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Integer Linear Programming Tricks with DEA (Data Envelopment Analysis) Applications
Mehdi Toloo, Full Professor, Technical University of Ostrava, Czech Republic
19 de junho (quarta), 11h
The fastest and most powerful solution methods are those for linear programming models. It is often advisable to use this format instead of solving a nonlinear model where possible. It is interesting to note that several practical problems can be transformed into linear integer programs. For example, integer variables can be introduced so that a nonlinear function can be approximated by a "piecewise linear" function. We first introduce some tricks in order to deal with nonlinearity issues in the following cases:
1. When a variable taking discontinuous values
2. Fixed costs
3. Either-or constraints
4. Conditional constraints
5. Elimination of products of variables
Moreover, we illustrate that how practically these tricks help us to address some problems in performance evaluation context.
Nowadays, it is necessary to evaluate efficiency (doing things right), effectiveness (doing the right things) and economy (doing things at a low price) in an organization. However, it is difficult to do this when there are multiple inputs and multiple outputs to the system. Data Envelopment Analysis (DEA) is a powerful nonparametric quantitative method in operations research and economics for evaluating the relative efficiency score of a set of Decision Making Units (DMUs), such as universities, car makers, hospitals, banks and so on.
Mehdi Toloo, B.Sc. (Pure Mathematics), M.Sc. (Applied Mathematics), Ph.D. (Operations Research), professor in the Department of Systems Engineering and Informatics, Technical University of Ostrava, Czech Republic. Areas of interest include Operations Research, Optimization, Linear Programming, Data Envelopment Analysis, Multi-Objective Programming, and Network Flows. He acts as an area editor in Computers & Industrial Engineering at ELSEVIER and Rairo - Operations Research. He has written fourteen books and his research has been published in top-tier journals including OMEGA, Energy, European Journal of Operational Research, Computers & Industrial Engineering, Computers & Operations Research, International Journal of Production Research, Journal of the Operational Research Society, Annals of Operations Research, Applied Mathematics and Computers, Applied Mathematical Modelling, Expert Systems with Applications, International Journal of Advanced Manufacturing Technology, Computers and Mathematics with Applications and Measurement.
