Normative properties of multi-criteria choice procedures and their superpositions: I
The paper examines the choice problem when the total number of observations and criteria is too large. There are many different procedures, which are used for decision-making process under multiple criteria; however, most of them cannot be applied to large datasets due to their computational complexity while others provide sufficient accuracy. To solve the problem, we consider the idea of superposition, which consists in the sequential application of choice functions where the result of the previous function is the input for the next function. Among the main benefits of the superposition are its manageable computational complexity and high performance. We analyze normative properties of the superposition that characterize how stable and sensible the final choice is. We also consider the application of superposition to tornado prediction and search problems. As a result, we show that superposition of choice functions provides higher efficiency values compared to traditional solutions.
The problem of management is formalized for the first time by purchases as a problem of a choice of the best decision at many criteria. Thus some of private criteria allow to consider demanded risk factors. Possibilities of the decision of problems of this kind on the basis of a method of a tree of decisions are illustrated.
Analysis of problems of utilization of oil associated gas is given. Method for optimal distribution of expenses to laying of gas pi peline, taking into account a financing from oil companies and possible participation of government, is proposed. A multi-criteria model for selection of optimal alternative of utilization of oil associated gas is given. Software is made implementing the developed algorithms.
In this paper, the application of two-stage superposition choice procedures to the choice problem when the number of alternatives is too large is studied. Two-stage superposition choice procedures consist in sequential application of two choice procedures where the result of the first choice procedure is the input for the second choice procedures. We focus on the study of properties of such choice procedures and evaluate its computational complexity in order to determine which of two-stage superposition choice procedures can be applied in the case of large amount of alternatives.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
We address the external effects on public sector efficiency measures acquired using Data Envelopment Analysis. We use the health care system in Russian regions in 2011 to evaluate modern approaches to accounting for external effects. We propose a promising method of correcting DEA efficiency measures. Despite the multiple advantages DEA offers, the usage of this approach carries with it a number of methodological difficulties. Accounting for multiple factors of efficiency calls for more complex methods, among which the most promising are DMU clustering and calculating local production possibility frontiers. Using regression models for estimate correction requires further study due to possible systematic errors during estimation. A mixture of data correction and DMU clustering together with multi-stage DEA seems most promising at the moment. Analyzing several stages of transforming society’s resources into social welfare will allow for picking out the weak points in a state agency’s work.