Competition and Coordination in Two‐Tier Public Service Systems under Government Fiscal Policy

As a result of government budgetary limits and rapid market growth, many public service systems—such as health care—are characterized by extensive customer wait times that have become a serious problem. This problem might be solved by allowing private firms to enter these markets, which would provide customers with a choice between a free (governmental) public service provider (SP) and a fee‐charging (or “toll”) private SP. In such a two‐tier service system, the two SPs are differentiated by service quality and cost efficiency. This study focuses on the competition and coordination issues for two‐tier service systems with customers who are sensitive to both service quality and delay. The free system attempts to maximize its expected total customer utility with limited capacity, whereas the toll system attempts to maximize its profit. Neither goal is aligned with the social welfare goal of the public service. To achieve the social welfare goal, the government plays a crucial role in coordinating the two‐tier service system via the budget, the tradeoff of social members' goals, and tax‐subsidy policies. Using a mixed duopoly game, we establish Nash equilibrium strategies and identify the conditions for the existence of the two‐tier service system. We employ several interesting and counter‐intuitive managerial insights generated by the model to show that the public service can be delivered more efficiently via customer choice and SP competition. In addition, we show that a relatively low tax‐subsidy rate can almost perfectly coordinate the two SPs to achieve most of the maximum possible benefit of the two‐tier service system.     

Call Center Delay Announcement Using a Newsvendor‐Like Performance Criterion

The problem of estimating delays experienced by customers with different priorities, and the determination of the appropriate delay announcement to these customers, in a multi‐class call center with time varying parameters, abandonments, and retrials is considered. The system is approximately modeled as an M(t)/M/s(t) queue with priorities, thus ignoring some of the real features like abandonments and retrials. Two delay estimators are proposed and tested in a series of simulation experiments. Making use of actual state‐dependent waiting time data from this call center, the delay announcements from the estimated delay distributions that minimize a newsvendor‐like cost function are considered. The performance of these announcements is also compared to announcing the mean delay. We find that an Erlang distribution‐based estimator performs well for a range of different under‐announcement penalty to over‐announcement penalty ratios.     

Replenishment Policies for Multi‐Product Stochastic Inventory Systems with Correlated Demand and Joint‐Replenishment Costs

This study analyzes optimal replenishment policies that minimize expected discounted cost of multi‐product stochastic inventory systems. The distinguishing feature of the multi‐product inventory system that we analyze is the existence of correlated demand and joint‐replenishment costs across multiple products. Our objective is to understand the structure of the optimal policy and use this structure to construct a heuristic method that can solve problems set in real‐world sizes/dimensions. Using an MDP formulation we first compute the optimal policy. The optimal policy can only be computed for problems with a small number of product types due to the curse of dimensionality. Hence, using the insight gained from the optimal policy, we propose a class of policies that captures the impact of demand correlation on the structure of the optimal policy. We call this class (s, c, d, S)‐policies, and also develop an algorithm to compute good policies in this class, for large multi‐product problems. Finally using an exhaustive set of computational examples we show that policies in this class very closely approximate the optimal policy and can outperform policies analyzed in prior literature which assume independent demand. We have also included examples that illustrate performance under the average cost objective.     

Would Allowing Privately Funded Health Care Reduce Public Waiting Time? Theory and Empirical Evidence from Canadian Joint Replacement Surgery Data

This study develops a theoretical model and then, using Canadian joint replacement surgery data, empirically tests the relationship between government policies that promote privately funded health care and patients’ waiting time in the public health care system. Two policies are tested: one policy allows opt‐out physicians to extra‐bill private patients, and the other provides public subsidies to private patients. We find that both policies are associated with shorter public waiting time, and that the subsidy policy appears to be more effective in waiting time reduction than the extra‐billing policy. Our findings are consistent with a dominant demand‐side effect in that these policies would provide patients an option, and some incentive, to opt out of the public health system, shifting the demand from the public health system to the private care market.     

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。     

投资政策不确定条件下的寡头发电容量投资分析

投资政策是影响发电容量投资策略的重要因素之一。论文运用实物期权理论,构建电力需求与投资政策双重不确定条件下的发电容量投资模型,在模型的求解与分析基础上,对两个投资阈值进行数值仿真分析,分析结果表明：（1）当投资补贴比率较低时,取消“投资补贴”政策预期越大,发电商越延迟其容量投资,而当补贴比率较高时则抢先投资,在“投资补贴”政策即将被取消时发电商投资积极性最大;（2）实施“投资补贴”政策预期越大,发电商越延迟其容量投资,在“投资补贴”政策即将实施时发电商尽最大可能延迟其投资。     

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.     

Optimal Policies for Perishable Products When Transportation to Export Market Is Disrupted

We consider a problem where a firm produces a variety of fresh products to supply two markets: an export market and a local market. A public transportation service is utilized to deliver the products to the export market, which is cheap, but its schedule is often disrupted severely. Each time this happens, the firm faces the following questions. (i) For a product that has been finished and is waiting for delivery to the export market, should it continue to wait, at an increasing risk of decay, and when should the waiting be terminated and the product be put to the local market? (ii) For a product that has not been finished, should its processing be postponed, so as to reduce the loss from decay after its completion? (iii) What is the best sequence to process the remaining products, according to the information available? We develop, in this study, a model to address these and other related questions. We find optimal policies that minimize the total expected loss in both the make‐to‐order and make‐to‐stock production systems, respectively. For each finished product, we reveal relationships among the desirable waiting time, the price at the local market, and the decaying cost. For unfinished products, we find the optimal start times and processing sequence. Numerical experiments are also conducted to evaluate the optimal policies.     

Finding the anti-block vital edge of a shortest path between two nodes

Let P _G (s,t) denote a shortest path between two nodes s and t in an undirected graph G with nonnegative edge weights. A detour at a node u∈P _G (s,t)=(s,…,u,v,…,t) is defined as a shortest path P _G−e (u,t) from u to t which does not make use of (u,v). In this paper, we focus on the problem of finding an edge e=(u,v)∈P _G (s,t) whose removal produces a detour at node u such that the ratio of the length of P _G−e (u,t) to the length of P _G (u,t) is maximum. We define such an edge as an anti-block vital edge (AVE for short), and show that this problem can be solved in O(mn) time, where n and m denote the number of nodes and edges in the graph, respectively. Some applications of the AVE for two special traffic networks are shown. This research is supported by NSF of China under Grants 70471035, 70525004, 701210001 and 60736027, and PSF of China under Grant 20060401003.     

INSIGHTS ON SERVICE SYSTEM DESIGN FROM A NORMAL APPROXIMATION TO ERLANG'S DELAY FORMULA

We show how a simple normal approximation to Erlang's delay formula can be used to analyze capacity and staffing problems in service systems that can be modeled as M/M/s queues. The numbers of servers, s, needed in an M/M/s queueing system to assure a probability of delay of, at most, p can be well approximated by s ≅ p + z_***I-p+, where z_1-p, is the (1 - p)th percentile of the standard normal distribution and ρ, the presented load on the system, is the ratio of Λ, the customer arrival rate, to μ, the service rate. We examine the accuracy of this approximation over a set of parameters typical of service operations ranging from police patrol, through telemarketing to automatic teller machines, and we demonstrate that it tends to slightly underestimate the number of servers actually needed to hit the delay probability target—adding one server to the number suggested by the above formula typically gives the exact result. More importantly, the structure of the approximation promotes operational insight by explicitly linking the number of servers with server utilization and the customer service level. Using a scenario based on an actual teleservicing operation, we show how operations managers and designers can quickly obtain insights about the trade-offs between system size, system utilization and customer service. We argue that this little used approach deserves a prominent role in the operations analyst's and operations manager's toolbags.     

Managing the Revenue of Sales Platforms: Insights into Service Fees

Online sales platforms have grown substantially in recent years. These platforms assist sellers to conduct sales, and in return, collect service fees from sellers. We study the fee policies by considering a fee‐setting platform, on which a seller may conduct a sale with a reserve price to a group of potential buyers: the seller retains the object for sale if the final trading price is below the reserve price. The platform may charge two types of fees as in current practice: a reserve fee as a function of the seller's reserve price and a final value fee as a function of the sale's final trading price. We derive the optimality condition for fee policies, and show that the platform can use either just a final value fee or just a reserve fee to achieve optimality. In the former case, the optimal final value fee charged by the platform is independent of the number of buyers. In the latter case, the optimal reserve fee is often a decreasing, instead of increasing, function of the seller's reserve price. An increasing reserve fee may make the seller reluctant to use a positive reserve price and hurt the platform's revenue. In general, the optimal fees are nonlinear functions, but in reality, linear fees are commonly used because of their simplicity for implementation. We show that a linear fee policy is indeed optimal in the case that the seller's valuation follows a power distribution. In other cases, our numerical analysis suggests close‐to‐optimal performance of the linear policy.     

MANAGED COMPETITION IN HEALTH INSURANCE

Rising healthcare costs have sparked debate about the best way to provide high‐quality affordable health insurance. We discuss the potential for regulated insurance markets to outperform single‐payer public insurance. We use as an example the private Medicare plans that now provide insurance to almost a third of seniors in the United States. The evidence suggests that private plans can limit costs and potentially appeal to enrollees, and that well‐designed risk adjustment can mitigate market failures due to adverse selection. However, fostering competition between insurers, especially in smaller markets, is difficult. We discuss how future research might illuminate the relative advantages of public and private health insurance.     

Multiperson Bargaining and Strategic Complexity

We investigate the effect of introducing costs of complexity in the n‐person unanimity bargaining game. As is well‐known, in this game every individually rational allocation is sustainable as a Nash equilibrium (also as a subgame perfect equilibrium if players are sufficiently patient and if n & 2). Moreover, delays in agreement are also possible in such equilibria. By limiting ourselves to a plausible notion of complexity that captures length of memory, we find that the introduction of complexity costs (lexicographically with the standard payoffs) does not reduce the range of possible allocations but does limit the amount of delay that can occur in any agreement. In particular, we show that in any n‐player game, for any allocation z, an agreement on z at any period t can be sustained as a Nash equilibrium of the game with complexity costs if and only if t≤n. We use the limit on delay result to establish that, in equilibrium, the strategies implement stationary behavior. Finally, we also show that ‘noisy Nash equilibrium’ with complexity costs sustains only the unique stationary subgame perfect equilibrium allocation.     

Finding an anti-risk path between two nodes in undirected graphs

Given a weighted graph G=(V,E) with a source s and a destination t, a traveler has to go from s to t. However, some of the edges may be blocked at certain times, and the traveler only observes that upon reaching an adjacent site of the blocked edge. Let ℘={P _G (s,t)} be the set of all paths from s to t. The risk of a path is defined as the longest travel under the assumption that any edge of the path may be blocked. The paper will propose the Anti-risk Path Problem of finding a path P _G (s,t) in ℘ such that it has minimum risk. We will show that this problem can be solved in O(mn+n ²log n) time suppose that at most one edge may be blocked, where n and m denote the number of vertices and edges in G, respectively. This research is supported by NSF of China under Grants 70525004, 60736027, 70121001 and Postdoctoral Science Foundation of China under Grant 20060401003.     

Risk Management in Public–Private Partnership Contracts

Public–private partnerships (PPPs) allow private companies to build, own and operate public projects such as schools and hospitals on behalf of the public sector. PPP contracts commonly require the private agent to take responsibilities for the performance of the asset over a long term, at least for a significant part of its useful life, so that efficiencies arising from long-term investment and asset management can be realized. However, the evidence is finely balanced on the effectiveness of such initiatives in obtaining the intended goals. This brings to the fore the challenge of designing and implementing innovative partnership plans to manage public services more effectively. More emphasis needs to be placed on strategies for the transfer of risk for the successful conclusion of PPP contracts.

Strategic Supply Function Competition With Private Information

A finite number of sellers (n) compete in schedules to supply an elastic demand. The cost of each seller is random, with common and private value components, and the seller receives a private signal about it. A Bayesian supply function equilibrium is characterized: The equilibrium is privately revealing and the incentives to rely on private signals are preserved. Supply functions are steeper with higher correlation among the cost parameters. For high (positive) correlation, supply functions are downward sloping, price is above the Cournot level, and as we approach the common value case, price tends to the collusive level. As correlation becomes maximally negative, we approach the competitive outcome. With positive correlation, private information coupled with strategic behavior induces additional distortionary market power above full information levels. Efficiency can be restored with appropriate subsidy schemes or with a precise enough public signal about the common value component. As the market grows large with the number of sellers, the equilibrium becomes price‐taking, bid shading is on the order of 1/n, and the order of magnitude of welfare losses is 1/n². The results extend to inelastic demand, demand uncertainty, and demand schedule competition. A range of applications in product and financial markets is presented.     

Appointment scheduling in tandem-type service systems

Appointment-based service systems arise in a broad variety of healthcare settings (for example an outpatient clinic or a dentist). Where most existing algorithms specifically consider the situation of the patient undergoing a single service, in many practical situations multiple services have to be sequentially performed. Modeling the service system as a tandem queue, the main objective of this paper is to generate schedules that soundly balance the interests of patients (i.e., low waiting times) and staff (i.e., low idle times). Importantly, following up on prior work for the single-node queue, we advocate a phase-type based technique that can deal with any service-time distribution (which may, in addition, vary across patients). Relying on a novel recursive scheme to evaluate the sojourn-time distribution of clients in such tandem systems, we show how optimal schedules can be computed. Our technique is illustrated by extensive numerical experimentation, also leading to practical guidelines that apply to a broad range of parameter settings.     

Performance Management Strategy: Waiting Time in the English National Health Services

The difficulty of measuring public services outcome results in governments adopting some quality performance measurements to oversee the standards and characteristics of the presented services. The study empirically tests the theory of performance management and the extent the waiting time policy would result in higher quality service and better health outcomes in 161 trusts in England from 2010/2011 to 2013/2014. The results show that higher waiting admission share has significant adverse effect on quality standards in terms of mortality rate. Moreover, the findings show that shorter range of waiting time is statistically associated with higher patients’ reported heath gains. However, the paper shows evidence of the presence of the output distortions effect of performance management strategy. The study shows that hospitals with lower mean waiting time have significantly higher readmission rate within 28 days of discharge.

     

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。