Comparison of Multi-objective Linear Programming Solutions Using Performance Metrics Based on Data Envelopment Analysis Models

In this study, three performance metrics based on data envelopment analysis (DEA) are proposed, aiming to evaluate and compare solution methods for solving multi-objective linear programming (MOLP) models. Particularly, the proposed metrics are based on the slack-based measure (SBM) model and the super-efficiency DEA model (SE-DEA). For the SBM model, an integer version is formulated (INT-SBM model), which offers the advantage of evaluating non-dominated solutions in the non-convex region of the Pareto frontier. In this study, this case is demonstrated through an example. The SE-DEA model has the advantage of identifying the non-dominated solutions that define the Pareto frontier. Furthermore, each metric is associated to one of the cardinality, accuracy, and diversity categories, and are classified as unary or binary. The cardinality and accuracy metrics are estimated by using a procedure where the INT-SBM model is applied. On the other hand, the diversity metric is calculated in a procedure by using the SE-DEA model. In order to compare two sets of solutions obtained for a MOLP tactical harvest planning model based on two strategies of the multi-objective greedy randomized adaptive search procedure (MO-GRASP), the proposed metrics are applied. The results indicate that the metrics effectively discriminate between the MOLP solution methods and can support the selection of a suitable method for solving a MOLP model.