Linear, Integer, Separable and Fuzzy Programming Problems: A Unified Approach towards Reformulation
| Autor: | Cormac Lucas, Ken Darby-Dowman, J. Yadegar, Gautam Mitra |
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| Rok vydání: | 1988 |
| Předmět: |
Marketing
Mathematical optimization Linear programming Computer science business.industry Strategy and Management Fuzzy set Management Science and Operations Research Fuzzy logic Management Information Systems Nonlinear programming Separable space Software Software system business Integer programming |
| Zdroj: | Journal of the Operational Research Society. 39:161-171 |
| ISSN: | 1476-9360 0160-5682 |
| Popis: | For mathematical programming (MP) to have greater impact as a decision tool, MP software systems must offer suitable support in terms of model communication and modelling techniques. In this paper, modelling techniques that allow logical restrictions to be modelled in integer programming terms are described, and their implications discussed. In addition, it is illustrated that many classes of non-linearities which are not variable separable may be, after suitable algebraic manipulation, put in a variable separable form. The methods of reformulating the fuzzy linear programming problem as a max-min problem is also introduced. It is shown that analysis of bounds plays a key role in the following four important contexts: model reduction, reformulation of logical restrictions as 0-1 mixed integer programmes, reformulation of non-linear programmes as variable separable programmes and reformulation of fuzzy linear programmes. It is observed that, as well as incorporating an interface between the modeller and the optimizer, there is a need to make available to the modeller software facilities which support the model reformulation techniques described here. |
| Databáze: | OpenAIRE |
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