Alternative Formulations of the Transhipment Problem

The problem of determining simultaneously the flows of primary products through processors to the market as final products has been formulated alternatively as a transhipment model by King and Logan and as a reduced matrices model by Rhody. An extension of this problem to a multiregion, multiproduct, and multiplant problem formulated in the general linear programming framework has been proposed by Judge et al. This article presents some alternative formulations of the problem within the framework of the transportation model that permit solution of problems of the type discussed by King and Logan without the need for subtraction of artificial variables; solution of problems of the transhipment type where processing capacity in any one or all of the regions is limited, but where the total processing capacity of all regions is enough or more than enough to handle the supply of the raw product; and solution of multiregion, multiplant, multiprocessing, and multiproduct problems of the type discussed by Judge.