An Integer Programming Approach to the Path Selection Problems
نویسندگان
چکیده
We consider two types of path selection problems for arc capacitated network. Given an arc capacitated network and a set of commodities, one problem is to find a subset of commodities to be routed and an assignment of them to the paths so that profit is maximized. The other problem is to route all given commodities in the network so that cost is minimized. Bifurcation of flow is not allowed in both cases. We formulate the problems as integer programming models and solve them. Column generation technique to solve the linear programming relaxation is proposed with two types of columns. To obtain an optimum integer solution for the problems, we propose a branching strategy in the branch-and-price scheme. Computational experiments show that the algorithm gives optimal solutions within reasonably small computing time. keywords Routing, Network Models, Integer Multicommodity Flow, Path Selection, Integer Programming
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