Abstract
Data envelopment analysis (DEA) is a non-parametric technique to measure the efficiency of productive units as they transform inputs into outputs. A productive unit has, in DEA terms, an all-encompassing definition. It may as well refer to a factory whose products were made from raw materials and labor or to a school that, from prior knowledge and lessons time, produces more knowledge. All these units are usually named decision making units (DMU). So, DEA is a technique enabling the calculation of a single performance measure to evaluate a system. Although some DEA techniques that cater for decision makers’ preferences or specialists’ opinions do exist, they do not allow for interactivity. Inversely, interactivity is one of the strongest points of many of the multi-criteria decision aid (MCDA) approaches, among which those involved with multi-objective linear programming (MOLP) are found. It has been found for several years that those methods and DEA have several points in common. So, many works have taken advantage of those common points to gain insight from a point of view as the other is being used. The idea of using MOLP, in a DEA context, appears with the Pareto efficiency concept that both approaches share. However, owing to the limitations of computational tools, interactivity is not always fully exploited. In this article we shall show how one, the more promising model in our opinion that uses both DEA and MOLP (Li & Reeves, 1999), can be better exploited with the use of TRIMAP (Climaco & Antunes, 1987, 1989). This computational technique, owing in part to its graphic interface, will allow the MCDEA method potentialities to be better used. MOLP and DEA share several concepts. To avoid naming confusion, the word weights will be used for the weighing coefficients of the objective functions in the multi-objective problem. For the input and output coefficients the word multiplier shall be used. Still in this context, the word efficient shall be used only in a DEA context and, for the MOLP problems, the optimal Pareto solutions will be called non-dominated solutions.
Key Terms in this Chapter
TRIMAP: TRIMAP is an interactive tri-objective interactive solver package.
Decision Making Unit (DMU): DMU is a unit under evaluation in DEA.
Multiple Objective Linear Programming (MOLP): MOLP is a linear program with more than one objective function.
Data Envelopment Analysis (DEA): DEA is a non-parametric approach to efficiency measurement.
Non-Dominated Solution: A feasible solution is non-dominated whether does not exist another feasible solution better than the current one in some objective function without worsening other objective function.
Efficient DMU: An efficient DMU is one located on the efficient frontier.
Benchmark: Benchmark is an efficient DMU with management practices that are reference for some inefficient DMUs.
Target: Target is a point in the efficient frontier that is used as a goal for an inefficient DMU.
Multiple Criteria Data Envelopment Analysis (MCDEA): MCDEA is a tri-objective linear model proposed by Li and Reeves (1999).