Article ID: | iaor20081486 |
Country: | United States |
Volume: | 55 |
Issue: | 1 |
Start Page Number: | 182 |
End Page Number: | 187 |
Publication Date: | Jan 2007 |
Journal: | Operations Research |
Authors: | Orlin James B., Nace Dritan |
Keywords: | game theory, programming: multiple criteria, networks |
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.