Transportation model Table
A more compact method for representing the transportation model than the linear equations is to use what we call the transportation tableau. It is a matrix form with its rows symbolizing the sources and its columns the destinations. The cost element cij are summarized in the northeast corner of the matrix cell (i,j). This will be the basis for the development of a special simplex-based method for solving the transportation problem.
In some cases, the problem could be unbalanced because the total supply does not equal the total demand.
Where demand exceeds supply, a fictitious or dummy source (plant) can be added with its capacity equal to the difference. The cost of shipping will be 0. Physically, the amount shipped to a destination from a dummy plant will represent the shortage quantity at that destination. We may look at the situation differently, however, by saying that a penalty cost is incurred for every unsatisfied demand unit at the destination centers. In this case the unit transportation cost will equal the unit penalty costs at the various destinations.
In a similar manner, if the supply exceeds the demand, we can add a fictitious or dummy destination that will absorb the difference. Any quantity shipped from a plant to a dummy destination represents a surplus quantity at that plant. The associated unit transportation cost is zero. However, we can charge a storage cost for holding these commodities at the plant, in which case the unit transportation cost will equal the unit storage cost.
At times we can find cells where we cannot allocate any unit due to physical constraints. In that case the transportation cost should be shown as M—being M a very high cost.