Asked by Madeline Boutot on Jun 10, 2024
Verified
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? COSTS Dest. 1 Dest. 2 Dest. 3 Dest . 4 Supply Source 1 121891145 Source 2 1973015145 Source 3 810141650 Demand 80307060240/240\begin{array}{|l|r|r|r|r|r|}\hline \text { COSTS } & \text { Dest. 1 } & \text { Dest. 2 } & \text { Dest. 3 } & \text { Dest . 4 } & \text { Supply } \\\hline \text { Source 1 } & 12 & 18 & 9 & 11 & 45 \\\hline \text { Source 2 } & 19 & 7 & 30 & 15 & 145 \\\hline \text { Source 3 } & 8 & 10 & 14 & 16 & 50 \\\hline \text { Demand } & 80 & 30 & 70 & 60 & 240 /240 \\\hline\end{array} COSTS Source 1 Source 2 Source 3 Demand Dest. 1 1219880 Dest. 2 1871030 Dest. 3 9301470 Dest . 4 11151660 Supply 4514550240/240
Shipments Dest. 1 Dest. 2 Dest. 3 Dest 4 Row Total Source 1 4500045 Source 2 35307010145 Source 3 0005050 Col. Total 80307060240/240\begin{array}{|lrrrrr|}\hline \text { Shipments } & \text { Dest. 1 } & \text { Dest. 2 } & \text { Dest. 3 } & \text { Dest 4 } & \text { Row Total } \\\text { Source 1 } & 45 & 0 & 0 & 0 & 45 \\\text { Source 2 } & 35 & 30 & 70 & 10 & 145 \\\text { Source 3 } & 0 & 0 & 0 & 50 & 50 \\\text { Col. Total } & 80 & 30 & 70 & 60 & 240/240 \\\hline\end{array} Shipments Source 1 Source 2 Source 3 Col. Total Dest. 1 4535080 Dest. 2 030030 Dest. 3 070070 Dest 4 0105060 Row Total 4514550240/240
A) 0
B) -14
C) -23
D) -70
E) 115
Improvement Index
A metric used to quantify the gain or improvement in performance of a process or product after enhancements have been implemented.
Empty Cell
In the context of spreadsheets or databases, an empty cell refers to a cell that contains no data or value.
Source 1 - Destination 3
A model representing the transportation or transmission of resources, information, or goods from one source point to three distinct destination points.
- Decode progress indices in the optimization of solutions.
Verified Answer
MV
Marelle ValenciaJun 13, 2024
Final Answer :
B
Explanation :
The improvement index for an empty cell in a transportation problem is calculated by adding the costs of the occupied cells in the smallest closed path that includes the empty cell and subtracting the costs of the occupied cells that would be removed if the empty cell were filled. For Source 1 - Destination 3, the smallest closed path involves Source 1 - Destination 1, Source 2 - Destination 1, and Source 2 - Destination 3. The costs are 12 (Source 1 - Destination 1) + 30 (Source 2 - Destination 3) - 19 (Source 2 - Destination 1) = 23. The improvement index is the cost of the empty cell (9) minus this sum, which is 9 - 23 = -14.
Learning Objectives
- Decode progress indices in the optimization of solutions.