رضایت رویکرد نظریه بازی برای ارزیابی گروهی واحدهای تولیدی

The problem under consideration in this paper is that of analysing the performance of a production unit in two directions: resource utilization versus output perfomance on the one hand and inter-unit comparison (within-group evaluation) on the other hand, all this subjected to possible subjective intervention of a decision maker or group of decision makers (DMs). A well known method that deals mainly with the second point (without intervention of DMs) of this problem which is widely covered in the literature is the so called data envelopment analysis (DEA). The point of view that will be expressed in this paper can be thought of as complementary to the DEA approach giving a more complete analysis in terms of the weak points of units identification and DMs' recommendations. The performance of each decision unit is evaluated through the so called satisfiability functions in the framework of satisficing game theory.

The problem of evaluating production units' performance is of great importance for efficient management decision making such as restructuring an organization, rewarding production teams, etc. We understand by production unit, a system that utilizes some input items (resources) to produce some goods or to deliver some service. It could be a hospital, a manufacturing plant, a university, a police department, etc. The purpose here is to evaluate the efficiency in terms of resource utilization versus output performance of each production unit of an organization UU that consists of n production units. Each production unit is evaluated individually as well as with regard to its counterparts' efficiency. We suppose that each unit of UU uses p input items expressed as positive numbers Iij (value of item j used by unit i) to deliver m output items valued by Oij (value of item j produced by unit i). A first idea could be to define the efficiency ei of unit i by but this definition leads to some problems as all input items or output items do not have the same importance in practice. It is then tempting to weight items in order to take into account this relative importance so that the efficiency is defined by but here again, a problem relative to the determination of weights αij and βij is raised. A method to deal with the determination of these weights in the literature is the so called data envelopment analysis (DEA) established by [1]. It is an extreme point method that determines weights αij and βij in order to define a relative efficiency of each unit compared to the best production unit (possibly virtual) by solving n linear programs (see for instance [2] for definition of linear programming concepts). But this approach has some technical drawbacks that will be recalled in the next Section and more importantly, we consider that the spirit of comparing each unit to the “best unit” is not necessarily how humans proceed in practice. They often evaluate each unit firstly with regard to how efficiently it uses its resources to produce its output and secondly they look at how good this unit is compared to its counterparts. If we think of how students are evaluated, we see that each student is first evaluated individually (their marks reflecting the effort they have made) and then compared to the best student of the same class. This observation suggests that a production unit should be evaluated by comparing its positive attributes (output performance) to its negative attributes (input or resource consumption) at first and with regard to the other units in a second stage. Another important issue in the process of evaluating production units is the possible existence of different decision makers that do not have the same point of view regarding the importance of input items and/or output items and this constraint should be taken into account. A framework that seems interesting to tackle this problem with is the recently developed satisficing game theory [3] that, basically for our problem, will consist in defining selectability (with regard to output items) and rejectability (with regard to input items) functions known as satisfiability functions. These functions must have a probability structure (they are non-negative and sum to one on UU) which can be thought of as units sharing a unity of input item to produce a unity of output item. An efficient production unit will be that for which the selectability is at least equal to the rejectability. We consider here that there are d decision makers that express their point of view regarding input items and output items by weighting them. The remainder of this paper is organized as follows: in the Second section the DEA method is briefly presented with its strengths and its drawbacks; the Third section is devoted to a rapid presentation of satisficing game theory that is relevant to our problem and the Fourth section shows how to cast performance evaluation problems into the framework of this theory and finally, in Section five, the approach we have established is applied to a real world problem.

In this paper, a problem of evaluating a group of production units by a group of decision makers (managers, administrators, politicians, experts, etc.) has been formulated and solved using the satisficing game theory paradigm. Data that are used for evaluation are input items in terms of resource consumption and output items in terms of products or delivered services in a data envelopment (DEA) type framework. A method based on the satisficing game theory has been established that allows a unit to be evaluated “individually” in terms of its resource consumption versus its delivery performance as well as how good it is performing with regard to its counterparts, a within-group evaluation. This method can be used as a complement to the DEA approach to integrate a subjective point of view of decision makers and for analysis of causes of possible inefficiency. The application considered (a real world problem) shows the feasibility of this approach and its low demand on computational power makes it suitable for integration in computer aid decision support systems; this point will be considered in future work.