2008国际大学生数学建模一等奖论文--历年数学建模优秀论文大全

2008 国际大学生数学建模比赛参赛作品国际大学生数学建模比赛参赛作品 -WHO 所属成员国卫生系统绩效评估 作品名称：作品名称：Less Resources, more outcomes 参赛参赛单位单位： 重庆大学重庆大学 参赛时间：参赛时间：2008 年年 2 月月 15 日至日至 19 日日 指导老师：指导老师： 何仁斌何仁斌 参赛队员：参赛队员：舒强舒强 机械工程学院机械工程学院 05 级级 罗双才罗双才 自动化学院自动化学院 05 级级 黎璨黎璨 计算机学院计算机学院 05 级级 2008 年国际大学生数学建模比赛参赛作品 作者：舒强、罗双才、黎璨 2 / 29 Content Less Resources, More Outcomes . 4 1. Summary . 4 2. Introduction . 5 3. Key Terminology . 5 4. Choosing output metrics for measuring health care system. 5 4.1 Goals of Health Care System . 6 4.2 Characteristics of a good health care system . 6 4.3 Output metrics for measuring health care system . 6 5. Determining the weight of the metrics and data processing . 8 5.1 Weights from statistical data . 8 5.2 Data processing . 9 6. Input and Output of Health Care System . 9 6.1 Aspects of Input . 10 6.2 Aspects of Output . 11 7. Evaluation System I : Absolute Effectiveness of HCS . 11 7.1Background . 11 7.2Assumptions . 11 7.3Two approaches for evaluation . 11 1. Approach A : Weighted Average Evaluation Based Model . 11 2. Approach B: Fuzzy Comprehensive Evaluation Based Model 1920 . 12 7.4 Applying the Evaluation of Absolute Effectiveness Method . 14 8. Evaluation system II: Relative Effectiveness of HCS . 16 8.1 Only output doesnt work . 16 8.2 Assumptions . 16 8.3 Constructing the Model . 16 8.4 Applying the Evaluation of Relative Effectiveness Method . 17 9. EAE VS ERE: which is better? . 17 9.1 USA VS Norway . 18 9.2 USA VS Pakistan . 18 10. Less Resources, more outcomes . 19 10.1Multiple Logistic Regression Model . 19 10.1.1 Output as function of Input . 19 10.1.2Assumptions . 19 10.1.3Constructing the model. 19 10.1.4. Estimation of parameters . 20 10.1.5How the six metrics influence the outcomes? . 20 10.2 Taking USA into consideration . 22 10.2.1Assumptions . 22 10.2.2 Allocation Coefficient . 22 10.3 Scenario 1: Less expenditure to achieve the same goal . 24 10.3.1 Objective function： . 24 10.3.2 Constraints . 25 2008 年国际大学生数学建模比赛参赛作品 作者：舒强、罗双才、黎璨 3 / 29 10.3.3 Optimization model 1 . 25 10.3.4 Solutions of the model . 25 10.4. Scenario2: More outcomes with the same expenditure . 26 10.4.1Objective function . 26 10.4.2Constraints . 26 10.4.3 Optimization model 2 . 26 10.4.4Solutions to the model . 27 15. Strengths and Weaknesses . 27 Strengths . 27 Weaknesses . 27 16. References . 28 2008 年国际大学生数学建模比赛参赛作品 作者：舒强、罗双才、黎璨 4 / 29 Less Resources, More Outcomes 1. Summary In this paper, we regard the health care system (HCS) as a system with input and output, representing total expenditure on health and its goal attainment respectively. Our goal is to minimize the total expenditure on health to archive the same or maximize the attainment under given expenditure. First, five output metrics and six input metrics are specified. Output metrics are overall level of health, distribution of health in the population,etc. Input metrics are physician density per 1000 population, private prepaid plans as % private expenditure on health, etc. Second, to evaluate the effectiveness of HCS, two evaluation systems are employed in this paper: Evaluation of Absolute Effectiveness(EAE) This evaluation system only deals with the output of HCS，and we define Absolute Total Score (ATS) to quantify the effectiveness. During the evaluation process, weighted average sum of the five output metrics is defined as ATS, and the fuzzy theory is also employed to help assess HCS. Evaluation of Relative Effectiveness(ERE) This evaluation system deals with the output as well as its input, and also we define Relative Total Score (RTS) to quantify the effectiveness. The measurement to ATS is units of output produced by unit of input. Applying the two kinds of evaluation system to evaluate HCS of 34 countries (USA included), we can find some countries which rank in a higher position in EAE get a relatively lower rank in ERE, such as Norway and USA, indicating that their HCS should have been able to archive more under their current resources . Therefore, taking USA into consideration, we try to explore how the input influences the output and archive the goal: less input, more output. Then three models are constructed to our goal: Multiple Logistic Regression We model the output as function of input by the logistic equation. In more detains, we model ATS (output) as the function of total expenditure on health system. By curve fitting, we estimate the parameters in logistic equation, and statistical test presents us a satisfactory result. Linear Optimization Model on minimizing the total expenditure on health We try to minimize the total expenditure and at the same time archive the same, that is to get a ATS of 0.8116. We employ software to solve the model, and by the analysis of the results. We cut it to 2023.2 billion dollars, compared to the original data 2109.8 billion dollars. Linear Optimization Model on maximizing the attainment . We try to maximize the attainment (absolute total score) under the same total expenditure in2007.And we optimize the ATS to 0.8823, compared to the original data 0.8116. Finally, we discuss strengths and weaknesses of our models and make necessary recommendations to the policy-makers。 2008 年国际大学生数学建模比赛参赛作品 作者：舒强、罗双才、黎璨 5 / 29 2. Introduction Today and every day, the lives of vast numbers of people lie in the hands of health systems. From the safe delivery of a healthy baby to the care with dignity of the frail elderly, health systems have a vital and continuing responsibility to people throughout the lifespan. They are crucial to the healthy development of individuals, families and societies everywhere. Due to the irreplaceable role that the health care systems play in residents life, better health care system is needed. “Improving performance” is therefore the key words today. However, nowadays health care systems in many countries do not exhibit enough high effectiveness in guaranteeing residents good health and a long life expectancy. In some countries, their government invests large amount of money on the health care systems, however, they didnt archive what they should have been to archive. We try to explore an optimized system in this paper. 3. Key Terminology Health Care System (HCS) Health Care System is such a system that has its input and output, representing total expenditure on health and its goal attainment respectively. Evaluation of Absolute Effectiveness of Health Care System (EAE) It is a kind of evaluation system that only considers the outcomes of the health care system, saying nothing to do with the input (resources), and adapts the outcomes as measurement to effectiveness. Evaluation of Relative Effectiveness of Health Care System (ERE) It is a kind of evaluation system that considers the outcomes of the health care system as well its inputs, and adapts units of output produced by unit of input as measurement to effectiveness. Absolute Total Score (ATS) Overall score for the evaluation of absolute effectiveness of health care systems Relative Total Score (RTS) Overall score for the evaluation of relative effectiveness of health care systems Input Metrics (IM) Metrics that are specified to assess input of HCS Output Metrics (OM) Metrics that are specified to assess output of HCS 4. Choosing output metrics for measuring health care system 2008 年国际大学生数学建模比赛参赛作品 作者：舒强、罗双才、黎璨 6 / 29 Table 1. Notation for goals and metrics Goals of Health System Notation Metrics for Evaluation Notation Health U1 Overall level of health u1 Distribution of health in the population u2 Responsiveness U2 Overall level of responsiveness u3 Distribution of responsiveness u4 Fairness in Finance U3 Distribution of financial contribution u5 4.1 Goals of Health Care System According to the World Health Report in 2000, the WHO pointed out the three goal of health care system, each goal with different priority WHO 2000. Better Health Better health is unquestionably the primary goal of a health system, with the highest priority. Fairness in financial contribution. Fairness in financial contribution is the second goal, with a relatively lower priority to health. Responsiveness Responsiveness to peoples expectations in regard to non-health matters reflects the importance of respecting peoples dignity, autonomy and the confidentiality of information, and is the third goal ,with the lowest priority. 4.2 Characteristics of a good health care system Goodness (2) Client orientation (including prompt attention, access to social support networks during care, quality of basic amenities and choice of provider). The level of responsiveness was based on a survey of key informants in selected countries. And WHO defined the index of Overall level of responsiveness as weighted average of its seven components: WHO 2000 111 Re 333 13 Pr 520 11 1020 Level ofsponsivenessDignitConfidentialityAutonomy ompt attentionQuality of amentities Access to social Support networkChoice of provider （2） Distribution of responsiveness We use a simple approach to quantize the distribution of responsiveness. That is respondents in the key informant survey were asked to identify groups who were disadvantaged with regard to responsiveness. The number of times a particular group was identified as disadvantaged was used to calculate a key informant intensity score. Four groups had high key informant intensity scores: poor people, women, old people, and indigenous groups or racially disadvantaged groups (in most instances minorities). The key informant intensity scores for these four groups were multi- plied by the actual percentage of the population within these vulnerable groups in a country to calculate a simple measure of responsiveness inequality ranging from 0 to 1. The total score was calculated taking into account the fact that some individuals belong to more than one disadvantaged group. Distribution of financial contribution 2008 年国际大学生数学建模比赛参赛作品 作者：舒强、罗双才、黎璨 8 / 29 The fair financing measure estimates the degree to which health funding is raised according to the ability to pay for all members of the population. It captures concerns such as progressivity, and protection from catastrophic health costs. Fair financing is only concerned with distribution. In order that complete equality of household contributions is 1 and 0 is below the largest degree of inequality observed across countries, WHO defined the in fairness index. And the index is of the form:WHO2000 3 1 1 4(3) 0.125 n i i HFCHFC Fairness of finance contribution n Where HFC is the financial contribution of a given household and HFC is the average financial contribution across households. 5. Determining the weight of the metrics and data processing 5.1 Weights from statistical data The key informant survey, consisting of 1791 interviews in 35 countries, yielded scores (from 0 to 10) on each element of responsiveness, as well as overall scores. A second, Internet-based survey of 1006 participants (half from within WHO) generated opinions about the relative importance of the elements, which were used to combine the element scores into an overall score instead of just taking the mean or using the key informants overall responsesWorld Health Report 2000.See figure 1 and 2: Figure 1 Weights for the three goals of health system 50% 25% 25% Health Responsiveness Fairness inFinance 2008 年国际大学生数学建模比赛参赛作品 作者：舒强、罗双才、黎璨 9 / 29 Figure 2 Weights of the five metrics Figure1 and figure 2 illustrate the weights of three goals of health system and five metrics respectively. 5.2 Data processing Data Source We get our data from WHO Statistical Information System on the official web site of WHO (/whosis/en/index.html) And data in THE WORLD HEALTH STATISTICS REPORT from 2005 to 2007 and World Health Report in 2000 is now accessible. Normalization To ensure comparability of effectiveness of health care system, metrics must be normalized by the following given formulation: min() max()min() RawDataRawData Normalized Data RawDataRawData (4) Where max greatest number of Raw Data and min is the least one. 6. Input and Output of Health Care System In this paper, we consider Health Care System a system with both input and output (see fig.3). Five output metrics and six input metrics are specified in this paper. 25% 25% 12.50% 12.50% 25% Overall level of health Distribution of health in the population Overall level of responsiveness Distribution of responsiveness Distribution of financia