On a class of three-dimensional transshipment problems

The transshipment technique is used to find the shortest route from one point in a network to another point and is very useful to reduce the cost of transportation. In this article, we have formulated a three‐dimensional linear transshipment problem. Sometimes, because of the budget/political constraints, the total flow of transportation is specified by some external decision maker which thereby results in restricted and enhanced flow in the market. The optimal solution of such problems is of practical interest to the decision maker and thus has motivated us to discuss such problems as a particular case of the original problem. The optimal solution of the specified problem is obtained by transforming it into an equivalent transportation problem by adding an additional row and a column and avoids the necessity of determining a least‐cost route for every origin‐destination pair. The algorithm is easy to understand and apply and it can serve the managers by providing a solution to a variety of production‐distribution problems having heterogeneous commodities. Numerical examples are also included to support the theory.