A further study on inverse linear programming problems

In this paper we continue our previous study (Zhang and Liu, J. Comput. Appl. Math. 72 (1996) 261–273) 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 part...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 106; no. 2; pp. 345 - 359
Main Authors: Zhang, Jianzhong, Liu, Zhenhong
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 30.06.1999
Elsevier
Subjects:
Applied sciences
Complementary slackness
Convex and discrete geometry
Exact sciences and technology
Geometry
Inverse problem
Linear programming
Mathematical programming
Mathematics
Minimum spanning tree
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Operational research and scientific management
Operational research. Management science
Sciences and techniques of general use
Shortest path
52A20
65K05
52B12
Minimum spanning tree
Shortest path
Linear programming
Complementary slackness
90C27
90C08
Inverse problem
Dual problem
Assignment problem
Spanning tree
Optimal solution
Unimodular matrix
ISSN:0377-0427, 1879-1778
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Summary:In this paper we continue our previous study (Zhang and Liu, J. Comput. Appl. Math. 72 (1996) 261–273) 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, we 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, we also consider the inverse LP problems under l ∞ measure and propose solution methods.
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(99)00080-1