14a. Determine the placement of departments for a newly designed facility that will minimize total transportation costs using the data in the following tables. Assume that reverse distances are the same. The locations are shown in the grid. Use a cost of $1 per trip yard.
Location
A Location
B Location
C
Location
D
DISTANCE BETWEEN LOCATIONS (YARDS) NUMBER OF TRIPS PER DAY BETWEEN DEPARTMENTS
From To A B C D From To 1 2 3 4
A --- 40 80 70 1 --- 10 20 80
B --- 40 50 2 --- 40 90
C --- 60 3 --- 55
D --- 4 ---
Determine the placement of departments for a newly designed facility that will minimize total transportation costs using the data in the following tables. Assume that reverse distances are the same. The locations are shown in the grid. Use a cost of $1 per trip yard.
To determine the placement of departments that will minimize total transportation costs, we need to consider both the distances between locations and the number of trips between departments per day.
First, let's calculate the transportation costs between each pair of locations. We will assume a cost of $1 per trip yard.
1. Calculate transportation costs between each pair of locations:
- From A to B: 40 yards * $1 = $40
- From A to C: 80 yards * $1 = $80
- From A to D: 70 yards * $1 = $70
- From B to C: 40 yards * $1 = $40
- From B to D: 50 yards * $1 = $50
- From C to D: 60 yards * $1 = $60
Next, let's calculate the total transportation costs for each placement scenario:
Scenario 1: A-B-C-D
- Transportation costs: $40 (A to B) + $40 (B to C) + $60 (C to D) = $140
Scenario 2: A-C-B-D
- Transportation costs: $80 (A to C) + $50 (C to B) + $60 (B to D) = $190
Scenario 3: A-D-B-C
- Transportation costs: $70 (A to D) + $50 (D to B) + $40 (B to C) = $160
Scenario 4: B-A-C-D
- Transportation costs: $40 (B to A) + $40 (A to C) + $60 (C to D) = $140
Scenario 5: B-C-A-D
- Transportation costs: $40 (B to C) + $80 (C to A) + $60 (A to D) = $180
Scenario 6: B-D-A-C
- Transportation costs: $50 (B to D) + $70 (D to A) + $40 (A to C) = $160
Based on the calculations above, scenario 1 (A-B-C-D) and scenario 4 (B-A-C-D) have the minimum total transportation costs of $140.
To determine the placement of departments for a newly designed facility that will minimize total transportation costs, we need to calculate the transportation costs between departments and find the configuration that minimizes these costs.
First, let's calculate the total transportation costs between departments based on the distance and the number of trips per day. We'll assume a cost of $1 per trip yard.
The total transportation cost between departments A and B = distance (40 yards) * trips per day (40) * cost per trip yard ($1) = $1600
The total transportation cost between departments A and C = distance (80 yards) * trips per day (70) * cost per trip yard ($1) = $5600
The total transportation cost between departments A and D = distance (70 yards) * trips per day (1) * cost per trip yard ($1) = $70
The total transportation cost between departments B and C = distance (40 yards) * trips per day (50) * cost per trip yard ($1) = $2000
The total transportation cost between departments B and D = distance (50 yards) * trips per day (2) * cost per trip yard ($1) = $100
The total transportation cost between departments C and D = distance (60 yards) * trips per day (3) * cost per trip yard ($1) = $180
Next, let's list all the possible configurations of department placements and calculate the total transportation costs for each configuration:
1. A-B-C-D:
Total transportation cost = $1600 + $5600 + $70 + $2000 + $100 + $180 = $9450
2. A-B-D-C:
Total transportation cost = $1600 + $100 + $70 + $2000 + $5600 + $180 = $9450
3. A-C-B-D:
Total transportation cost = $5600 + $2000 + $70 + $1600 + $100 + $180 = $9450
4. A-C-D-B:
Total transportation cost = $5600 + $1600 + $70 + $2000 + $100 + $180 = $9450
5. A-D-B-C:
Total transportation cost = $70 + $100 + $1600 + $2000 + $5600 + $180 = $9450
6. A-D-C-B:
Total transportation cost = $70 + $1600 + $5600 + $2000 + $100 + $180 = $9450
Based on the calculations, all the possible configurations of department placements result in the same total transportation cost of $9450. Therefore, any of these configurations can be chosen as they will minimize the total transportation costs.
$14,350.00
A (2) B (4) C (1)
D (3)