A nonatomic‐game model for timing clearance sales under competition

We deal with dynamic revenue management (RM) under competition using the nonatomic‐game approach. Here, a continuum of heterogeneous sellers try to sell the same product over a given time horizon. Each seller can lower his price once at the time of his own choosing, and faces Poisson demand arrival with a rate that is the product of a price‐sensitive term and a market‐dependent term. Different types of sellers interact, and their respective prices help shape the overall market in which they operate, thereby influencing the behavior of all sellers. Using the infinite‐seller approximation, which deprives any individual seller of his influence over the entire market, we show the existence of a certain pattern of seller behaviors that collectively produce an environment to which the behavior pattern forms a best response. Such equilibrium behaviors point to the suitability of threshold‐like pricing policies. Our computational study yields insights to RM under competition, such as profound ways in which consumer and competitor types influence seller behaviors and market conditions. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 365–385, 2014     

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, 2016     

Optimal inventory and dynamic admission policies for a retailer of seasonal products with affiliate programs and drop‐shipping

This article investigates the optimal inventory and admission policies for a “Clicks‐and‐Bricks” retailer of seasonal products that, in addition to selling through its own physical and online stores, also sells through third‐party websites by means of affiliate programs. Through postings on partners' webpages, an affiliate program allows a retailer to attract customers who would otherwise be missed. However, this retailer needs to pay a commission for each sale that originates from the website operators participating in the program. The retailer may also refer online orders to other sources (such as distributors and manufacturers) for fulfillment through a drop‐shipping agreement and thus earns commissions. This would be an option when, for example, the inventories at the physical stores were running low. Therefore, during the selling horizon, the retailer needs to dynamically control the opening/closing of affiliate programs and decide on the fulfillment option for online orders. On the basis of a discrete‐time dynamic programming model, the optimal admission policy of the retailer is investigated in this paper, and the structural properties of the revenue function are characterized. Numerical examples are given to show the revenue impact of optimal admission control. The optimal initial stocking decisions at the physical stores are also studied. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Flexible capacity strategy in an asymmetric oligopoly market with competition and demand uncertainty

This article studies flexible capacity strategy (FCS) under oligopoly competition with uncertain demand. Each firm utilizes either the FCS or inflexible capacity strategy (IFCS). Flexible firms can postpone their productions until observing the actual demand, whereas inflexible firms cannot. We formulate a new asymmetrical oligopoly model for the problem, and obtain capacity and production decisions of the firms at Nash equilibrium. It is interesting to verify that cross‐group competition determines the capacity allocation between the two groups of firms, while intergroup competition determines the market share within each group. Moreover, we show that the two strategies coexist among firms only when cost differentiation is medium. Counterintuitively, flexible firms benefit from increasing production cost when the inflexible competition intensity is sufficiently high. This is because of retreat of inflexible firms, flexibility effect, and the corresponding high price. We identify conditions under which FCS is superior than IFCS. We also demonstrate that flexible firms benefit from increasing demand uncertainty. However, when demand variance is not very large, flexible firms may be disadvantaged. We further investigate the effects of cross‐group and intergroup competition on individual performance of the firms. We show that as flexible competition intensity increases, inflexible firms are mainly affected by the cross‐group competition first and then by the intergroup competition, whereas flexible firms are mainly affected by the intergroup competition. Finally, we examine endogenous flexibility and identify its three drivers: cost parameters, cross‐group competition, and intergroup competition. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 117–138, 2017     

A refined deterministic linear program for the network revenue management problem with customer choice behavior

We present a new deterministic linear program for the network revenue management problem with customer choice behavior. The novel aspect of our linear program is that it naturally generates bid prices that depend on how much time is left until the time of departure. Similar to the earlier linear program used by van Ryzin and Liu (2004), the optimal objective value of our linear program provides an upper bound on the optimal total expected revenue over the planning horizon. In addition, the percent gap between the optimal objective value of our linear program and the optimal total expected revenue diminishes in an asymptotic regime where the leg capacities and the number of time periods in the planning horizon increase linearly with the same rate. Computational experiments indicate that when compared with the linear program that appears in the existing literature, our linear program can provide tighter upper bounds, and the control policies that are based on our linear program can obtain higher total expected revenues. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Discounted production scheduling and employment smoothing

We consider the problem of minimizing the sum of production, employment smoothing, and inventory costs over a finite number of time periods where demands are known. The fundamental difference between our model and that treated in [1] is that here we permit the smoothing cost to be nonstationary, thereby admitting a model with discounting. We show that the values of the instrumental variables are nondecreasing in time when demands are nondecreasing. We also derive some asymptotic properties of optimal policies.     

Untruthful probabilistic demand forecasts in vendor‐managed revenue‐sharing contracts: Coordinating the chain

Vendor‐managed revenue‐sharing arrangements are common in the newspaper and other industries. Under such arrangements, the supplier decides on the level of inventory while the retailer effectively operates under consignment, sharing the sales revenue with his supplier. We consider the case where the supplier is unable to predict demand, and must base her decisions on the retailer‐supplied probabilistic forecast for demand. We show that the retailer's best choice of a distribution to report to his supplier will not be the true demand distribution, but instead will be a degenerate distribution that surprisingly induces the supplier to provide the system‐optimal inventory quantity. (To maintain credibility, the retailer's reports of daily sales must then be consistent with his supplied forecast.) This result is robust under nonlinear production costs and nonlinear revenue‐sharing. However, if the retailer does not know the supplier's production cost, the forecast “improves” and could even be truthful. That, however, causes the supplier's order quantity to be suboptimal for the overall system. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Economic and environmental impacts of vertical and horizontal competition and integration

We explore the economic and environmental impacts of market structures (competition or integration at vertical and horizontal levels). We consider a bilateral duopoly consisting of two manufacturers and two retailers in which each manufacturer offers a wholesale price contract to the respective retailer. The manufacturers decide on wholesale prices and abatement efforts concerning pollution emissions related to manufacturing processes, whereas the retailers compete in quantities in the consumer market. To understand the comprehensive effects of market structures on economic competitiveness and environmental sustainability, we examine a measure of eco‐friendly social welfare, which is the ratio of social welfare and environmental pollution. Interestingly, we find that the market structures that have been believed to be more efficient are less efficient from a broader perspective: (1) double marginalization can generate higher eco‐friendly social welfare, and (2) horizontal competition between firms can result in lower eco‐friendly social welfare. Although vertical integration and horizontal competition yield greater social welfare by facilitating more production activities, these market structures often fail to induce sufficient abatement efforts to balance the polluting effect of the large volume, resulting in more significant environmental degradation. We also show that, despite the pollution‐curbing effect, higher emission penalties can result in less eco‐friendly social welfare. They can even curtail the abatement efforts of firms under particular circumstances. When products become more substitutable, the eco‐friendly social welfare can decrease depending upon the market structure.     

Inventory control and periodic price discounting campaigns

This paper develops an inventory model that determines replenishment strategies for buyers facing situations in which sellers offer price‐discounting campaigns at random times as a way to drive sales or clear excess inventory. Specifically, the model deals with the inventory of a single item that is maintained to meet a constant demand over time. The item can be purchased at two different prices denoted high and low. We assume that the low price goes into effect at random points in time following an exponential distribution and lasts for a random length of time following another exponential distribution. We highlight a replenishment strategy that will lead to the lowest inventory holding and ordering costs possible. This strategy is to replenish inventory only when current levels are below a certain threshold when the low price is offered and the replenishment is to a higher order‐up‐to level than the one currently in use when inventory depletes to zero and the price is high. Our analysis provides new insight into the behavior of the optimal replenishment strategy in response to changes in the ratio of purchase prices together with changes in the ratio of the duration of a low‐price period to that of a high‐price period. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007.     

Sojourn times in a two‐stage queueing network with blocking

The model considered in this paper involves a tandem queue consisting of a sequence of two waiting lines. The main feature of our model is blocking, i.e., as soon as the second waiting line reaches a certain upper limit, the first line is blocked. The input of units to the tandem queue is the MAP (Markovian arrival process), and service requirements are of phase type. Our objective is to study the sojourn time distribution under the first‐come‐first‐serve discipline by analyzing the sojourn time through times until absorption in appropriately defined quasi‐birth‐and‐death processes and continuous‐time Markov chains. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

A dynamic inventory system with recycling

This paper deals with a periodic review inventory system in which a constant proportion of stock issued to meet demand each period feeds back into the inventory after a fixed number of periods. Various applications of the model are discussed, including blood bank management and the control of reparable item inventories. We assume that on hand inventory is subject to proportional decay. Demands in successive periods are assumed to be independent identically distributed random variables. The functional equation defining an optimal policy is formulated and a myopic base stock approximation is developed. This myopic policy is shown to be optimal for the case where the feedback delay is equal to one period. Both cost and ordering decision comparisons for optimal and myopic policies are carried out numerically for a delay time of two periods over a wide range of input parameter values.     

A sequential dynamic pricing model and its applications

Consider a sequential dynamic pricing model where a seller sells a given stock to a random number of customers. Arriving one at a time, each customer will purchase one item if the product price is lower than her personal reservation price. The seller's objective is to post a potentially different price for each customer in order to maximize the expected total revenue. We formulate the seller's problem as a stochastic dynamic programming model, and develop an algorithm to compute the optimal policy. We then apply the results from this sequential dynamic pricing model to the case where customers arrive according to a continuous‐time point process. In particular, we derive tight bounds for the optimal expected revenue, and develop an asymptotically optimal heuristic policy. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Optimal replacement of continuously degrading systems in partially observed environments

Motivated by wind energy applications, we consider the problem of optimally replacing a stochastically degrading component that resides and operates in a partially observable environment. The component's rate of degradation is modulated by the stochastic environment process, and the component fails when it is accumulated degradation first reaches a fixed threshold. Assuming periodic inspection of the component, the objective is to minimize the long‐run average cost per unit time of performing preventive and reactive replacements for two distinct cases. The first case examines instantaneous replacements and fixed costs, while the second considers time‐consuming replacements and revenue losses accrued during periods of unavailability. Formulated and solved are mixed state space, partially observable Markov decision process models, both of which reveal the optimality of environment‐dependent threshold policies with respect to the component's cumulative degradation level. Additionally, it is shown that for each degradation value, a threshold policy with respect to the environment belief state is optimal if the environment alternates between two states. The threshold policies are illustrated by way of numerical examples using both synthetic and real wind turbine data. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 395–415, 2015     

Optimal staffing in nonstationary service centers with constraints

This paper considers optimal staffing in service centers. We construct models for profit and cost centers using dynamic rate queues. To allow for practical optimal controls, we approximate the queueing process using a Gaussian random variable with equal mean and variance. We then appeal to the Pontryagin's maximum principle to derive a closed form square root staffing (SRS) rule for optimal staffing. Unlike most traditional SRS formulas, the main parameter in our formula is not the probability of delay but rather a cost‐to‐benefit ratio that depends on the shadow price. We show that the delay experienced by customers can be interpreted in terms of this ratio. Throughout the article, we provide theoretical support of our analysis and conduct extensive numerical experiments to reinforce our findings. To this end, various scenarios are considered to evaluate the change in the staffing levels as the cost‐to‐benefit ratio changes. We also assess the change in the service grade and the effects of a service‐level agreement constraint. Our analysis indicates that the variation in the ratio of customer abandonment over service rate particularly influences staffing levels and can lead to drastically different policies between profit and cost service centers. Our main contribution is the introduction of new analysis and managerial insights into the nonstationary optimal staffing of service centers, especially when the objective is to maximize profitability. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 615–630, 2017     

Designing and pricing menus of extended warranty contracts

Extended warranties provide “piece of mind” to a consumer in that product failures which occur after the base warranty expires are rectified at little or no cost. They also provide an additional source of revenue for manufacturers or third‐party providers, such as retailers or insurance providers, and help cultivate consumer loyalty. In this article, we analyze a number of extended warranty contracts which differ in design, including restrictions on deferrals and renewals. With the use of dynamic programming, we compute the optimal strategy for a consumer with perfect information and determine the optimal pricing policy for the provider given the consumer's risk characterization. We also provide insight into when different contracts should be issued. Finally, we illustrate how profits can be dramatically increased by offering menus of warranty contracts, as opposed to stand alone contracts, with the use of integer programming. Surprisingly, risk‐taking consumers provide the greatest benefit to offering menus. These insights can help a company develop a comprehensive warranty planning strategy for given products or product lines. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Coordination mechanisms for a three‐stage reverse supply chain to increase profitable returns

In this article, we consider a generic electronic product that can be remanufactured or recycled at the end of its life cycle to generate new profit. We first describe the product return process and then present a customer segmentation model to capture consumers' different behaviors with respect to product return so that the retailer can work more effectively to increase the return volume. In regard to the collaboration between the retailer and the manufacturer, we explore a revenue‐sharing coordination mechanism for achieving a win‐win outcome. The optimality and sensitivity of the critical parameters in four strategies are obtained and examined both theoretically and numerically, which generate insights on how to manage an efficient consumer‐retailer‐manufacturer reverse supply chain, as well as on the feasibility of simplifying such a three‐stage chain structure. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Environmental regulation in project‐based industries

We study the environmental regulation of industrial activities that are organized as projects. Applications arise in construction, ship and aircraft building, and film making, among other industries. Relative to manufacturing, environmental regulation is different in project‐based industries, due to the uniqueness and geographical diversity of projects, and a lack of product takeback programs. Because the amount of waste and pollution generated by project companies can be large, regulators need environmental policies to ensure reduction of waste and pollution. We consider a regulator who attempts to maximize social welfare. We model this problem as a bilevel nonlinear program. The upper level regulator specifies waste reduction targets, which the lower level project companies meet using waste stream reduction and remediation of pollution, while attempting to control their project costs. We find that high waste diversion targets lead to outcomes with little pollution, but excessive project costs and only modest waste stream reduction. Projects that have lower task precedence density, or that have pollutants with different environmental impacts, show larger increases in project cost and time resulting from regulation. We describe a subsidy for waste stream reduction that coordinates the system, and we estimate the value of coordination. We also describe a bonus that encourages truthful reporting by project companies, and evaluate the relative cost and effectiveness of the subsidy and the bonus. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 228–247, 2015     

“Government contracting options: A model and application“∗

This paper models and simulates a government‐contractor principal‐agent weapon system repair model. Insights are derived as to how government repair contracts should be constructed so as to induce optimal contractor behavior. The paper's general conclusion is that the best contracting approach combines a lump‐sum payment that does not vary with the number of units repaired, expensive item cost‐sharing, and a contractor‐provided availability guarantee. Provided there is intercontractor competition, this type of contract performs well even if the government is poorly informed about weapon system break patterns or repair costs.     

Formulations for dynamic lot sizing with service levels

In this article, we study deterministic dynamic lot‐sizing problems with a service‐level constraint on the total number of periods in which backlogs can occur over a finite planning horizon. We give a natural mixed integer programming formulation for the single item problem (LS‐SL‐I) and study the structure of its solution. We show that an optimal solution to this problem can be found in \begin{align*}\mathcal O(n^2\kappa)\end{align*} time, where n is the planning horizon and \begin{align*}\kappa=\mathcal O(n)\end{align*} is the maximum number of periods in which demand can be backlogged. Using the proposed shortest path algorithms, we develop alternative tight extended formulations for LS‐SL‐I and one of its relaxations, which we refer to as uncapacitated lot sizing with setups for stocks and backlogs. {We show that this relaxation also appears as a substructure in a lot‐sizing problem which limits the total amount of a period's demand met from a later period, across all periods.} We report computational results that compare the natural and extended formulations on multi‐item service‐level constrained instances. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Many‐server loss models with non‐poisson time‐varying arrivals

This article proposes an approximation for the blocking probability in a many‐server loss model with a non‐Poisson time‐varying arrival process and flexible staffing (number of servers) and shows that it can be used to set staffing levels to stabilize the time‐varying blocking probability at a target level. Because the blocking probabilities necessarily change dramatically after each staffing change, we randomize the time of each staffing change about the planned time. We apply simulation to show that (i) the blocking probabilities cannot be stabilized without some form of randomization, (ii) the new staffing algorithm with randomiation can stabilize blocking probabilities at target levels and (iii) the required staffing can be quite different when the Poisson assumption is dropped. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 177–202, 2017