Transshipment Problem

Transshipment Problem
There could be a situation where it might be more economical to transport consignments that is initially within certain origins and destinations and finally to the ultimate receipt points, instead of transporting the consignments from an origin to a destination as in the transportation problem.
The movement of consignment involves two different modes of transport road and railways or between stations connected by meter gauge and broad gauge lines. These different modes require transshipment. Thus for the purpose of transshipment the distinction between an origin and destination is dropped so that from a transportation problem with m origins and n destinations we obtain a transshipment problem with m + n origins and m + n destinations. The formulation and solution of a transshipment problem is illustrated with the following example.
Example:
Consider the following transportation problem where the origins are plants and destinations are depots.

When each plant is also considered as a destination and each depot is also considered as an origin, there are exactly five origins and five destinations. So, some additional cost data are necessary, they are as follows:



Table 3
Unit transportation cost From Depot to Depot
To
Depot X Depot Y Depot Z




Table 4: Unit transportation cost From Depot to Plant


Now, from the tables 1, 2, 3 and 4 we obtain the transportation formulation of the transshipment problem, which is shown in the table 5.

The total supply and total demand in the original transportation problem (450) is added to each row and column of the transshipment problem. The resulting transportation problem has m + n = 5 origins and m + n = 5 destinations.
By solving the transportation problem presented in table 5, we obtain:
x11=150, x13=300, x14=150, x21=300, x22=450, x33=300, x35=150, x44=450, x55=450
The transshipment problem explanation is as follows:
1. Transport x13=300 from plant A to depot X and x14=150 to depot Y.
2. Transport x21=300 from plant B to plant A.
3. Transport x35=150 from depot X to depot Z.
Thus, the total cost of transshipment is:
1*300 + 3 * 150 + 2*300 + 2*150 = $1650
Note: The minimum transportation cost = 3450.
Thus, transshipment reduces the cost of consignment movement.