Centralized versus Decentralized Competition for Price and Lead‐Time Sensitive Demand

We study two firms that compete on price and lead‐time decisions in a common market. We explore the impact of decentralizing these decisions, as made by the marketing and production departments, respectively, with either marketing or production as the leader. We compare scenarios in which none, one, or both of the firms are decentralized to see whether decentralization can be the equilibrium strategy. We find that under intense price competition, with intensity characterized by the underlying parameters of market demand, firms may suffer from a decentralized structure, particularly under high flexibility induced by high capacity, where revenue‐based sales incentives motivate sales/marketing to make aggressive price cuts that often erode profit margins. In contrast, under intense lead‐time competition, a decentralized strategy with marketing as the leader can not only result in significantly higher profits, but also be the equilibrium strategy. Moreover, decentralization may no longer lead to lower prices or longer lead‐times if the production department chooses capacity along with lead‐time.      

A Note on the Relationship Among Capacity,Pricing, and Inventory in a Make‐to‐Stock System

We address the simultaneous determination of pricing, production, and capacity investment decisions by a monopolistic firm in a multi‐period setting under demand uncertainty. We analyze the optimal decision with particular emphasis on the relationship between price and capacity. We consider models that allow for either bi‐directional price changes or models with markdowns only, and in the latter case we prove that capacity and price are strategic substitutes.     

Decision Making and the Price Setting Newsvendor: Experimental Evidence

We present an experimental study of the price‐setting newsvendor problem, which extends the traditional framework by allowing the decision maker to determine both the selling price and the order quantity of a given item. We compare behavior under this model with two benchmark conditions where subjects have a single decision to make (price or quantity). We observe that subjects deviate from the theoretical benchmarks when they are tasked with a single decision. They also exhibit anchoring behavior, where their anchor is the expected demand when quantity is the decision variable and is the initial inventory level when price is the decision variable. When decision makers set quantity and price concurrently, we observe no significant difference between the normative (i.e., expected profit‐maximizing) prices and the decision makers’ price choices. Quantity decisions move further from the normative benchmarks (compared to when subjects have a single decision to make) when the ratio of cost to price is less than half. When this ratio is reversed, there is no significant difference between order levels in single‐ and multi‐task settings. In the multidecision framework, we also observe a tendency to match orders and expected demand levels, which subjects can control using prices.     

Quality‐Speed Competition in Customer‐Intensive Services with Boundedly Rational Customers

We consider a system in which two competing servers provide customer‐intensive services and the service reward is affected by the length of service time. The customers are boundedly rational and choose their service providers according to a logit model. We demonstrate that the service provider revenue function is unimodal in the service rate, its decision variable, and show that the service rate competition has a unique and stable equilibrium. We then study the price decision under three scenarios with the price determined by a revenue‐maximizing firm, a welfare‐maximizing social planner, or two servers in competition. We find that the socially optimal price, subject to the requirement that the customer actual utility must be non‐negative, is always lower than the competition equilibrium price which, in turn, is lower than the revenue‐maximizing monopoly price. However, if the customer actual utility is allowed to be negative in social optimization, the socially optimal price can be higher than the other two prices in a large market.     

Ordering,Pricing, and Lead‐Time Quotation Under Lead‐Time and Demand Uncertainty

In this article, we study the newsvendor problem with endogenous setting of price and quoted lead‐time. This problem can be observed in situations where a firm orders semi‐finished product prior to the selling season and customizes the product in response to customer orders during the selling season. The total demand during the selling season and the lead‐time required for customization are uncertain. The demand for the product depends not only on the selling price but also on the quoted lead‐time. To set the quoted lead‐time, the firm has to carefully balance the benefit of increasing demand as the quoted lead‐time is reduced against the cost of increased tardiness. Our model enables the firm to determine the optimal selling price, quoted lead‐time, and order quantity simultaneously, and provides a new set of insights to managers.     

An Advanced Heuristic for Multiple‐Option Spare Parts Procurement after End‐of‐Production

After‐sales service is a major source of profit for many original equipment manufacturers in industries with durable products. Successful engagement in after‐sales service improves customer loyalty and allows for competitive differentiation through superior service like an extended service period during which customers are guaranteed to be provided with service parts. Inventory management during this period is challenging due to the substantial uncertainty concerning demand over a long time horizon. The traditional mechanism of spare parts acquisition is to place a large final order at the end of regular production of the parent product, causing major holding costs and a high level of obsolescence risk. With an increasing length of the service period, more flexibility is needed and can be provided by adding options like extra production and remanufacturing. However, coordinating all three options yields a complicated stochastic dynamic decision problem. For that problem type, we show that a quite simple decision rule with order‐up‐to levels for extra production and remanufacturing is very effective. We propose a heuristic procedure for parameter determination which accounts for the main stochastic and dynamic interactions in decision making, but still consists of relatively simple calculations that can be applied to practical problem sizes. A numerical study reveals that the heuristic performs extremely well under a wide range of conditions, and therefore can be strongly recommended as a decision support tool for the multi‐option spare parts procurement problem. A comparison with decision rules adapted from practice demonstrates that our approach offers an opportunity for major cost reductions.     

Panel Size and Overbooking Decisions for Appointment‐Based Services under Patient No‐Shows

Many service systems that work with appointments, particularly those in healthcare, suffer from high no‐show rates. While there are many reasons why patients become no‐shows, empirical studies found that the probability of a patient being a no‐show typically increases with the patient's appointment delay, i.e., the time between the call for the appointment and the appointment date. This paper investigates how demand and capacity control decisions should be made while taking this relationship into account. We use stylized single server queueing models to model the appointments scheduled for a provider, and consider two different problems. In the first problem, the service capacity is fixed and the decision variable is the panel size; in the second problem, both the panel size and the service capacity (i.e., overbooking level) are decision variables. The objective in both cases is to maximize some net reward function, which reduces to system throughput for the first problem. We give partial or complete characterizations for the optimal decisions, and use these characterizations to provide insights into how optimal decisions depend on patient's no‐show behavior in regards to their appointment delay. These insights especially provide guidance to service providers who are already engaged in or considering interventions such as sending reminders in order to decrease no‐show probabilities. We find that in addition to the magnitudes of patient show‐up probabilities, patients' sensitivity to incremental delays is an important determinant of how demand and capacity decisions should be adjusted in response to anticipated changes in patients' no‐show behavior.     

A Maximum Entropy Joint Demand Estimation and Capacity Control Policy

We propose a tractable, data‐driven demand estimation procedure based on the use of maximum entropy (ME) distributions, and apply it to a stochastic capacity control problem motivated from airline revenue management. Specifically, we study the two fare class “Littlewood” problem in a setting where the firm has access to only potentially censored sales observations; this is also known as the repeated newsvendor problem. We propose a heuristic that iteratively fits an ME distribution to all observed sales data, and in each iteration selects a protection level based on the estimated distribution. When the underlying demand distribution is discrete, we show that the sequence of protection levels converges to the optimal one almost surely, and that the ME demand forecast converges to the true demand distribution for all values below the optimal protection level. That is, the proposed heuristic avoids the “spiral down” effect, making it attractive for problems of joint forecasting and revenue optimization problems in the presence of censored observations.     

A WTP‐Choice Model: Empirical Validation,Competitive and Centralized Pricing

Willingness To Pay (WTP) of customers plays an anchoring role in pricing. This study proposes a new choice model based on WTP, incorporating sequential decision making, where the products with positive utility of purchase are considered in the order of customer preference. We compare WTP‐choice model with the commonly used (multinomial) Logit model with respect to the underlying choice process, information requirement, and independence of irrelevant alternatives. Using WTP‐choice model, we find and compare equilibrium and centrally optimal prices and profits without considering inventory availability. In addition, we compare equilibrium prices and profits in two contexts: without considering inventory availability and under lost sales. One of the interesting results with WTP‐choice model is the “loose coupling” of retailers in competition; prices are not coupled but profits are. That is, each retailer should charge the monopoly price as the collection of these prices constitute an equilibrium but each retailer's profit depends on other retailers' prices. Loose coupling fails with dependence of WTPs or dependence of preference on prices. Also, we show that competition among retailers facing dependent WTPs can cause price cycles under some conditions. We consider real‐life data on sales of yogurt, ketchup, candy melt, and tuna, and check if a version of WTP‐choice model (with uniform, triangle, or shifted exponential WTP distribution), standard or mixed Logit model fits better and predicts the sales better. These empirical tests establish that WTP‐choice model compares well and should be considered as a legitimate alternative to Logit models for studying pricing for products with low price and high frequency of purchase.     

Dynamic Pricing and Demand Estimation for a Single Unique Asset*

We address the situation of a firm that needs to dispose of a large, expensive asset (e.g., car, machine tool, earth mover, turbine, house, airplane), with or without a given deadline (and either known or unknown to the buyer). If a deadline exists, the asset is salvaged at a known value which may be zero, or even negative if there is a disposal cost. The asset has a known holding cost and may also have an initial nominal (undiscounted) price. The question is how, if at all, the price should be discounted as time progresses to maximize the expected proceeds. We use a dynamic recursion where each decision stage can be optimized based on classic economic monopoly pricing theory with a demand intensity function estimated from sales data, and show that the model is well‐behaved in the sense that the optimal price and optimal expected revenue monotonically decline as the deadline approaches. We test the model by comparing its optimal price pattern to the official pricing policy practiced at a used‐car dealer. We then extend the model to situations where the buyer knows the seller's deadline and thus may alter his behavior as the deadline approaches.     

Lot‐sizing Decisions Under Limited‐time Price Reduction*

We consider the optimal lot‐sizing policy for an inventoried item when the vendor offers a limited‐time price reduction. We use the discounted cash flow (DCF) approach in our analysis, thereby eliminating the sources of approximation found in most of the earlier studies that use an average annual cost approach. We first characterize the optimal lot‐sizing policies and their properties, then develop an algorithm for determining the optimal lot sizes. We analytically demonstrate that the lot sizes derived using an average annual cost approach for the different variants of the problem are, in general, larger than the DCF optimum. While DCF analysis is more rigorous and yields precise lot sizes, we recognize that the associated mathematical models and the solution procedure are rather complex. Since simple and easy‐to‐understand policies have a strong practical appeal to decision makers, we propose a DCF version of a simple and easy‐to‐implement heuristic called the “Early Purchase” (EP) strategy and discuss its performance. We supplement our analytical developments with a detailed computational analysis and discuss the implications of our findings for decision making.     

End‐of‐Life Inventory Problem with Phaseout Returns

We consider the service parts end‐of‐life inventory problem of a capital goods manufacturer in the final phase of its life cycle. The final phase starts as soon as the production of parts terminates and continues until the last service contract expires. Final order quantities are considered a popular tactic to sustain service fulfillment obligations and to mitigate the effect of obsolescence. In addition to the final order quantity, other sources to obtain serviceable parts are repairing returned defective items and retrieving parts from phaseout returns. Phaseout returns happen when a customer replaces an old system platform with a next‐generation one and returns the old product to the original equipment manufacturer (OEM). These returns can well serve the demand for service parts of other customers still using the old generation of the product. In this study, we study the decision‐making complications as well as cost‐saving opportunities stemming from phaseout occurrence. We use a finite‐horizon Markov decision process to characterize the structure of the optimal inventory control policy. We show that the optimal policy consists of a time‐varying threshold level for item repair. Furthermore, we study the value of phaseout information by extending the results to cases with an uncertain phaseout quantity or an uncertain schedule. Numerical analysis sheds light on the advantages of the optimal policy compared to some heuristic policies.     

Managing Retail Shelf and Backroom Inventories When Demand Depends on the Shelf‐Stock Level

Inventory displayed on the retail sales floor not only performs the classical supply function but also plays a role in affecting consumers’ buying behavior and hence the total demand. Empirical evidence from the retail industry shows that for some types of products, higher levels of on‐shelf inventory have a demand‐increasing effect (“billboard effect”) while for some other types of products, higher levels of on‐shelf inventory have a demand‐decreasing effect (“scarcity effect”). This suggests that retailers may use the amount of shelf stock on display as a tool to influence demand and operate a store backroom to hold the inventory of items not displayed on the shelves, introducing the need for efficient management of the backroom and on‐shelf inventories. The purpose of this study is to address such an issue by considering a periodic‐review inventory system in which demand in each period is stochastic and depends on the amount of inventory displayed on the shelf. We first analyze the problem in a finite‐horizon setting and show under a general demand model that the system inventory is optimally replenished by a base‐stock policy and the shelf stock is controlled by two critical points representing the target levels to raise up/drop down the on‐shelf inventory level. In the infinite‐horizon setting, we find that the optimal policies simplify to stationary base‐stock type policies. Under the billboard effect, we further show that the optimal policy is monotone in the system states. Numerical experiments illustrate the value of smart backroom management strategy and show that significant profit gains can be obtained by jointly managing the backroom and on‐shelf inventories.     

Pareto‐Improving Contracts for Express Package Delivery Services

We address the problem of an express package delivery company in structuring a long‐term customer contract whose terms may include prices that differ by day‐of‐week and by speed‐of‐service. The company traditionally offered speed‐of‐service pricing to its customers, but without day‐of‐week differentiation, resulting in customer demands with considerable day‐of‐week seasonality. The package delivery company hoped that using day‐of‐week and speed‐of‐service price differentiation for contract customers would induce these customers to adjust their demands to become counter‐cyclical to the non‐contract demand. Although this usually cannot be achieved by pricing alone, we devise an approach that utilizes day‐of‐week and speed‐of‐service pricing as an element of a Pareto‐improving contract. The contract provides the lowest‐cost arrangement for the package delivery company while ensuring that the customer is at least as well off as he would have been under the existing pricing structure. The contract pricing smoothes the package delivery company's demand and reduces peak requirements for transport capacity. The latter helps to decrease capital costs, which may allow a further price reduction for the customer. We formulate the pricing problem as a biconvex optimization model, and present a methodology for designing the contract and numerical examples that illustrate the achievable savings.     

Sequential and Simultaneous Decision Making for Optimizing Health Care Resource Flexibilities

Health care administrators commonly employ two types of resource flexibilities (demand upgrades and staffing flexibility) to efficiently coordinate two critical internal resources, nursing staff and beds, and an external resource (contract nurses) to satisfy stochastic patient demand. Under demand upgrades, when beds are unavailable for patients in a less acute unit, patients are upgraded to a more acute unit if space is available in that unit. Under staffing flexibility, nurses cross‐trained to work in more than one unit are used in addition to dedicated and contract nurses. Resource decisions (beds and staffing) can be made at a single point in time (simultaneous decision making) or at different points in time (sequential decision making). In this article, we address the following questions: for each flexibility configuration, under sequential and simultaneous decision making, what is the optimal resource level required to meet stochastic demand at minimum cost? Is one type of flexibility (e.g., demand upgrades) better than the other type of flexibility (e.g., staffing flexibility)? We use two‐stage stochastic programming to find optimal resource levels for two nonhomogeneous hospital units that face stochastic demand following a continuous, general distribution. We conduct a full‐factorial numerical experiment and find that the benefit of using staffing flexibility on average is greater than the benefit of using demand upgrades. However, the two types of flexibilities have a positive interaction effect and they complement each other. The type of flexibility and decision timing has an independent effect on system performance (capacity and staffing costs). The benefits of cross‐training can be largely realized even if beds and staffing levels have been determined prior to the establishment of a cross‐training initiative.     

Capacity Planning and Allocation for Web‐Based Applications

Motivated by the technology division of a financial services firm, we study the problem of capacity planning and allocation for Web‐based applications. The steady growth in Web traffic has affected the quality of service (QoS) as measured by response time (RT), for numerous e‐businesses. In addition, the lack of understanding of system interactions and availability of proper planning tools has impeded effective capacity management. Managers typically make decisions to add server capacity on an ad hoc basis when systems reach critical response levels. Very often this turns out to be too late and results in extremely long response times and the system crashes. We present an analytical model to understand system interactions with the goal of making better server capacity decisions based on the results. The model studies the relationships and important interactions between the various components of a Web‐based application using a continuous time Markov chain embedded in a queuing network as the basic framework. We use several structured aggregation schemes to appropriately represent a complex system, and demonstrate how the model can be used to quickly predict system performance, which facilitates effective capacity allocation decision making. Using simulation as a benchmark, we show that our model produces results within 5% accuracy at a fraction of the time of simulation, even at high traffic intensities. This knowledge helps managers quickly analyze the performance of the system and better plan server capacity to maintain desirable levels of QoS. We also demonstrate how to utilize a combination of dedicated and shared resources to achieve QoS using fewer servers.     

Distributionally Robust Optimization of Two‐Stage Lot‐Sizing Problems

This paper studies two‐stage lot‐sizing problems with uncertain demand, where lost sales, backlogging and no backlogging are all considered. To handle the ambiguity in the probability distribution of demand, distributionally robust models are established only based on mean‐covariance information about the distribution. Based on shortest path reformulations of lot‐sizing problems, we prove that robust solutions can be obtained by solving mixed 0‐1 conic quadratic programs (CQPs) with mean‐risk objective functions. An exact parametric optimization method is proposed by further reformulating the mixed 0‐1 CQPs as single‐parameter quadratic shortest path problems. Rather than enumerating all potential values of the parameter, which may be the super‐polynomial in the number of decision variables, we propose a branch‐and‐bound‐based interval search method to find the optimal parameter value. Polynomial time algorithms for parametric subproblems with both uncorrelated and partially correlated demand distributions are proposed. Computational results show that the proposed models greatly reduce the system cost variation at the cost of a relative smaller increase in expected system cost, and the proposed parametric optimization method is much more efficient than the CPLEX solver.     

Electricity Time‐of‐Use Tariff with Stochastic Demand

In this article, we study the electricity time‐of‐use (TOU) tariff for an electricity company with stochastic demand. The electricity company offers the flat rate (FR) and TOU tariffs to customers. Under the FR tariff, the customer pays a flat price for electricity consumption in both the peak and non‐peak periods. Under the TOU tariff, the customer pays a high price for electricity consumption in the peak period and a low price for electricity consumption in the non‐peak period. The electricity company uses two technologies, namely the base‐load and peak‐load technologies, to generate electricity. We derive the optimal capacity investment and pricing decisions for the electricity company. Furthermore, we use real data from a case study to validate the results and derive insights for implementing the TOU tariff. We show that in almost all the cases, the electricity company needs less capacity for both technologies under the TOU tariff than under the FR tariff, even though the expected demand in the non‐peak period increases. In addition, except for some extreme cases, there is essentially no signicant reduction in the total demand of the two periods, although the TOU tariff can reduce the demand in the peak period. Under the price‐cap regulation, the customer may pay a lower price on average under the TOU tariff than under the FR tariff. We conduct an extensive numerical study to assess the impacts of the model parameters on the optimal solutions and the robustness of the analytical results, and generate managerial implications of the research findings.     

Cross‐Training with Imperfect Training Schemes

Cross‐training workers is one of the most efficient ways of achieving flexibility in manufacturing and service systems for increasing responsiveness to demand variability. However, it is generally the case that cross‐trained employees are not as productive on a specific task as employees who were originally trained for that task. Also, the productivity of the cross‐trained workers depends on when they are cross‐trained. In this work, we consider a two‐stage model to analyze the effects of variations in productivity levels on cross‐training policies. We define a new metric called achievable capacity and show that it plays a key role in determining the structure of the problem. If cross‐training can be done in a consistent manner, the achievable capacity is not affected when the training is done, which implies that the cross‐training decisions are independent of the opportunity cost of lost demand and are based on a trade‐off between cross‐training costs at different times. When the productivities of workers trained at different times differ, there is a three‐way trade‐off between cross‐training costs at different times and the opportunity cost of lost demand due to lost achievable capacity. We analyze the effects of variability and show that if the productivity levels of workers trained at different times are consistent, the decision maker is inclined to defer the cross‐training decisions as the variability of demand or productivity levels increases. However, when the productivities of workers trained at different times differ, an increase in the variability may make investing more in cross‐training earlier more preferable.