(486) the simplex multipliers and the shadow price in linear programming مضاعفات سيمبلكس وسعر الظل في البرمجة الخطية
The study begins by presenting the theoretical foundations of the simplex multiplier method and explains that the approach relies on matrix representations of the relationships among basic and non-basic variables within a linear programming model. The study demonstrates that matrix-based procedures...
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| Materyal Türü: | Kitap |
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معهد التخطيط القومي
2026
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| Online Erişim: | https://repository.inp.edu.eg/handle/123456789/6425 |
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| Özet: | The study begins by presenting the theoretical foundations of the simplex multiplier method and explains that the approach relies on matrix representations of the relationships among basic and non-basic variables within a linear programming model. The study demonstrates that matrix-based procedures reduce computational requirements, particularly in problems characterized by a large number of variables relative to constraints. Consequently, this approach saves computational time and reduces storage requirements. Additionally, because the original model data remain unchanged throughout iterative procedures, cumulative numerical errors can be minimized and calculations can be verified more efficiently.
Particular attention is given to the concept of shadow prices as economic indicators measuring the expected change in the objective function resulting from a one-unit change in available resources or constraints. The study emphasizes that shadow prices are important not only for economic interpretation but also for sensitivity analysis and post-optimization studies examining the effects of modifications in model parameters.
The study also discusses degeneracy problems and their treatment through the lexicographic rule, together with the role of shadow prices in large-scale programming models and decomposition techniques. It concludes that simplex multipliers and shadow prices provide effective tools not only for obtaining optimal solutions but also for interpreting and evaluating solution flexibility and supporting scientifically based managerial and economic decision-making processes. |
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