Structural Properties of Markov Modulated Revenue Management Problems

Abstract The admission decision is one of the fundamental categories of demand-management decisions. In the dynamic model of the single-resource capacity control problem, the distribution of demand does not explicitly depend on external conditions. However, in reality, demand may depend on the current external environment which represents the prevailing economic, financial, social or other factors that affect customer behavior. We formulate a Markov Decision Process (MDP) to maximize expected revenues over a finite horizon that explicitly models the current environment. We derive some structural results of the optimal admission policy, including the existence of an environment-dependent thresholds and a comparison of threshold levels in different environments. We also present some computational results which illustrate these structural properties. Finally, we extend some of the results to a related dynamic pricing formulation

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

Optimisation of stochastic networks with blocking: a functional-form approach

This paper introduces a class of stochastic networks with blocking, motivated by applications arising in cellular network planning, mobile cloud computing, and spare parts supply chains. Blocking results in lost revenue due to customers or jobs being permanently removed from the system. We are interested in striking a balance between mitigating blocking by increasing service capacity, and maintaining low costs for service capacity. This problem is further complicated by the stochastic nature of the system. Owing to the complexity of the system there are no analytical results available that formulate and solve the relevant optimization problem in closed form. Traditional simulation-based methods may work well for small instances, but the associated computational costs are prohibitive for networks of realistic size. We propose a hybrid functional-form based approach for finding the optimal resource allocation, combining the speed of an analytical approach with the accuracy of simulation-based optimisation. The key insight is to replace the computationally expensive gradient estimation in simulation optimisation with a closed-form analytical approximation that is calibrated using a single simulation run. We develop two implementations of this approach and conduct extensive computational experiments on complex examples to show that it is capable of substantially improving system performance. We also provide evidence that our approach has substantially lower computational costs compared to stochastic approximation

Dynamic Product Assembly and Inventory Control for Maximum Profit

We consider a manufacturing plant that purchases raw materials for product assembly and then sells the final products to customers. There are M types of raw materials and K types of products, and each product uses a certain subset of raw materials for assembly. The plant operates in slotted time, and every slot it makes decisions about re-stocking materials and pricing the existing products in reaction to (possibly time-varying) material costs and consumer demands. We develop a dynamic purchasing and pricing policy that yields time average profit within epsilon of optimality, for any given epsilon>0, with a worst case storage buffer requirement that is O(1/epsilon). The policy can be implemented easily for large M, K, yields fast convergence times, and is robust to non-ergodic system dynamics.Comment: 32 page

Revenue Management In Manufacturing: A Research Landscape

Revenue management is the science of using past history and current levels of order activity to forecast demand as accurately as possible in order to set and update pricing and product availability decisions across various sales channels to maximize profitability. In much the same way that revenue management has transformed the airline industry in selling tickets for the same flight at markedly different rates based upon product restrictions, time to departure, and the number of unsold seats, many manufacturing companies have started exploring innovative revenue management strategies in an effort to improve their operations and profitability. These strategies employ sophisticated demand forecasting and optimization models that are based on research from many areas, including management science and economics, and that can take advantage of the vast amount of data available through customer relationship management systems in order to calibrate the models. In this paper, we present an overview of revenue management systems and provide an extensive survey of published research along a landscape delineated by three fundamental dimensions of capacity management, pricing, and market segmentation

Stochastic Dynamic Programming and Stochastic Fluid-Flow Models in the Design and Analysis of Web-Server Farms

A Web-server farm is a specialized facility designed specifically for housing Web servers catering to one or more Internet facing Web sites. In this dissertation, stochastic dynamic programming technique is used to obtain the optimal admission control policy with different classes of customers, and stochastic uid- ow models are used to compute the performance measures in the network. The two types of network traffic considered in this research are streaming (guaranteed bandwidth per connection) and elastic (shares available bandwidth equally among connections). We first obtain the optimal admission control policy using stochastic dynamic programming, in which, based on the number of requests of each type being served, a decision is made whether to allow or deny service to an incoming request. In this subproblem, we consider a xed bandwidth capacity server, which allocates the requested bandwidth to the streaming requests and divides all of the remaining bandwidth equally among all of the elastic requests. The performance metric of interest in this case will be the blocking probability of streaming traffic, which will be computed in order to be able to provide Quality of Service (QoS) guarantees. Next, we obtain bounds on the expected waiting time in the system for elastic requests that enter the system. This will be done at the server level in such a way that the total available bandwidth for the requests is constant. Trace data will be converted to an ON-OFF source and fluid- flow models will be used for this analysis. The results are compared with both the mean waiting time obtained by simulating real data, and the expected waiting time obtained using traditional queueing models. Finally, we consider the network of servers and routers within the Web farm where data from servers flows and merges before getting transmitted to the requesting users via the Internet. We compute the waiting time of the elastic requests at intermediate and edge nodes by obtaining the distribution of the out ow of the upstream node. This out ow distribution is obtained by using a methodology based on minimizing the deviations from the constituent in flows. This analysis also helps us to compute waiting times at different bandwidth capacities, and hence obtain a suitable bandwidth to promise or satisfy the QoS guarantees. This research helps in obtaining performance measures for different traffic classes at a Web-server farm so as to be able to promise or provide QoS guarantees; while at the same time helping in utilizing the resources of the server farms efficiently, thereby reducing the operational costs and increasing energy savings

Supply Chain and Revenue Management for Online Retailing

This dissertation focuses on optimizing inventory and pricing decisions in the online retail industry. Motivated by the importance of great customer service quality in the online retail marketplace, we investigate service-level-constrained inventory control problems in both static and dynamic settings. The first essay studies multi-period production planning problems (with or without pricing options) under stochastic demand. A joint service-level constraint is enforced to restrict the joint probability of having backorders in any period. We use the Sample Average Approximation (SAA) approach to reformulate both chance-constrained models as mixed-integer linear programs (MILPs). Via computations of diverse instances, we demonstrate the effectiveness of the SAA approach, analyze the solution feasibility and objective bounds, and conduct sensitivity analysis. The approaches can be generalized to a wide variety of production planning problems. The second essay investigates the dynamic versions of the service-level-constrained inventory control problems, in which retailers have the flexibility to adjust their inventory policies in each period. We formulate two periodic-review stochastic inventory models (backlogging model and remanufacturing model) via Dynamic Programs (DP), and establish the optimality of generalized base-stock policies. We also propose 2-approximation algorithms for both models, which is computationally more efficient than the brute-force DP. The core concept developed in our algorithms is called the delayed marginal cost, which is proven effective in dealing with service-level-constrained inventory systems. The third essay is motivated by the exploding use of sales rank information in today's internet-based e-commerce marketplace. The sales rank affects consumers' shopping preference and therefore, is critical for retailers to utilize when making pricing decisions. We study periodic-review dynamic pricing problems in presence of sales rank, in which customers' demand is a function of both prices and sales rank. We propose rank-based pricing models and characterize the structure and monotonicity of optimal pricing policies. Our numerical experiments illustrate the potential of revenue increases when strategic cyclic policy is used.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144159/1/ycjiang_1.pd

Going Bunkers: The Joint Route Selection and Refueling Problem

Managing shipping vessel profitability is a central problem in marine transportation. We consider two commonly used types of vessels—“liners” (ships whose routes are fixed in advance) and “trampers” (ships for which future route components are selected based on available shipping jobs)—and formulate a vessel profit maximization problem as a stochastic dynamic program. For liner vessels, the profit maximization reduces to the problem of minimizing refueling costs over a given route subject to random fuel prices and limited vessel fuel capacity. Under mild assumptions about the stochastic dynamics of fuel prices at different ports, we provide a characterization of the structural properties of the optimal liner refueling policies. For trampers, the vessel profit maximization combines refueling decisions and route selection, which adds a combinatorial aspect to the problem. We characterize the optimal policy in special cases where prices are constant through time and do not differ across ports and prices are constant through time and differ across ports. The structure of the optimal policy in such special cases yields insights on the complexity of the problem and also guides the construction of heuristics for the general problem setting