Outline
- Abstract
- Keywords
- References
رئوس مطالب
- چکیده
- کلیدواژه ها
- 1 مقدمه
- 2 تحلیل پوششی داده ها و حل شدن مسئله
- 3 روش های ابتکاری برای دستیابی به راه حل معتبر
- 3.1 روش 1
- 3.2 روش 2
- 4 الگوریتم ژنتیک
- 5 نتایج تجربی
- 6 نتیجه گیری ها و آثار آتی
Abstract
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.
Keywords: Closest targets - Data Envelopment Analysis - Efficiency Methodologies - Genetic Algorithms - Mathematical Programming6 Conclusions and Future Works
Maximizing technical efficiency or, equivalently, determining least distance measures are topics of relevance in recent DEA literature. However, it is well-known that from a computational point of view this has usually been solved by unsatisfactory approaches associated with a combinatorial NP-hard problem.
This paper improves previous heuristics for the generation of valid solutions for an optimization problem for DEA. The new heuristic provides more valid solutions which satisfy all the constraints in the model and with a lower execution time. A Genetic Algorithm has been developed working with this initial population of valid and non-valid solutions to generate more valid solutions and to improve the best fitness obtained. The Genetic Algorithm gives solutions close to the optimum and is competitive with an exact method with high computational cost, which can not be used for large problems.
A deeper analysis should be made to tune the Genetic Algorithm to the problem to obtain better solutions with lower execution times. We have studied the problem associated with the so-called Enhanced Russell Graph measure. Nevertheless, there are a lot of measures in DEA that can be used in the maximization of technical efficiency. In this way, programming the approach based on metaheuristic algorithms to solve all of them can be seen as appropriate and interesting future work.