Fixed input allocation methods based on super CCR efficiency invariance and practical feasibility

Abstract

This paper distinguishes two kinds of fixed input allocation problems: the problem of allocating a fixed cost across a set of comparable decision making units (DMUs) and that of allocating a fixed resource along with sharing a common output target among DMUs. Based on super CCR efficiency invariance and practical feasibility, we adopt the data envelopment analysis technique to build three models for solving the two problems of allocating the above two kinds of fixed inputs among all DMUs and the common output target sharing problem companying with the fixed resource allocation, respectively. The main contributions of this paper include: we illustrate that the economic explanation “pareto-minimality” for the equality constraints introduced by Cook and Kress [5] is not appropriate; we introduce the concept of the obligation ratio, propose a minimax model and the corresponding algorithm to obtain a unique fixed cost allocation; we introduce the concept of the benefit ratio, design a maximin model and the corresponding algorithm to find a unique fixed resource allocation; we propose a method for getting a unique target setting companying with the fixed resource allocation, based on the sizes of individual DMUs’ existing inputs and allocated resources. Numerical results show the practicality and advantages of our new methods when compared with typical methods in the literature.