Competition under different reimbursement systems: The concept of an internet-based hospital management game

We have developed an internet-based management game to illustrate the economic and organisational decision-making process in a hospital by using discrete event simulation. Up to six hospitals compete against each other for inpatients with different disease categories and budget depending on hospital mission, regional health policy, inpatient reimbursement system (day-, case- and global-budget based) as well as labour and radiology technology market for 12 decision periods. Players can evaluate alternative actions for capacity planning as well as patient scheduling and control problems depending on different game situations. The uniqueness of COREmain hospital game consists of the internet-based framework, the combination of resource, process and financial result management, the competition of hospitals within a region and the consideration of different inpatient reimbursement systems. The deployment of this game in teaching, policy and research might improve policy making both at a hospital, regional and national level and also induce further research in these fields.     

政府监管下的医院医疗信息分享演化博弈分析

在分析政府监管下医院间医疗信息分享特征的基础上,结合我国当前正在推行的医联体医院间信息分享运作模式,引入梅特卡夫定律并考虑患者评价的影响,分析了监管部门与医院各自的利益组成,建立了监管部门与医院两者之间的演化博弈模型,并采用复制动态方程研究了不同情形下医院间信息分享的演化博弈轨迹。研究表明,政府通过监管并建立激励惩罚机制等引导措施对医院最终达到的演化稳定态具有极大影响;降低医院主体信息分享的风险成本、规范提高医院分享信息的质量、引导患者增强对医院信息分享的关注、制定有吸引力和威慑力的奖惩政策,是促进医院医疗信息分享的关键。研究结果可为政府监管部门预测医院间的信息分享趋势和制定精准化政策以促进分享提供参考。     

New insights on integer-programming models for the kidney exchange problem

In recent years several countries have set up policies that allow exchange of kidneys between two or more incompatible patient–donor pairs. These policies lead to what is commonly known as kidney exchange programs.     

基于分级诊疗体系的转诊与政府投资决策研究

针对我国分级诊疗实施过程中,由于基层医疗机构服务能力不足所造成的“上转容易下转难”的困境,研究了政府部门对社区医院服务能力进行投资以促进病人下转的问题.通过构建四阶段的博弈模型,探讨了为实现医疗系统总病人效用最大化的政府资金均衡投入策略,为实现三甲医院期望效益最大化的病人下转策略,病人效用最大化下的社区医院服务能力规划以及基于期望效益最大化下的病人选择.研究发现：1)三甲医院的期望效益受到政府投资金额的影响,当政府投资金额不足时,三甲医院的期望效益仅能达到次优;2)三甲医院病人的均衡转诊率受到三甲医院的治疗价格和政府的资金投入量的影响;3)在实现整个医疗系统总病人效用最大化上,虽然总病人效用随政府投入金额的增加而增加,但从政府角度来讲,政府投资金额不宜过大.     

The Impact of Teaching on Hospital Costs: A Budgetary Approach to Non-market Institutions

NHS hospitals contribute to medical education, training nurses and research, as well as to the care of patients. In the past they have been funded largely on the basis of resources employed, with additional funding for medical education and training nurses. The intellectual basis for the funding of medical education is a single econometric study of English hospitals in the financial year 1969-70. The methodology used has since been criticized, and it has been suggested that actual expenditure has been very much less than that earmarked by the health departments. New estimates are obtained using Scottish data for the financial year 1985-86. The method used is to proceed in a two-stage fashion, identifying via regression techniques variables measuring hospital activity and resources which contribute significantly to hospital costs. We then assess the significance of medical education, nurse training and hospitals' teaching status against this background. Our conclusions include: (1) actual expenditure on medical education was probably less than the funding formula allowed, but the error of margin is too large to suggest overfunding; (2) training nurses incurs significant financial costs, even after the explicit allowances made; and (3), major teaching hospitals tended to cost more, but not significantly more than their non-teaching counterparts. These financial implications for NHS hospitals should be borne in mind given the current NHS review.     

A game semantics for disjunctive logic programming

Denotational semantics of logic programming and its extensions (by allowing negation, disjunctions, or both) have been studied thoroughly for many years. In 1998, a game semantics was given to definite logic programs by Di Cosmo, Loddo, and Nicolet, and a few years later it was extended to deal with negation by Rondogiannis and Wadge. Both approaches were proven equivalent to the traditional semantics. In this paper we define a game semantics for disjunctive logic programs and prove soundness and completeness with respect to the minimal model semantics of Minker. The overall development has been influenced by the games studied for PCF and functional programming in general, in the styles of Abramsky–Jagadeesan–Malacaria and Hyland–Ong–Nickau.     

A theory of money and financial institutions: Fiat money and noncooperative equilibrium in a closed economy

Fiat money is a type paper or symbol with which any individual may buy most things by law. It has virtually no intrinsic value but immediately assumes a trading value when its shortage (i.e., when it is no longer a slack variable to everyone in the appropriate set of simultaneous programs) can prevent trades that would have been deemed profitable in a nonmonetary competitive equilibrium system. This paper sketches an approach to a theory of fiat money by investigating the properties of a noncooperative dynamic trading game embedded within a closed economic system. Among the conclusions are that inflation and deflation are not symmetric, and that it is not possible to define a noncooperative game involving borrowing without specifying “rules of borrowing” or a bankruptcy law.     

Workforce staffing and scheduling: Hospital nursing specific models

Decisions relating to hospital nurse staffing and scheduling are among the most important decisions made in hospitals today. Staffing and scheduling choices must be made which will result in timely and high-quality care to patients. These choices are complicated by the requirement for round-the-clock staffing in many hospital nursing units, a severe nursing shortage, and an outcry from many quarters to cut costs of health care. In general, patients today are kept in hospitals only if they are in need of highly skilled nursing care. In this paper we present a review of some of the issues in health care currently influencing the hospital nurse staffing and scheduling environment. In addition, we review the literature that illustrates nurse manager's concerns, and approaches taken in the past by operations researchers to address those concerns. We present some data from a recent study of nurse managers in 31 hospitals that illustrates the complexity of the issues. We conclude with a discussion of future research directions in hospital nurse staffing and scheduling.     

Managing the overflow of intensive care patients

Many hospitals in the Netherlands are confronted with capacity problems at their intensive care units (ICUs) resulting in cancelling operations, overloading the staff with extra patients, or rejecting emergency patients. In practice, the last option is a common choice because for legal reasons, as well as for hospital logistics, rejecting emergency patients has minimal consequences for the hospital. As a result, emergency patients occasionally have to be transported to hospitals far away. In this work, we propose a cooperative solution for the ICU capacity problem. In our model, several hospitals in a region jointly reserve a small number of beds for regional emergency patients. We present a mathematical method for computing the number of regional beds for any given acceptance rate. The analytic approach is inspired by overflow models in telecommunication systems with multiple streams of telephone calls. Simulation studies show that our model is quite accurate. We conclude that cooperation between hospitals helps to achieve a high acceptance level with a smaller number of beds resulting in improved service for all patients.     

Health network mergers and hospital re-planning

This paper presents an integer programming formulation for the hospital re-planning problem which arises after hospital network mergers. The model finds the best re-allocation of resources among hospitals, the assignment of patients to hospitals and the service portfolio to minimize the system costs subject to quality and capacity constraints. An application in the Turkish hospital networks case is illustrated to show the implications of consolidation of health insurance funds on resource allocations and flow of patients in the system.     

Measuring the price of anarchy in critical care unit interactions

Hospital throughput is often studied and optimised in isolation, ignoring the interactions between hospitals. In this paper, critical care unit (CCU) interaction is placed within a game theoretic framework. The methodology involves the use of a normal form game underpinned by a two-dimensional continuous Markov chain. A theorem is given that proves that a Nash Equilibrium exists in pure strategies for the games considered. In the United Kingdom, a variety of utilisation targets are often discussed: aiming to ensure that wards/hospitals operate at a given utilisation value. The effect of these target policies is investigated justifying their use to align the interests of individual hospitals and social welfare. In particular, we identify the lowest value of a utilisation target that aligns these.     

Asymptotic equivalence between Cournot–Nash and Walras equilibria in exchange economies with atoms and an atomless part

In this paper, we consider an exchange economy à la Shitovitz (Econometrica 41:467–501, 1973), with atoms and an atomless set. We associate with it a strategic market game of the kind first proposed by Lloyd S. Shapley, known as the Shapley window model. We analyze the relationship between the set of the Cournot–Nash allocations of the strategic market game and the Walras allocations of the exchange economy with which it is associated. We show, with an example, that even when atoms are countably infinite, any Cournot–Nash allocation of the game is not a Walras allocation of the underlying exchange economy. Accordingly, in the original spirit of Cournot (Recherches sur les principes mathématiques de la théorie des richesses. Hachette, Paris, 1838), we partially replicate the mixed exchange economy by increasing the number of atoms, without affecting the atomless part, and ensuring that the measure space of agents remains finite. Our main theorem shows that any sequence of Cournot–Nash allocations of the strategic market games associated with the partial replications of the exchange economy has a limit point for each trader and that the assignment determined by these limit points is a Walrasian allocation of the original economy.     

Estimating bed requirements for an intermediate care facility

Concern has been expressed in the United Kingdom regarding the proportion of beds intended for acute care that are occupied by patients who do not require acute care. One solution to this problem that is being investigated by some hospitals is the establishment of an intermediate care facility devoted to non-acute care. A key question faced by hospital planners is how many beds such an intermediate care facility should have. We report on a study consisting of a bed use survey and a stochastic analysis exercise that was conducted at the Whittington Hospital NHS Trust in London in order to address this question. Rather than focus on the whether patients in acute beds required acute care throughout their stay in hospital, the study concentrated on identifying periods in patients’ stays when they would have been transferred to an intermediate care facility if one had been available.     

On market prices in linear production games

Consider a game in which resources may be combined to produce products of known values. For linear production processes, the game may be characterized by a family of linear programs. It is shown that appropriately defined market prices for the resources coincide with the set of optimal dual solutions to one of these linear programs. This result generalizes and unifies the known cases in game theory, in which the core of a game coincides with the set of dual optimal solutions to a corresponding master linear programming problem.Based on working papers by Engelbrecht-Wiggans (1982) and Granot (1983). The work was motivated by an application, reported in Engelbrecht-Wiggans (1983), supported by the US EPA.Research was partially supported by the Natural Science and Engineering Research Council of Canada Grant A4181.     

Two-person zero-sum stochastic games

Two-person zero-sum stochastic games with finite state and action spaces are considered. The expected average payoff criterion is introduced. In the special case of single controller games it is shown that the optimal stationary policies and the value of the game can be obtained from the optimal solutions to a pair of dual programs. For multichain structures, a decomposition algorithm is given which produces such optimal stationary policies for both players. In the case of both players controlling the transitions, a generalized game is obtained, the solution of which gives the optimal policies.     

Use of VNS heuristics for scheduling of patients in hospital

One of the important problems in hospital management is how to schedule the treatments of resident patients in hospital for a given day due to the restrictions imposed by their medical condition as well as restrictions on medical machines and qualified medical personnel availability. Patients are to be subjected to different kinds of treatments, each requiring a medical machine of a certain type as well as a physician being qualified to operate it. This is a highly complex problem not yet adequately addressed in the literature. At present in most hospitals the problem is being solved manually by specialized personnel. However, the resulting schedules are very often inaccurate and inefficient with patients waiting for a long time to be treated and medical personnel often working overtime. In this paper we formulate the model for this problem and develop a simple and efficient method based on Variable Neighbourhood Search for solving it. The heuristics has been tested on real-life as well as on generated instances. Numerical results show that the heuristics proposed outperform commercial software for optimization as well as manual solutions both in quality of solution and in computational time.     

A comparison of shadow prices and reimbursement rates of hospital services

The purpose of this paper is to calculate shadow prices of hospital services and compare them to the reimbursement rates those hospitals receive. These shadow prices are calculated by estimating a multiple-output distance function and applying a dual Shephard's lemma, a technique suggested by Färe and Grosskopf [8]. In contrast to cost functions, distance functions require no price data and do not presume cost minimization. We apply this technique to a sample of California hospitals operating in 1986. We find that hospitals engaged in selective contracting for Medi-Cal patients exhibit closer agreement between relative shadow prices and relative reimbursement rates (Medi-Cal relative to private patients) than noncontracting hospitals.Contact author.     

On multi-choice TU games arising from replica of economies

In this paper we derive a multi-choice TU game from r-replica of exchange economy with continuous, concave and monetary utility functions, and prove that the cores of the games converge to a subset of the set of Edgeworth equilibria of exchange economy as r approaches to infinity. We prove that the dominance core of each balanced multi-choice TU game, where each player has identical activity level r, coincides with the dominance core of its corresponding r-replica of exchange economy. We also give an extension of the concept of the cover of the game proposed by Shapley and Shubik (J Econ Theory 1: 9-25, 1969) to multi-choice TU games and derive some sufficient conditions for the nonemptyness of the core of multi-choice TU game by using the relationship among replica economies, multi-choice TU games and their covers.     

Competitive outcomes in the cores of market games

The competitive outcomes of an economic system are known, under quite general conditions, always to lie in the core of the associated cooperative game. It is shown here that every “market game” (i.e., one that arises from an exchange economy with money) can be represented by a “direct market” whose competitive outcomes completely fill up the core. It is also shown that it can be represented by a market having any given core outcome as itsunique competitive outcome, or, more generally, having any given compact convex subset of the core as its full set of competitive outcomes.     

On the nucleolus of NTU-games defined by multiple objective linear programs

In this article we derive a class of cooperative games with non-transferable utility from multiple objective linear programs. This is done in order to introduce the nucleolus, a solution concept from cooperative game theory, as a solution to multiple objective linear problems.We show that the nucleolus of such a game is a singleton, which is characterized by inclusion in the least core and the reduced game property. Furthermore the nucleolus satisfies efficiency, anonymity and strategic equivalence.We also present a polynomially bounded algorithm for computation of the nucleolus. Letn be the number of objective functions. The nucleolus is obtained by solving at most2n linear programs. Initially the ideal point is computed by solvingn linear programs. Then a sequence of at mostn linear programs is solved, and the nucleolus is obtained as the unique solution of the last program.Financial support from Nordic Academy for Advanced Study (NorFA) is gratefully acknowledged. Part of this work was done during autumn 1993 at Institute of Finance and Management Science, Norwegian School of Economics and Business Administration.