The Impact of Revenue‐Maximizing Priority Pricing on Customer Delay Costs

Speed is an increasingly important determinant of which suppliers will be given customers' business and is defined as the time between when an order is placed by the customer and when the product is delivered, or as the amount of time customers must wait before they receive their desired service. In either case, the speed a customer experiences can be enhanced by giving priority to that particular customer. Such a prioritization scheme will necessarily reduce the speed experienced by lower‐priority customers, but this can lead to a better outcome when different customers place different values on speed. We model a single resource (e.g., a manufacturer) that processes jobs from customers who have heterogeneous waiting costs. We analyze the price that maximizes priority revenue for the resource owner (i.e., supplier, manufacturer) under different assumptions regarding customer behavior. We discover that a revenue‐maximizing supplier facing self‐interested customers (i.e., those that independently minimize their own expected costs) charges a price that also minimizes the expected total delay costs across all customers and that this outcome does not result when customers coordinate to submit priority orders at a level that seeks to minimize their aggregate costs of priority fees and delays. Thus, the customers are better off collectively (as is the supplier) when the supplier and customers act independently in their own best interests. Finally, as the number of priority classes increases, both the priority revenues and the overall customer delay costs improve, but at a decreasing rate.     

基于异质性顾客心理期望等待时间的优先权服务定价研究

本文以非抢占式M/M/1排队系统为背景,以企业收益最大化为目标,基于顾客异质性(单位时间等待成本不同)将顾客分为两类,针对顾客的心理期望等待时间对服务提供商最优定价策略的影响进行研究。首先研究优先权顾客心理期望等待时间对企业收益的影响以及相应的优先权定价,然后研究优先权顾客和普通顾客同时存在心理期望等待时间对企业收益的影响和相应的优先权定价。研究表明:仅考虑优先权顾客的心理期望等待时间,企业应通过提高优先权定价来获得最优收益;当优先权顾客和普通顾客同时存在心理期望等待时间时,企业仍然采取提高优先权定价的策略,若普通顾客的价值大(获取服务的基本费用大),企业应对普通顾客提供一定的折扣来消除其心理期望等待时间增加企业收益;如果普通顾客的价值较小,企业应"有意"流失部分普通顾客,吸引更多顾客到优先权队列获取服务来获得更多收益。本文研究对于服务提供商在考虑顾客心理期望等待时间基础上设置最合理的队列机制有一定的指导意义和实际应用价值。     

Two Backorder Compensation Mechanisms in Inventory Systems with Impatient Customers

We study a compensation mechanism design problem with customer‐choice behavior in a continuous review setting where the production and demand processes are stochastic. When a stockout occurs, the firm controls backorders on the basis of certain compensation policies. Customers make decisions to maximize their utility, which is decreasing in the price, the waiting time, and the customer's impatience factor. We assume that the impatience factor is private information held by the customer only. Two compensation mechanisms are designed to control backorders, namely uniform compensation and priority auction with an admission price. Under uniform compensation, the firm offers the same discount to all customers, whereas under auction compensation, priority is granted according to the customers' bid prices. We obtain the optimal stockout price and base stock level under each mechanism, and analyze the properties of the respective optimal policies. Assuming linear waiting costs with uniformly distributed impatience factor, we find that the auction mechanism (1) maintains a lower base stock level and results in greater profit and (2) benefits customers with relatively lower or higher impatience factors, but customers with a medium impatience factor may be rendered worse off. We further show that both compensation mechanisms are suitable for products with a high unit profit, a high lost sales penalty cost, and a high holding cost.     

基于顾客公平偏好的服务机制与定价研究

由于顾客异质性（单位时间等待成本不同）,服务提供商通常对顾客采取分类服务策略,然而分类服务会引起服务系统中不同类型顾客之间等待时间和服务价值的差异性,从而给顾客带来心理上的不公平感,进而引起顾客在服务系统中的流动和转移,进一步影响企业收益和社会福利。本文针对非抢占M/M/1服务系统顾客分类情形为背景,由两种顾客之间期望等待时间的不同和公平偏好参数相结合构建普通顾客的公平心理效用模型,以垄断型服务系统为背景,分别从企业收益、社会福利与顾客效用三个视角进行分析。研究表明,服务提供商应对顾客采取可观测型的分类服务机制来获得最大收益;从社会福利视角,服务提供商应对顾客采取不可观测型的分类服务机制;从顾客效用视角,服务提供商应取消顾客分类服务,仅保留普通顾客。最后同现有结论进行比较分析,并进行拓展研究。本文研究对服务提供商采取合理的服务机制及相应的服务定价具有重要参考价值和指导意义。     

基于顾客不公平规避的服务定价研究

设计合理的服务机制和定价策略对于企业运营至关重要。由于顾客异质性（等待时间成本不同）企业通常对顾客进行分类服务,然而分类服务会引发顾客的不公平心理,并带来负效用,从而引起顾客流动与转移,进而影响企业收益与社会成本。本文针对垄断型服务系统中,顾客不公平规避心理（用参数α表示）对于企业优化目标的影响进行分析,在此基础之上,研究企业是否对顾客采取分类服务以及如何合理定价。结果表明,当顾客不公平规避偏好心理较弱时,从社会成本最小化和企业收益最大化的角度都应该对顾客进行分类服务并收取优先服务费用。当顾客不公规避心理较强时,从企业收益最大化的角度应仅保留优先权顾客并收取优先服务费用,从社会成本最小化的角度则应取消优先服务费用仅保留普通顾客。最后,通过数值模拟和理论分析对上述结论进行验证。     

Are Self‐Service Customers Satisfied or Stuck?

This paper investigates the impact of self‐service technology (SST) usage on customer satisfaction and retention. Specifically, we disentangle the distinct effects of satisfaction and switching costs as drivers of retention among self‐service customers. Our empirical analysis examines 26,924 multi‐channel customers of a nationwide retail bank. We track each customer's channel usage, overall satisfaction, and retention over a 1‐year period. We find that, relative to face‐to‐face service, customers who use self‐service channels for a greater proportion of their transactions are either no more satisfied, or less satisfied with the service they receive, depending on the channel. However, we also find that these same customers are predictably less likely to defect to a competitor if they are heavily reliant on self‐service channels characterized by high switching costs. Through a mediation model, we demonstrate that, when self‐service usage promotes retention, it does so in a way that is consistent with switching costs. As a robustness check, we examine the behavior of channel enthusiasts, who concentrate transactions among specific channels. Relative to more diversified customers, we find that self‐service enthusiasts in low switching cost channels defect with greater frequency, while self‐service enthusiasts in high switching cost channels are retained with greater frequency.     

Self‐Service Operations at Retail Stores: The Role of Inter‐Customer Interactions

Inter‐customer interactions are important to the operation of self‐services in retail settings. More specifically, when self‐service terminals are used as part of customers’ checkout processes in retail operations without the explicit involvement of retailers as the direct service providers, inter‐customer interactions become a significant managerial issue. In this article, we examine the impact of inter‐customer interactions at retail self‐service terminals on customers’ service quality perceptions and repeat purchase intentions at retail stores. We conduct a scenario‐based experimental design (N = 674) using a 2 × 2 factorial design in which inter‐customer interactions are divided into “positive” vs. “negative” and occur during the “waiting” or during the actual “transaction” stages of self‐services at a retail store. We use attribution theory to develop the hypotheses. The results demonstrate that, through their interactions, fellow customers can exert influences on a focal customer's quality perceptions and repeat purchasing intentions toward a retail store. Furthermore, these influences were impacted by how customers attribute blame or assign responsibility toward the retail store. Service operations managers should leverage these interactions by designing into self‐service settings the capacities and interfaces that are best suited for customers’ co‐production of their self‐service experiences.     

Equilibrium Joining Strategies and Optimal Control of a Make‐to‐Stock Queue

We consider a make‐to‐stock, finite‐capacity production system with setup cost and delay‐sensitive customers. To balance the setup and inventory related costs, the production manager adopts a two‐critical‐number control policy, where the production starts when the number of waiting customers reaches a certain level and shuts down when a certain quantity of inventory has accumulated. Once the production is set up, the unit production time follows an exponential distribution. Potential customers arrive according to a Poisson process. Customers are strategic, i.e., they make decisions on whether to stay for the product or to leave without purchase based on their utility values, which depend on the production manager's control decisions. We formulate the problem as a Stackelberg game between the production manager and the customers, where the former is the game leader. We first derive the equilibrium customer purchasing strategy and system performance. We then formulate the expected cost rate function for the production system and present a search algorithm for obtaining the optimal values of the two control variables. We further analyze the characteristics of the optimal solution numerically and compare them with the situation where the customers are non‐strategic.     

Modeling and Managing the Percentage of Satisfied Customers in Hidden and Revealed Waiting Line Systems

We perform an analysis of various queueing systems with an emphasis on estimating a single performance metric. This metric is defined to be the percentage of customers whose actual waiting time was less than their individual waiting time threshold. We label this metric the Percentage of Satisfied Customers (PSC.) This threshold is a reflection of the customers' expectation of a reasonable waiting time in the system given its current state. Cases in which no system state information is available to the customer are referred to as “hidden queues.” For such systems, the waiting time threshold is independent of the length of the waiting line, and it is randomly drawn from a distribution of threshold values for the customer population. The literature generally assumes that such thresholds are exponentially distributed. For these cases, we derive closed form expressions for our performance metric for a variety of possible service time distributions. We also relax this assumption for cases where service times are exponential and derive closed form results for a large class of threshold distributions. We analyze such queues for both single and multi‐server systems. We refer to cases in which customers may observe the length of the line as “revealed” queues.“ We perform a parallel analysis for both single and multi‐server revealed queues. The chief distinction is that for these cases, customers may develop threshold values that are dependent upon the number of customers in the system upon their arrival. The new perspective this paper brings to the modeling of the performance of waiting line systems allows us to rethink and suggest ways to enhance the effectiveness of various managerial options for improving the service quality and customer satisfaction of waiting line systems. We conclude with many useful insights on ways to improve customer satisfaction in waiting line situations that follow directly from our analysis.     

An Analysis of Dual‐Kanban Just‐In‐Time Systems in a Non‐Repetitive Environment

Recent advances in approaches and production technologies for the production of goods and services have made just‐in‐time (JIT) a strong alternative for use in intermittent and small batch production systems, especially when time‐based competition is the norm and a low inventory is a must. However, the conventional JIT system is designed for mass production with a stable master production schedule. This paper suggests supplementing the information provided by production kanbans with information about customer waiting lines to be used by operators to schedule production in each work‐station of intermittent and small batch production systems. This paper uses simulation to analyze the effect of four scheduling policy variables—number of kanbans, length of the withdrawal cycle, information about customer waiting lines, and priority rules on two performance measures—customer wait‐time and inventory. The results show that using information about customer waiting lines reduces customer wait‐time by about 30% while also reducing inventory by about 2%. In addition, the effect of information about customer waiting lines overshadows the effect of priority rules on customer wait‐time and inventory.     

A Queueing Theoretic Approach to Set Staffing Levels in Time‐Dependent Dual‐Class Service Systems*

This article addresses the optimal staffing problem for a nonpreemptive priority queue with two customer classes and a time‐dependent arrival rate. The problem is related to several important service settings such as call centers and emergency departments where the customers are grouped into two classes of “high priority” and “low priority,” and the services are typically evaluated according to the proportion of customers who are responded to within targeted response times. To date, only approximation methods have been explored to generate staffing requirements for time‐dependent dual‐class services, but we propose a tractable numerical approach to evaluate system behavior and generate safe minimum staffing levels using mixed discrete‐continuous time Markov chains (MDCTMCs). Our approach is delicate in that it accounts for the behavior of the system under a number of different rules that may be imposed on staff if they are busy when due to leave and involves explicitly calculating delay distributions for two customer classes. Ultimately, we embed our methodology in a proposed extension of the Euler method, coined Euler Pri, that can cope with two customer classes, and use it to recommend staffing levels for the Welsh Ambulance Service Trust (WAST).     

Pricing in a Transportation Station with Strategic Customers

We consider a transportation station, where customers arrive according to a Poisson process, observe the delay information and the fee imposed by the administrator and decide whether to use the facility or not. A transportation facility visits the station according to a renewal process and serves all present customers at each visit. We assume that every customer maximizes her individual expected utility and the administrator is a profit maximizer. We model this situation as a two‐stage game among the customers and the administrator, where customer strategies depend on the level of delay information provided by the administrator. We consider three cases distinguished by the level of delay information: observable (the exact waiting time is announced), unobservable (no information is provided) and partially observable (the number of waiting customers is announced). In each case, we explore how the customer reward for service, the unit waiting cost, and the intervisit time distribution parameters affect the customer behavior and the fee imposed by the administrator. We then compare the three cases and show that the customers almost always prefer to know their exact waiting times whereas the administrator prefers to provide either no information or the exact waiting time depending on system parameters.     

Customer Learning Processes,Strategy Selection,and Performance in Business‐to‐Business Service Firms*

Learning about customers takes place through relevant dialogues with those customers, also known as customer relationship management (CRM). As relationships develop, information about the customer is gathered in the firm's customer information systems (CIS): the content, processes, and assets associated with gathering and moving customer information throughout the firm. This research develops a measure of CIS management capabilities based on learning organization theory and measured by the ability to get, store, move, and use information throughout the business unit. This measure is then used to analyze customer learning processes and associated performance in the context of marketing strategic decision making. This study of 209 business services firms finds that generic marketing strategy positioning (low‐cost and differentiation) and the marketing tactics of personalization and customization are related to CIS development. Customer information systems development in turn is associated with higher levels of customer‐based performance, which in turn is associated with increased business growth. Since the strongest association with customer‐based performance is strategy selection, the long‐term benefits of the knowledge gained from the CIS may be in the ability to assist in measuring customer‐based performance, rather than in the ability to immediately contribute to performance. Finally, for these firms, customization and personalization are not directly associated with performance and thus may not be necessary to support every firm's marketing strategy.     

基于顾客心理期望等待时间的服务策略研究

顾客在排队系统获取服务时,会存在心理上的期望等待时间,该期望会影响顾客在排队系统中的行为变化和流动,从而影响企业收益。本文以传统的M/M/1排队系统为背景,基于顾客存在期望等待时间的前提下,以企业收益最大化为优化目标进行研究。首先,对相应基础理论和模型假设进行介绍;其次,对顾客存在心理期望等待时间情形提出三种新的策略：重新定价、通过折扣对顾客期望值进行调整、提高服务率;然后,分别对上述三种策略进行优化分析,并同现有结果进行比较;研究表明：三种策略都比维持原有定价带来更大收益;当折扣力度较小时或顾客对费用感知强于时间感知时,折扣策略优于重新定价策略;当折扣力度较大或顾客对时间感知强于费用感知时,重新定价策略优于折扣策略;最后,通过对最优结果分析提出相应管理启示。本文的研究对于顾客存在心理期望等待时间的服务定价具有重要的指导意义和实际应用价值。     

A Stochastic Inventory Model With Fast‐Ship Commitments

We present a multiperiod model of a retail supply chain, consisting of a single supplier and a single retailer, in which regular replenishment occurs periodically but players have the option to support fast delivery when customers experience a stockout during a replenishment period. Because expedited shipments increase the supplier's transportation cost, and possibly production/inventory costs, the supplier typically charges a markup over and above the prevailing wholesale price for fast‐shipped items. When fast shipping is not supported, items are backordered if customers are willing to wait until the start of the next replenishment period. We characterize the retailers and the supplier's optimal stocking and production policies and then utilize our analytical framework to study how the two players respond to changes in supply chain parameters. We identify a sufficient condition such that the centralized supply chain is better off with the fast‐ship option. We find a range of markups for fast‐ship orders such that the fast‐ship option is preferred by both the supplier and the retailer in a decentralized chain. However, a markup that is a win–win for both players may not exist even when offering fast‐ship option is better for the centralized chain. Our analysis also shows that depending on how the markup is determined, greater customer participation in fast‐ship orders does not necessarily imply more profits for the two players. For some predetermined markups, the retailer's profit with the fast‐ship option is higher when more customers are willing to wait. However, the retailer may not be able to benefit from the fast‐ship option because the supplier may choose not to support the fast‐ship option when fast‐ship participation increases due to the fact that the fast‐ship participation rate adversely affects the initial order size.     

Option Contracts and Capacity Management—Enabling Price Discrimination under Demand Uncertainty

We explore using an option contract as a price discrimination tool under demand uncertainty. In our capacity game model, a monopolistic supplier has to build capacity before observing the uncertain demand. The demand is generated by two potential customers, who privately know their own types. The types could be either high or low, differing in willingness to pay for each unit of demand. To discriminate between the customer types, the supplier designs option contracts so that only the high type will buy options in advance. The high type will do so because the options can hedge their risk of demand loss when capacity is tight. The supplier profits in three ways. First, the high type customers pay higher marginal prices on average. Second, the high type customers' demand is satisfied as a first priority, guaranteeing allocation efficiency. Third, the supplier can observe the number of options being purchased and so determine customer types, improving capacity investment efficiency. We compare our results to those of classical second degree price discrimination. We show that our proposed framework guarantees the same level of supplier profit even when the supplier cannot discriminate between the customers by bundling products.     

Customer‐Base Concentration and Inventory Efficiencies: Evidence from the Manufacturing Sector

What is the link between customer‐base concentration and inventory efficiencies in the manufacturing sector? Using hand‐collected data from 10‐K Filings, we find that manufacturers with more concentrated customer bases hold fewer inventories for less time and are less likely to end up with excess inventories, as indicated by the lower likelihood and magnitude of inventory write‐downs and reversals. Using disaggregated inventory disclosures, we find that inventory efficiencies primarily flow through the finished goods inventory account, while raw material efficiencies are offset by higher work‐in‐process holdings and longer work‐in‐process cycles. In additional analysis, we document a valuation premium for more concentrated manufacturers after controlling for other firm characteristics, including default risk and cost of capital estimates. We conclude that investors trade off the costs and benefits of relationships with a limited number of major customers and, on balance, consider customer‐base concentration as a net positive for firm valuation. Overall, our study adds to interdisciplinary research in accounting and operations management by shedding new light on the relevance of major customer disclosures for fundamental analysis and valuation in the manufacturing sector.     

Revenue Management with End‐of‐Period Discounts in the Presence of Customer Learning

Consider a firm that sells identical products over a series of selling periods (e.g., weekly all‐inclusive vacations at the same resort). To stimulate demand and enhance revenue, in some periods, the firm may choose to offer a part of its available inventory at a discount. As customers learn to expect such discounts, a fraction may wait rather than purchase at a regular price. A problem the firm faces is how to incorporate this waiting and learning into its revenue management decisions. To address this problem we summarize two types of learning behaviors and propose a general model that allows for both stochastic consumer demand and stochastic waiting. For the case with two customer classes, we develop a novel solution approach to the resulting dynamic program. We then examine two simplified models, where either the demand or the waiting behavior are deterministic, and present the solution in a closed form. We extend the model to incorporate three customer classes and discuss the effects of overselling the capacity and bumping customers. Through numerical simulations we study the value of offering end‐of‐period deals optimally and analyze how this value changes under different consumer behavior and demand scenarios.     

Optimal Temporal Customer Purchasing Decisions Under Trade‐In Programs with Up‐Front Fees

To entice customers to purchase both current and new generation products over time, many firms offer different trade‐in programs including programs that require customers to pay an up‐front fee. To examine the effectiveness of the trade‐in programs, we develop a two‐period model in which a firm sells the first generation product in the first period and the second generation product in the second period; however, the firm offers a trade‐in program that customers can participate in when purchasing the first generation product in the first period. To participate, each customer has to pay a nonrefundable fee in the first period so that she has the option to trade‐in her first generation product and receive a prespecified trade‐in value to be used for the purchase of the second generation product in the second period. To capture market heterogeneity and market uncertainty, we examine the case when the valuation of the first generation product varies among customers and the valuation of the second generation product is uncertain a priori. By analyzing a two‐period game, we determine the optimal purchasing behavior of each rational customer, and we show that the firm is always better off by offering its own trade‐in programs. Also, our numerical analysis reveals that trade‐in programs can benefit the firm significantly especially when (i) the residual value of the first generation product is high; (ii) the expected incremental value of the second generation product is high; or (iii) the valuation of the second generation product is highly uncertain.     

A NOTE ON RENEGING DECISIONS

This note is an extension of the approach to the problem of reneging introduced in Parkan and Warren [1]. It is assumed customers consider joining an M/M/1 queuing system with a prior gamma distribution over the values of the mean service time. Thus, each customer has an initial estimate of his total waiting time in the system. The customers associate the same sunk value with the waiting time and obtain the same reward at service completion. Having joined a system each customer may consider reneging in view of his revision of his initial service time estimate based on service observations. The bounds on the stationary state probabilities for such a system are obtained and examples are provided to compare the cases with and without reneging.