Sensitivity Analysis In Transportation Model

Introduction:

SENSTIVITY analysis is the condition which occurred mostly in the management problem which affects the optimal solution parameter. It is, therefore, desirable to determine how sensitive the optimal solution is to different types of changes in the problem data and parameters. The changes, which have effect on the optimal solution, are: Change in objective function coefficients Resource or requirement levels, Possible addition or deletion of products or methods of production.

Sensitivity analysis:(a) Non - basic variables

a)      significance of implied cost, which fixes the upper limit of cost of the empty cell to entertain the cell in the next programme. sensitivity of optimal solution for the variations in the costs of empty cells and loaded cells.

b)      If unit cost of transportation of a particular non-basic variable changes, at what value of the cost of present optimum will no longer remain optimum, it is obvious that as the empty cell is not in the solution, any increase in its unit transportation cost will to qualify it for entering variable.

c)       But if the unit cost of empty cells is reduced the chances of changing the optimum value may be examined.

d)      Let us take an optimum solution :

a)      In the solution shown above as all the opportunity costs of empty cells are negative.

b)      Consider empty cell XA. Its opportunity cost is Rs. -3/- This means to say that the units cost of transportation of cell XA decreases by Rs.3/- or more i.e. Rs.10/- the unit cost of transportation of the empty cell XA minus 3 = 7, or less than 7 the optimal solution changes, i.e. the cell XA will become eligible for entering into solution. Hence this cost, which shows the limit of the unit cost of empty cell, is known as implied cost in transportation problems.

c)       opportunity cost of empty cell ZE is zero.

d)      This shows that the cell ZE is as good as a loaded cell and hence we can write alternate solutions by taking the cell ZE into consideration.

 Note:

·         No unit cost of transportation is given for the cellZC. Hence that cell should not be included in the programme.

·         For this purpose, we can crossthe cell or allocate very high unit cost of transportation for the cell.

·         In case zero or anynegative element is given as the unit cost of transportation for a cell, the value can be taken for further treatment.