A Negative-Cost Approach to the Formulation of a Transhipment Problem

Abstract

The transhipment problem formulation has been and is still being used extensively by researchers to solve spatial equilibrium and plant location problems. Hurt and Tramel, King and Logan, Rhody, and Judge et al. have all treated the subject of alternative formulations of transhipment problems. This paper (1) proposes an alternative formulation of these problems using a negative-cost technique and, (2) suggests a matrix reduction scheme which will reduce computational time for some problems.King and Logan used a three region, two-stage formulation of the transhipment model which was reformulated by Hurt and Tramel. As a point of departure, the same sample problem will be used to present the negative-cost formulation. This should enable the reader to more readily determine differences between formulations and decide which formulation best serves his particular needs.

Application of the Transhipment Model to Development of the Seed Industry in Northeast Brazil

“…Hurt and Tramel [3] presented an alternative formulation of the King-Logan transhipment model [4] which permits direct reading of the shipping pattern solution. Recently, Stennis and Hurt [12] developed an approach where the processing cost is inserted as a negative value on the main diagonal of the processor excess capacity submatrix, eliminating the necessity of combining processing cost with either transfer charge from producer to processor or the charge from processor to consumer.…”

“…Since details of the model, including matrix formats for input data and the solution, are given in a recent issue of this Journal [12], further discussion of the model is omitted.…”