Using DEA to obtain efficient solutions for multi-objective 0–1 linear programs

Abstract

This paper concerns the problem of a service-oriented public sector entity to allocate limited resources to different activities while keeping conflicting objectives in mind. The Multi-objective Resource Allocation Problem (MRAP) is to select activities to be performed. The authors formulate the problem as a multi-objective 0–1 linear problem. The authors implement Data Envelopment Analysis (DEA) with the Banker, Charnes and Cooper's (BCC) model to measure the Decision Making Unit's (DMU) efficiency. In this study, the production function is a mathematical statement relating the technological relationship between the objectives and resources of MRAP. Each DMU presents a technological relationship, i.e. DMU presents a relationship between resources and objectives. This relationship gives information about the use of resources and satisfactoriness of objectives. The inputs and outputs, respectively, outline resources and objectives. The production possibility set represents feasible solutions for MRAP. Moreover, due to the multiple objectives of problems, the method derives a solution set instead of an optimal solution in single objective ones. This solution set, a well-known efficient solutions set, forms the decision set of problems. Each DMU results from an alternative, a combination of activities. The production possibility set presents all the candidates of DMU. The set of alternatives resulting in efficient DMUs is efficient solutions of MRAP. The authors developed a two-stage algorithm to generate and evaluate DMUs. The first stage generates a DMU with the maximum of the distance function. The second stage is then used to evaluate the efficiency of the generated DMU.