ILOG CPLEX 11.0 User's Manual

-a 1 + a 2 - a 8 - a 9 + a 14 = 0- a 2 + a 3 + a 9 = 0- a 3 + a 4 + a 10 + a11 - a 12 = -15a 7 + a 8 - a 10 - a 13 = 5- a 5 + a 6 - a 11 + a 12 + a 13 - a 14 = 0- a 4 + a 5 = 0- a 6 - a 7 = -10with these bounds18≤ a 1 ≤ 24 0≤ a 2 ≤ 25 a 3 = 120≤ a 4 ≤ 10 0≤ a 5 ≤ 9 a 6 free0≤ a 7 ≤ 20 0≤ a 8 ≤ 10 0≤ a 9 ≤ 50≤ a 10 ≤ 15 0≤ a 11 ≤ 10 0≤ a 12 ≤ 110≤ a 13 ≤ 6 0≤ a 14In that formulation, in each column there is exactly one coefficient equal to 1 (one), exactlyone coefficient equal to -1, and all other coefficients are 0 (zero).Since a network-flow problem corresponds in this way to an LP problem, you can indeedsolve a network-flow problem by means of a ILOG CPLEX LP optimizer as well. If youread a network-flow problem into the Interactive Optimizer, you can transform it into its LPformulation with the command change problem lp. After this change, you can apply anyof the LP optimizers to this problem.When you change a network-flow problem into an LP problem, the basis information that isavailable in the network-flow problem is passed along to the LP formulation. In fact, if youhave already solved the network-flow problem to optimality, then if you call the primal ordual simplex optimizers (for example, with the Interactive Optimizer command primopt ortranopt), that simplex optimizer will perform no iterations.Generally, you can also use the same basis from a basis file for both the LP and the networkoptimizers. However, there is one exception: in order to use an LP basis with the networkoptimizer, at least one slack variable or one artificial variable needs to be basic. Startingfrom an Advanced Basis on page 178 explains more about this topic in the context of LPoptimizers.If you have already read the LP formulation of a problem into the Interactive Optimizer, youcan transform it into a network with the command change problem network. Given anyILOG CPLEX 11.0 — USER’ S MANUAL 225