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A further study on inverse linear programming problems. (English) Zbl 0971.90051
Summary: The authors continue their previous study [J. Comput. Appl. Math. 72, 261-273 (1996; Zbl 0856.65069)] on inverse linear programming problems which requires us to adjust the cost coefficients of a given LP problem as less as possible so that a known feasible solution becomes the optimal one. In particular, they consider the cases in which the given feasible solution and one optimal solution of the LP problem are 0-1 vectors which often occur in network programming and combinatorial optimization, and give very simple methods for solving this type of inverse LP problems. Besides, instead of the commonly used \(l_1\) measure, they also consider the inverse LP problems under \(l_\infty\) measure and propose solution methods.

MSC:
90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
90C27 Combinatorial optimization
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
52B12 Special polytopes (linear programming, centrally symmetric, etc.)
65K05 Numerical mathematical programming methods
Software:
DEA
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References:
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