Fusion of evaluation of possibility production function and DEA by introducing a fuzzy goal

Abstract

Efficiency evaluation for every DMU (decision-making unit) in a company is very important. Efficiency evaluation based on the production function is considered. Loglinear production function (Cobb-Douglas model) has been used. This loglinear model evaluates DMU by measuring the average. DEA (data envelopment analysis) is also suitable, as for example in CCR (Charnes-Cooper-Rhodes) and BCC (Banker-Charnes-Cooper) model, but it does not give the lower limit of the production set, only the upper one. We propose the possibility production function by introducing fuzziness into the loglinear production function. As we try to evaluate the efficiency by this possibility production function, efficiency ratings are obtained for the upper and lower limits. Though DEA and fuzzy loglinear model belong to the evaluating method in the sense of including all DMUs' data, DEA obtains lower limit inputs by the present output, and fuzzy loglinear approach obtains the possibility max output by the present inputs. Making full use of the difference of the two approaches, we try to fuse them by introducing the concept of a fuzzy goal. We propose to construct a fuzzy goal by the evaluating ratings for individual outputs by fuzzy loglinear analysis, and introduce this fuzzy goal into DEA. At all, by this fusion we can cover the important weak point in DEA which often evaluates one output and ignores the other outputs, and we can obtain the satisfactory evaluation ratings which considers possibility outputs from the present inputs.