Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present a column-generation model and branch-and-price-and-cut algorithm for origin-destination integer multicommodity flow problems. The origin-destination integer multicommodity flow problem is a constrained version of the linear multicommodity flow problem in which flow of a commodity (defined in this case by an origin-destination pair) may use only one path from origin to destination. Branch-and-price-and-cut is a variant of branch-and-bound, with bounds provided by solving linear programs using column-and-cut generation at nodes of the branch-and-bound tree. Because our model contains one variable for each origin destination path, for every commodity, the linear programming relaxations at nodes of the branch-and-bound tree are solved using column generation, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality.  devise a new branching rule that allows columns to be generated efficiently at each node of the branch-and-bound tree. Then,  describe cuts (cover inequalities) that can be generated at each node of the branch-and-bound tree. These cuts help to strengthen the linear programming relaxation and to mitigate the effects of problem symmetry.  detail the implementation of our combined column and- cut generation method and present computational results for a set of test problems arising from telecommunications applications.  illustrate the value of our branching rule when used to find a heuristic solution and compare branch-and-price and branch-and-price-and-cut methods to find optimal solutions for highly capacitated problems.
['Cynthia Barnhart', 'Christopher A. Hane', 'Pamela H. Vance']
I am writing a research paper on a idea Using Branch-and-Price-and-Cut to Solve Origin-Destination Integer Multicommodity Flow Problems
[{"from": "human", "value": "I am writing a research paper on a idea Using Branch-and-Price-and-Cut to Solve Origin-Destination Integer Multicommodity Flow Problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present a column-generation model and branch-and-price-and-cut algorithm for origin-destination integer multicommodity flow problems. The origin-destination integer multicommodity flow problem is a constrained version of the linear multicommodity flow problem in which flow of a commodity (defined in this case by an origin-destination pair) may use only one path from origin to destination. Branch-and-price-and-cut is a variant of branch-and-bound, with bounds provided by solving linear programs using column-and-cut generation at nodes of the branch-and-bound tree. Because our model contains one variable for each origin destination path, for every commodity, the linear programming relaxations at nodes of the branch-and-bound tree are solved using column generation, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality.  devise a new branching rule that allows columns to be generated efficiently at each node of the branch-and-bound tree. Then,  describe cuts (cover inequalities) that can be generated at each node of the branch-and-bound tree. These cuts help to strengthen the linear programming relaxation and to mitigate the effects of problem symmetry.  detail the implementation of our combined column and- cut generation method and present computational results for a set of test problems arising from telecommunications applications.  illustrate the value of our branching rule when used to find a heuristic solution and compare branch-and-price and branch-and-price-and-cut methods to find optimal solutions for highly capacitated problems."}]