Kyung S. Park

RAM: A Range Adjusted Measure of Inefficiency for Use with Additive Models, and Relations to Other Models and Measures in DEA

Generalized Efficiency Measures (GEMS) for use in DEA are developed and analyzed in a context of differing models where they might be employed. The additive model of DEA is accorded a central role and developed in association with a new measure of efficiency referred to as RAM (Range Adjusted Measure). The need for separately treating input oriented and output oriented approaches to efficient measurement is eliminated because additive models effect their evaluations by maximizing distance from the efficient frontier (in ℓ1, or weighted ℓ1, measure) and thereby simultaneously maximize outputs and minimize inputs. Contacts with other models and approaches are maintained with theorems and accompanying proofs to ensure the validity of the thus identified relations. New criteria are supplied, both managerial and mathematical, for evaluating proposed measures. The concept of “approximating models” is used to further extend these possibilities. The focus of the paper is on the “physical” aspects of performance involved in “technical” and “mix” inefficiencies. However, an Appendix shows how “overall,” “allocative” and “technical” inefficiencies may be incorporated in additive models.

Ranking fuzzy numbers with index of optimism

Abstract Fuzzy numbers are convenient for representing imprecise numerical quantities in a vague environment, and their comparison or ranking is very important for application purposes. Despite many methods suggested in the literature, there is no single measure that is universally applicable to a wide variety of situations. This paper suggests a new method for comparing fuzzy numbers based on the combination of maximizing possibility and minimizing possibility using an index of optimism in [0, 1] reflecting the decision makers risk taking attitude. The method is simple, but has many comparative advantages.

Tools for interactive multiattribute decisionmaking with incompletely identified information

Abstract The aim of this paper is to present tools or techniques for an interactive multiattribute decisionmaking with the decision makers incomplete information. That is: (1) We formally describe mathematical models under certainty and uncertainty for establishing pairwise dominance, where the incomplete information becomes the set of constraints in the model. (2) We present a description on styles of incomplete parameter value information. (3) The characteristic of a weak dominance is described. When the decision maker is not willing or able to provide more information on parameters, the weak dominance technique is useful for a final choicemaking. (4) We propose a dominance graph and also present an algorithm of generating the dominance graph based on the information of pairwise dominance. The dominance graph compactly displays the dominance structure of all alternatives, thus it can be used for aiding the selection of preferable alternatives.

Inventory model with partial backorders

This article presents a deterministic inventory model for situations in which, during the stockout period, a fraction j8 of the demand is backordered and the remaining fraction 1 — β is lost. By defining a time proportional backorder cost and a fixed penalty cost per unit lost, a convex objective function representing the average annual cost of operating the inventory system is obtained. The optimal operating policy variables are calculated directly. At the extremes β = 1 and β = 0 the model presented reduces to the usual backorders and lost sales case, respectively.

Fuzzy cognitive maps considering time relationships

Causal knowledge is often cyclic and fuzzy, thus it is hard to represent in the form of trees. A fuzzy cognitive map (FCM) can represent causal knowledge as a signed directed graph with feedback. It provides an intuitive framework in which to form decision problems as perceived by decision makers and to incorporate the knowledge of experts. This paper proposes a fuzzy time cognitive map (FTCM), which is a FCM introduced to a time relationship on arrows. We first discuss the characteristics and basic assumptions of the FCM, and present a description of causal propagations in a FCM with the causalities of negative-positive-neutral interval, -1, 1]. We develop a method of translating the FTCM, that has a different time lag, into the FTCM that has one or the same unit-time lag, which is a value-preserving translation. With the FTCM, we illustrate analysing the change of causalities among factors according to lapse of time.

A structured methodology for comparative evaluation of user interface designs using usability criteria and measures

Abstract Previous research in software ergonomics has indicated the importance of evaluating the usability of computer user interfaces. This paper presents a quantitative basis for selecting from among multiple alternative interfaces relative to multiple criteria of usability concern. The proposed model consists of two main phases: the prescreening phase and the evaluation phase. The prescreening phase involves expert judgment-based assessment with qualitative criteria. The first phase uses absolute measurement analytic hierarchy process (AHP) to filter possible alternative interfaces to a reasonable subset. The evaluation phase involves user-based assessment such as user testing, with quantitative criteria. The objective of the second phase is to evaluate a subset of alternatives using objective measures and to select the best alternative. A set of criteria and measures for evaluating the usability of computer software designs is presented. The proposed methodology is demonstrated in the interface design of a database system used to analyze trip cases information of nuclear power plant. Relevance to industry There is currently a focus on the usability of interactive computer software. Software developers, interface designers or human factors engineers often confront the task of comparative evaluation among systems, versions or interface designs. The proposed methodology provides practitioners with a structured approach to select the best interface based on usability criteria and measures.

An application of data envelopment analysis in telephone offices evaluation with partial data

Abstract The presence of partial data motivates the need to investigate how such factors can be incorporated into the existing measurement models. In this paper, a procedure is proposed for incorporating a set of factors with partial data into the DEA structure and restricting factor weights. The first DEA formulation is a complicated non-linear model issued from the set of partial data. In order to transform the first formulation into an ordinary linear programming model, both a linear scale transformation and variable change technique are used. The resulting linear programming model is then applied to the efficiency evaluation of telephone offices. Scope and purpose A procedure for handling both linear partial data on factor values and its weight preferences in data envelopment analysis (DEA) structure is presented. DEA is a methodology for driving the relative efficiencies of organizations or decision making units (DMUs) where there are multiple incommensurate inputs and outputs. The usual setting for many DEA applications involves a set of similar DMUs, for each of which there is an observable and measurable set of inputs and outputs. In some applications, however, a number of factors may be measurable only on partial data such as ordinal rankings and ratio bounds, owing mainly to intangible attributes to reflect social and environmental impacts. A model dealing with these partial data is presented and applied to the efficiency of telephone offices.

Comparing methods for multiattribute decision making with ordinal weights

This paper is concerned with procedures for ranking discrete alternatives when their values are evaluated precisely on multiple attributes and the attribute weights are known only to obey ordinal relations. There are a variety of situations where it is reasonable to use ranked weights, and there have been various techniques developed to deal with ranked weights and arrive at a choice or rank alternatives under consideration. The most common approach is to determine a set of approximate weights (e.g., rank-order centroid weights) from the ranked weights. This paper presents a different approach that does not develop approximate weights, but rather uses information about the intensity of dominance that is demonstrated by each alternative. Under this approach, several different, intuitively plausible, procedures are presented, so it may be interesting to investigate their performance. These new procedures are then compared against existing procedures using a simulation study. The simulation result shows that the approximate weighting approach yields more accurate results in terms of identifying the best alternatives and the overall rank of alternatives. Although the quality of the new procedures appears to be less accurate when using ranked weights, they provide a complete capability of dealing with arbitrary linear inequalities that signify possible imprecise information on weights, including mixtures of ordinal and bounded weights.

Establishing dominance and potential optimality in multi-criteria analysis with imprecise weight and value

Abstract The model presented in this paper does not require exact estimations of decision parameters such as attribute weights and values that may often be considerable cognitive burden of human decision makers. Information on the decision parameters is only assumed to be in the form of arbitrary linear inequalities which form constraints in the model. We consider two criteria, dominance and potential optimality, to check whether or not each alternative is outperform for a fixed feasible region denoted by the constraints. In particular, we develop a method to identify potential optimality of alternatives when all (or subsets) of the attribute values as well as weights are imprecisely know. This formulation becomes a nonlinear programming problem hard to be solved generally so that we provide in this paper how this problem is transformed into a linear programming equivalent. Scope and purpose Most managerial decisions involve choosing an optimal alternative from a number of available alternatives. Researchers have proposed a lot of methods to assist decision makers in choice making with a set of, usually conflicting, criteria or attributes. Many of these approaches require exact (or precise) information about either or both attribute values and/or trade-off weights. In some practice, however, it is not easy for decision makers to provide such exact data because, for example, intangible attributes to reflect social and environmental impacts may be included. To cope with such problem, a mathematical programming model-based approach to multi-criteria decision analysis is presented in this paper when both attribute weights and marginal values are imprecisely identified. A weighted additive rule is used to evaluate the performance of alternatives. We then show how to obtain non-dominated and potentially optimal alternatives in order to support choice making.

Sex differences in anthropometry for school furniture design

This paper is concerned with anthropometric dimensions of young Koreans and their interrelationships for school furniture design. Ten anthropometric measurements were taken from 1248 subjects, age range 6-17. The study investigated sex differences in interrelationships between body dimensions, to provide suitable sizes of chair and desk for boys and girls. The results showed that stature had a high relationship to body dimensions for school furniture design, and that there were significant sex differences in relationships between stature and the body dimensions. In particular, boys above 126 cm in stature required higher desk and chair heights than girls of the same stature. On the other hand, girls above 120 cm in stature required a larger depth and breadth of chair than boys of the same stature.