In this paper we use data from OECD countries participating in PISA 2012 to assess the efficiency of schools in a cross-country framework. In the analysis, and in contrast to previous applications, we consider that schools might concentrate their effort s on improving the results in one dimension of the educational output to a greater extent than in the other. To do this, we rely on non-radial efficiency measures of performance and the estimation of an educational production function based upon Data Envelopment Analysis (DEA) techniques. Specifically, DEA non-radial measures allow for identifying different levels of inefficiency for each output considered (reading and maths). In particular, we apply a non-radial measure based on Ando et al. [5] and Aparicio et al. [12]. Our results show that the majority of schools in OECD countries tend to be less efficient in reading than in mathematics.

Data Envelopment Analysis (DEA) is a non-parametric technique for estimating the technical efficiency of a set of Decision Making Units (DMUs) from a database consisting of inputs and outputs. This paper studies DEA models based on maximizing technical efficiency, which aim to determine the least distance from the evaluated DMU to the production frontier. Usually, these models have been solved through unsatisfactory methods used for combinatorial NP-hard problems. Here, the problem is approached by metaheuristic techniques and the solutions are compared with those of the methodology based on the determination of all the facets of the frontier in DEA. The use of metaheuristics provides solutions close to the optimum with low execution time.

Data Envelopment Analysis (DEA) is a nonparametric methodology for estimating technical efficiency of a set of Decision Making Units (DMUs) from a dataset of inputs and outputs. This paper is devoted to computational aspects of DEA models under the application of the Principle of Least Action. This principle guarantees that the efficient closest targets are determined as benchmarks for each assessed unit. Usually, these models have been addressed in the literature by applying unsatisfactory techniques, based fundamentally on combinatorial NPhard problems. Recently, some heuristics have been developed to partially solve these DEA models. This paper improves the heuristic methods used in previous works by applying a combination of metaheuristics and an exact method. Also, a parameterized scheme of metaheuristics is developed in order to implement metaheuristics and hybridations/combinations, adapting them to the particular problem proposed here. In this scheme, some parameters are used to study several types of metaheuristics, like Greedy Random Adaptative Search Procedure, Genetic Algorithms or Scatter Search. The exact method is included inside the metaheuristic to solve the particular model presented in this paper. A hyperheuristic is used on top of the parameterized scheme in order to search, in the space of metaheuristics, for metaheuristics that provide solutions close to the optimum. The method is competitive with exact methods, obtaining fitness close to the optimum with low computational time.

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Mixed Integer Linear Programs (MILPs) are usually NP-hard mathematical programming problems, which present difficulties to obtain optimal solutions in a reasonable time for large scale models. Nowadays, metaheuristics are one of the potential tools for solving this type of problems in any context. In this paper, we focus our attention on MILPs in the specific framework of Data Envelopment Analysis (DEA), where the determination of a score of technical efficiency of a set of Decision Making Units (DMUs) is one of the main objectives. In particular, we propose a new hyper-matheuristic grounded on a MILP-based decomposition in which the optimization problem is divided into two hierarchical subproblems. The new approach decomposes the model into discrete and continuous variables, treating each subproblem through different optimization methods. In particular, metaheuristics are used for dealing with the discrete variables, whereas exact methods are used for the set of continuous variables. The metaheuristics use an indirect representation that encodes an incomplete solution for the problem, whereas the exact method is applied to decode the solution and generate a complete solution. The experimental results, based on simulated data in the context of Data Envelopment Analysis, show that the solutions obtained through the new approach outperform those found by solving the problem globally using a metaheuristic method. Finally, regarding the new hyper-matheuristic scheme, the best algorithm selection is found for a set of cooperative metaheuristics ans exact optimization algorithms.