Using LP/MIP Packages
D.1 SOLVING LINEAR PROGRAMMING PROBLEMS USING MAPLE, MATLAB, AND CPLEX
Consider a network with two nodes and a demand of 10 units between them; the network is connected by two parallel paths (links) where capacity of one link is 10 while the other one is 15 (Figure D.1). The problem is to minimize the maximum utilization (or load-balance flows). If we denote the flows on two paths by x1 and x2, then the utilization of the first path is x1/10 while that of the second path is x2/15. Then, the optimization problem can be written as:
FIGURE D.1 Two-Node Network
(D.1.1)
By introducing the auxiliary variable r
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