Consider the transportation problem and its initial solution in the table below.What is the improvement index for the empty cell Source 1 - Destination 3?
A)0
B)-14
C)-23
D)-70
E)115

Question

Consider the transportation problem and its initial solution in the table below.What is the improvement index for the empty cell Source 1 - Destination 3? 
A)0 
B)-14 
C)-23 
D)-70 
E)115

Quizplus · Accepted Answer

To find the improvement index for the empty cell Source 1 - Destination 3, the calculation is:
- (Cost of allocation to cell Source 1 - Destination 3 in the initial solution) - (Cost of allocation to other cells in the same row or column in the initial solution)
In this case, the cost of allocation to cell Source 1 - Destination 3 in the initial solution is 0, and the costs of allocation to other cells in the same row or column are:
- Source 1 - Destination 1: 5
- Source 1 - Destination 2: 8
- Source 2 - Destination 3: 17
- Source 3 - Destination 3: 6
So, the improvement index for the empty cell Source 1 - Destination 3 is:
- 0 - (5 + 8 + 17 + 6) = -36
The improvement index is negative, which means that the current solution is optimal and there is no room for improvement through allocation to that cell. Therefore, the best choice is to leave the table as it is, without any changes.

Consider the Transportation Problem and Its Initial Solution in the Table