BUSN 312 Week 4 Assignment BUSN 312 Pharm: Transportation Models/Latest Updated Solution

BUSN 312 Week 4
Assignment
BUSN 312 Pharm: Transportation Models

, 1. Find the minimum cost solution for the following transportation problem
which has cost structure as:
To/From P Q R AVAILABILITY
A 16 19 12 14
B 22 13 19 16
C 14 28 18 12
REQUIREMENT 10 15 17
ANSWER:
- Step 1: Check balance
Total supply (Availability) = 14+16+12 = 42
Total demand (Requirement) = 10+15+17 = 42
Since supply equals demand, the problem is balanced (no dummy row or
column is required).
- Step 2: Find the minimum cost using Vogel’s Approximation Method
(VAM)
VAM works by computing penalties, which are the differences between the
two lowest costs in each row and column.
Find initial penalties:
o Row penalties:
A: 2 lowest costs are 12 and 16. Penalty= 16-12 = 4
B: 2 lowest costs are 13 and 19. Penalty= 19-13 = 6
C: 2 lowest costs are 14 and 18. Penalty= 18-14 = 4
o Column penalties:
P: 2 lowest costs are 14 and 16. Penalty= 16-14 = 2
Q: 2 lowest costs are 13 and 19. Penalty= 19-13 = 6
R: 2 lowest costs are 12 and 18. Penalty= 18-12 = 6
The highest penalty is 6, occurring in Row B, Column Q, and Column R. We
select one of these, choosing column Q is appropriate.
- Step 3: First allocation
In column Q, the lowest cost is B to Q = 13
Allocate min (Supply B = 16, Demand Q = 15) = 15
B supply becomes 1 (16-15)
Q demand becomes 0 (Column Q is satisfied and removed)
- Step 4: Recalculate penalties for the remaining table