A Noniterative Algorithm for Tridiagonal Transportation Problems and Its Generalization

Benjamin Lev
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Benjamin Lev: Temple University, Philadelphia, Pennsylvania

Operations Research, 1972, vol. 20, issue 1, 109-125

Abstract: Some 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. We present here a procedure that yields optimal solution to such tridiagonal problems in n steps for an n -origin, n -destination problem. We also suggest a method for solving any other model that is “close” to a tridiagonal one by Bender's Algorithm. The algorithm presented here works by eliminating all off-diagonal variables in terms of the diagonal ones, and then specifying values for the diagonal variables. The extension with Bender's Algorithm involves solution of a sequence of tridiagonal models and small linear programming problems.

Date: 1972
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