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A Noniterative Algorithm for Tridiagonal Transportation Problems and Its Generalization

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  • Benjamin Lev

    (Temple University, Philadelphia, Pennsylvania)

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.

Suggested Citation

  • Benjamin Lev, 1972. "A Noniterative Algorithm for Tridiagonal Transportation Problems and Its Generalization," Operations Research, INFORMS, vol. 20(1), pages 109-125, February.
    • Handle: RePEc:inm:oropre:v:20:y:1972:i:1:p:109-125
    DOI: 10.1287/opre.20.1.109
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