Non Iterative Algorithm Form Solving Special Types of Transportation Problems.
CASE WESTERN RESERVE UNIV CLEVELAND OHIO DEPT OF OPERATIONS RESEARCH
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Many transportation problems are such that, when origins and destinations are suitably indexed, the cost matrix contains elements along the main diagonal, a band above it, and a band below it, while the other elements of the cost matrix are infinite. A procedure has been developed which yields optimal solution to such tridiagonal problems in n steps for a n-origin, n-destination problem. A second model has been solved for a tridiagonal and a coupling column of the cost matrix. A third model, a four-diagonal one, has been partially solved. The author suggested and showed a method to solve any other model which is close to a tridiagonal one, by Benders Algorithm. The algorithm presented here works by eliminating all of diagonal variables in terms of the diagonal ones, and subsequentially models and small linear programming problems. Author
- Operations Research