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Transportation type problems with quantity discounts

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  • V. Balachandran
  • Avinoam Perry

Abstract

It is known to be real that the per unit transportation cost from a specific supply source to a given demand sink is dependent on the quantity shipped, so that there exist finite intervals for quantities where price breaks are offered to customers. Thus, such a quantity discount results in a nonconvex, piecewise linear functional. In this paper, an algorithm is provided to solve this problem. This algorithm, with minor modifications, is shown to encompass the “incremental” quantity discount and the “fixed charge” transportation problems as well. It is based upon a branch‐and‐bound solution procedure. The branches lead to ordinary transportation problems, the results of which are obtained by utilizing the “cost operator” for one branch and “rim operator” for another branch. Suitable illustrations and extensions are also provided.

Suggested Citation

  • V. Balachandran & Avinoam Perry, 1976. "Transportation type problems with quantity discounts," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 23(2), pages 195-209, June.
    • Handle: RePEc:wly:navlog:v:23:y:1976:i:2:p:195-209
    DOI: 10.1002/nav.3800230203
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    1. V. Balachandran, 1977. "A Survey of the Applications of the Operator Theory of Parametric Programming for the Transportation and Generalized Transportation Problems," Discussion Papers 300, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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