model in revenue management with nonstationary and correlated demands over a finite discrete time horizon. The arrival probabilities are updated by current available information, that is, past customer arrivals and some other exogenous information. We develop a regret‐based framework, which measures the difference in revenue between a clairvoyant optimal policy that has access to all realizations of randomness a priori and a given feasible policy which does not have access to this future information. This regret minimization framework better spells out the trade‐offs of each accept/reject decision. We proceed using the lens of approximation algorithms to devise a conceptually simple regret‐parity policy. We show the proposed policy achieves 2‐approximation of the optimal policy in terms of total regret for a two‐class problem, and then extend our results to a multiclass problem with a fairness constraint. Our goal in this article is to make progress toward understanding the marriage between stochastic regret minimization and approximation algorithms in the realm of revenue management and dynamic resource allocation. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 433–448, 2016Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135128/1/nav21704.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/135128/2/nav21704_am.pd

Pricing Analytics for Reusable Resources

First, we consider a fundamental pricing model for a single type of reusable resource in which a fixed number of units are used to serve stochastically arriving customers. Customers choose to purchase the resource based on their willingness-to-pay and the current price. If purchased, occupy one unit of the reusable resources for a random amount of time. The firm seeks to maximize a weighted combination of profit, market share, and service level. We establish a series of theoretical results that characterize the strong universal performance of static pricing in such an environment. Second, we describe a comprehensive approach to pricing analytics for reusable resources in the context of rotable spare parts with an industrial partner. We discuss the process of instilling a new pricing culture and developing a scalable new pricing methodology at a major aircraft manufacturer. We develop a novel pricing analytics approach for all rotable spare parts. The new approach tackles the challenges of limited data availability, minimal demand information, and complex inventory dynamics. We also present a successful large-scale implementation of our approach which led to significant profit gains. Third, we extend the pricing model for reusable resources to the setting of multiple customer classes. We describe two types of heuristics for this class of problem with accompanying numerical experiments. In addition, we provide a universal performance guarantee for a special case. We also discuss the role of substitution effects between different classes of customers