Sağlık sistemlerinde çok amaçlı karar verme

Abstract

Çok amaçlı karar verme yöntemleri birçok sektördeki probleme başarı ile uygulanmaktadır. Sağlık sistemlerinde ise bu yene yaklaşım çok sınırlı miktarda olmaktadır. Buna rağmen yöntemler kullanıldıkları alanlarda tatmin edici ve beklenenin üzerinde sonuçlar vermiştir. önceleri üretimde çok amaçlı yöntemlerin kullanılması maddi kazancı artırmıştır. Sosyal alanlarda matematik problemlerin modelleneme mesinin bir diğer nedeni de sistemlerin sınırlarının çok esnek olma sıdır. Bir sosyal alan olan sağlık sistemlerinin de sınırlarının tanımlarının netleşmesi ile matematik modeller ve özellikle çok öl çütlü karar verme modelleri yaygın bir biçimde kullanılacaktır. Makro düzeydeki sağlık planlarının incelenerek ulaşılmak istenilen hedeflerin değerlendirilmesi çok amaçlı karar problemleri için basit bir sağlık alanı uygulamasıdır.

The health systems have social, economical, medical and technological attributes and try to obtain a acceptable level about human healthness. The functional division of it like this: public and treatment medicine. Four steps of health service: diagnosing, treating, nursing and protec ting. The protecting and social subjects of nursing are releated of public medicine and diagnosing, treating and medical subjects of nur sing are releated treatment medicine. The health systems are consist of three main elements: the health re quirements of public, the resource of health system, the health mana gement and service policy. The protecting health services are applied for keeping the society against to infections by control ing the eatings and environment. The establishments that serve treatment medicine are health houses, health units, health centers and hospitals. The hospitals are divided as general hospitals, special branch hospitals, rehebilition centers and trainnig hospitals. The most important factors that effect the requirements : of public are the distrubition of population according to age, sex and working groups. Because of the nature of the system is dynamic the require ments of public can not be defined in the devoloping and development countries. ; As the pointed at the health model the resources of the system are defined at four main groups: i ) Manpower ii)Facilities iii)Materials n iv)Finance Multiple Criteria Decision Making (MCDM) refers to making decision:;! in the presence of multiple, usually conflicting, objectives. Some ofj the importand aspects of solving such problems and some methods deve loped for solving multiple criteria mathematical programming problems and discrete alternative models are presented in this study. In multiple criteria decision making there is a decision maker ( ;q makers ) who makes the decision, a set of objectives jthat are to Iqk pursued, and a set of alternatives from which one is to be selected: VI The objectives should have these five characteristics: i) Complete ii) Operational iii) Decomposable iv) Nonredundant v) Minimal While a desicion is making a decision maker makes a decision and the solution he chooses is optimal. An optimal decision is one that maxi- mazes decision maker's utility ( or satisfaction ). The general multiple criteria decision making problem may be formulated as follows: Maxsimize F(x) subject to: G(x) =" 0 where x is the vector of decision variables, and F(x) is the vector of objectives to be maximized. A linear version of this problem is as follows: Maximize Ox subject to: Ax £ b xj = 0, if needed, may be included in the constraints Ax = b. It is refrred to as the Multiple Objective Linear Programming prblem ( MOLP ) because it is a linear programming. problem with multiple objectives. The problem of choosing the best alternative from a discrete set of alternatives is shown by this formulation: Maximize F(d) subject to: d 6 D where d is a desicion and D is the set of possible desicions. There are several naive methods for solving multiple criteria mathema tical programming problems: setting levels of all objectives, setting minimal levels of all but one objective, finding all efficient extreme point solutions and using weights to combine objective functions. Each of these methods have been a starting point for developing more complex methods. The most important methods that developed based on this naive methods are: 1. Goal Programming 2. Wierbicki Method 3. Zionts-Wallenius Method 4. Geoff rian, Dyer and Feinberg Method j 5. The visual interactive method j 6. A Pareto Race ; 7. A dicrete alternatives method, ! Vll The main application of industrial engineering in health services is releated planning and management problems. To solve these problems a management information system shold be established. This system creates the alternatives and evaluate made desicions. The factors that effect the efficients of the health organizations are efficient of labour, capital, technology and materials. The applications of operation researchs have been made in hospitals at the beginning. Using these methods the solutions have been obtained at hospital management and the applications have began about on public medicine, local planning, national and international health problems. This applications are classified at the different types. The main classification is tactical and strategical levels. But more detailed another classification is that: The problems of national and local health systems: 1. The planning of health sector 2. The planning of health facilities and manpower 3. The efficients of health systems 4. The family planning 5. The struggle against to infections The individial problems of health organizations: 1. Budgeting and resource allocation 2. Queueing systems 3. Bold center planning 4. The planning of ambulance and first aid 5. The planning of operation rooms 6. Bed planning 7. The planning of nursing 8. Stock planning 9. The planning of lab 10. Personnel planning 11. Menu planning 12. The forecast of the demand In this study a resource allocation method is presented about the app lication of operation research in the health systems. Also in this study three applications are presented about the applica tions of multiple criteria decision making in the health systems. The first application presents a goal programming model devolopment and application for a state level public health care agency. Only limited applications of macro planning processes related to health care have been presented in the literature. This application describes briefly the goal programming model the background of the agency involved and the specific models developed. Three formulation of the model are pre sented involving (1) the resources required to achive all goals and viii (2) the goal attainment status utilizing a likely budget and (3) a pro posal for resolving the goal desire-resource limitation dilemma. An important problem facing decision makers is that of allocating scarce resource in multiple goal environments. This issue confrons managers in manufacturing, service and govermantal settings. This application describes how this problem was addressed in the State of Georgia Crippr led Children's Service using the goal programming techniques. The re maining sections of the application cover a description of the problem setting, development of the model and discussion of solutions. The fo cus of the research is one of a planning mode and, as such, deals with resource allocation from a macro perspective. While the problem, goal and resource parameters are all developed for a real organization many of the problem solutions are dealt with in a "what iff approach. This approach is preferred in order that the decision maker be presented with tradeoff options valuable in refining the planned allocations. In the second application an integer, nonlinear mathematical program ming model is developed to allocate emergency medical service ambulan ces to sectors within o county in order to meet a govermet-mandated response time criterion. In addition to the response time criterion, the model also reflects criteria for budget and workload, and, since ambulance response is best described within to context of a queueing system, several of the model system constraints are based on queueing formulations adapted to a mathematical programming format. The model is developed and demonstrated within the context of an example of a county encompassing rural, urban and mixed sectors which exhibit dif ferent demand and gegraphic characteristics. The example model is sol ved using an integer, nonlinear goal programming technique. The solu tion results provide ambulance allocations to sectors within the county the probability of an ambulance exceeding a prespecified response time and the utilization factor for ambulances per sector. Since the passage of the Emergency Medical Service Act in United States numerous analytical and heuristic models have been developed that seek to allocate and/or locate emergency medical service ambulance units, within a region in an efficient manner such that these government-man dated response times might be achieved. The majority of these models,; have been developed using ona of several solution approaches, inclu- : ding simulation, queueing and set-covering. However, these models all have limitations, not the least of which is their ability to reflect multiple criteria in the allocation decisions. The presented model employes several criteria for allocation, including the Emergency Medical Service response time criterion and..budgetary considerations. Because of these multiple criteria, and the fact that unitary items (ambulances) are being allocated, an integer goal prog-jj ramming model formulation is employed. However, although the ambulance allocation problem can be conveniently described within a mathematical programming framawork, the actual process of ambulances responding to calls is best described as a queuing system. As such, this model irjc1 ludes queuing-system formulations defined as goal constraints within the mathematical programming framework, which, on turn;, necessiates ix { a nonlinear solution approach. The model solution results are presen ted and discussed, and several sensivity analysis scenarios are ana lyzed. The third application presents a single-phase goal programming algo rithm for scheduling nurses in one unit of hospital. The goals rep resent the scheduling policies of the hospital, and nurses' preferen ces for weekends on and off. An application to one unitof the hospi tal with 11 nurses resulted in satisfactory schedules. The computer time to solve the problem using a goal programming algorithm was very reasonable. The problem of scheduling staff in hospitals, especially nursing staff has received considerable attention in the past. The mathematical programming models had been used to schedule nurses in different units of a hospital. The list processing and problem-oriented data struc tures is used for formulating the problem. The solution is obtained using a heuristic method. The mathematical programming models are not flexible in terms of relative rankjngs assigned to various types of goals. In this sense, a goal 'programming model would definitely be superior. Also, in addition to these three applications, a special application is presented in this study. In this application the health gols are determineted at the Sixth Five Year's Development Plan. Seven main goals are considered to establish the model: 1. The immunization 2. Increase the beds 3. Increase the doctors. 4. Increase the dentists 5. Increase the health units 6. Increase the sanitarians 7. Increase the nurses and the midwifes. The constraints are the number of students at the medicine schools and the financial constraints of Ministry of Health. The student number is obtained to multiple the entering student number by coefficient num ber for each medicine school. The financial constraints can be divided two main groups: personnel and investment expenditures. The constraints are supported by using Investment Plan 1990 and General Budget 1990. The data about each health personnel is obtained from Kartal General Hospital. As the result of this application there are excess at the number of i dentists and sanitarians. But "also there are deficiency at the number of doctors and nurses and midwifes. To balance the general butget the budget of Ministry of Health should be increase 2.5% in real amounts every year.