Lexicographically Minimum and Maximum Load Linear Programming Problems

Dritan Nace () and James B. Orlin ()
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Dritan Nace: Laboratoire Heudiasyc UMR CNRS 6599, Université de Technologie de Compiègne, 60205 Compiègne Cedex, France
James B. Orlin: Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Operations Research, 2007, vol. 55, issue 1, 182-187

Abstract: In this paper, we introduce the lexicographically minimum load linear programming problem, and we provide a polynomial approach followed by the proof of correctness. This problem has applications in numerous areas where it is desirable to achieve an equitable distribution or sharing of resources. We consider the application of our technique to the problem of lexicographically minimum load in capacitated multicommodity networks and discuss a special nonlinear case, the so-called Kleinrock load function. We next define the lexicographically maximum load linear programming problem and deduce a similar approach. An application in the lexicographically maximum concurrent flow problem is depicted followed by a discussion on the minimum balance problem as a special case of the lexicographically maximum load problem.

Keywords: networks/graphs; multicommodity; theory; programming; linear algorithms; multiple criteria; games/group decisions; cooperative (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (9)

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