Abstract
The purpose of this paper is to develop a method for solving mixed integer linear programming problems with angular structure. The method can be viewed as an extension of the Dantzig-Wolfe decomposition technique to mixed integer problems. The solution is obtained by solving a restricted master problem and subproblems iteratively. The master problem is a linear programming problem, while the subproblems are mixed integer problems which are smaller in sizes than the original problem.
The termination of this algorithm is checked in two stages. If the optimality test is satisfied, the procedure terminates and the optimal solution is obtained. If not, the search for improvement is continued within a restricted extent of the search region. The procedure is finite. If the procedure terminates with no improved solution, the best solution obtained so far is provided as a suboptimal solution.
With an application to the optimal planning of mixing raw coal in the iron industry, the present algorithm compares favourably with the conventional branch-and-bound method.
