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

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

Bounding Blocking Probabilities and Throughput in Queueing Networks With Buffer Capacity Constraints

this paper, we propose a new technique for estimating the performance of queueing networks with buffer capacity constraints i.e, queueing networks in which some of the buffers have finite capacity. Two performance measures of interest for such systems are the throughput and the blocking probabilities of various customer classes. Our technique allows us to obtain upper and lower bounds on such performance measures for a wide variety of systems. The proposed technique extends the technique of obtaining bounds on the mean delay and throughput of queueing networks described in [10]. It can be described as follows. Assuming the existence of a steady state, we study the evolution of multinomials of the state of the system in steady state. Knowing that such multinomials, if integrable with respect to the invariant measure, cannot evolve in the mean, we obtain constraints on the possible behavior of the system. Using these constraints, with a suitable choice of variables, we obtain linear programs whose values upper and lower bound the performance measures of interest, namely throughput or blocking probabilities. This differs from [10] in that the performance measures on which bounds are obtained are probabilities, and in that multinomials rather than quadratics are used. The main advantage of this new technique is that the computational complexity does not increase with the size of the finite buffers. Also, the technique is applicable to systems in which some buffers have infinite capacity. In some cases the bounds obtained are asymptotically exact, i.e., they approach the exact value as the degree of the multinomial considered increases. Another advantage of the method is that the main computation involved is the solution of a linear program which is rather routine with curre..

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

Pricing in Network Revenue Management Systems with Reusable Resources

This thesis focuses on the problem of pricing reusable products in the network revenue management setting. In a nutshell, dynamic pricing problem concerns pricing and selling a finite inventory of products within a given time horizon so as to maximize the total revenue. Most of the existing literature studies the setting with perishable products in which the products sold are permanently removed from inventory. In this thesis, we tackle a different and arguably more challenging problem with reusable products wherein the products are returned back to the seller upon serving a customer and can be used to serve another customer. This class of problems finds a broad range of applications including hotel management, cloud computing, workforce management, call center service, and car rental management. In the first chapter of the thesis, we address the pricing of reusable resources with advance reservation when the demand function is known as a function of price and the demand follows a Poisson point process. We demonstrate that a simple static pricing policy is asymptotically optimal when demand and capacity are scaled without bound. The performance of the policy is measured as a ratio with respect to the policy that does not exhibit any blocking. We also show that the static policy becomes optimal at a rate close to 1 over the square root of n, where n is a scaling factor. Simulation results show the asymptotic behavior but additionally, it shows that for small-scaled systems, the static pricing policy performs very well relative to the no-blocking policy. In the second chapter of the thesis, we consider the learning variant of the same problem in which the customer’s response to selling price and the demand distribution are not known a priori. Connecting this problem to multi-armed bandits (MAB), we propose a variant of the upper confidence bounds (UCB) algorithm. The setting is different from literature in that capacity constraints exist and booking profile is dynamically updated. We solve an LP in every period where the UCB estimates guides the right-hand side parameter and outputs a distribution over the finite pricing actions. We demonstrate that for some large scaling factor n, with high probability, the seller will always choose the optimum after the testing phase and will not exhibit any blocking. In the third and final chapter of the thesis, we employ unsupervised learning methods to tackle the pricing policy from a practical point-of-view. In particular, model-free reinforcement learning method is used to implicitly learn the transition dynamics that governs the reward process to maximize revenue. Deep neural networks are used to parametrize the action policy and value function and through a simulated environment. We show that the generated pricing policy, using purely data, achieved good performance with respect to traffic, revenue, and blocking.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155046/1/abernal_1.pd