
To determine: The new placement of departments that will minimize the total transportation costs.
Introduction:
Product layouts:
Product layout is a production system where the equipment and workstations are placed along the production and assembly lines. A conveyor is used to move the production units along the line. Product layouts have specialized labor to perform specific functions with the help of equipment (programmed to do a specific tasks in a repetitive manner). The layout is mostly based on the processing sequence.
Process layouts:
Process layout is a production system where the equipment is placed in a system based on their functions. The production line is planned to eliminate wastes. In certain process layouts, the machineries and work settings are not arranged as per the standardized production sequence. However, there would be an assembly having similar machineries and operational activities depending on the requirement. For example, paint department.

Answer to Problem 15P
Arrangement:
The total transportation cost for the arrangement is $143, 650 per day.
Explanation of Solution
Given information:
- Work centers 1 and 3 are assigned in two locations and cannot be moved.
- There are 8 work centers.
- Cost is $1 per load per meter.
- The departments are 1, 2, 3, 4, 5, 6, 7, and 8.
- The locations are A, B, C, D, E, F, G, and H.
Distances between locations (meters):
To | A | B | C | D | E | F | G | H |
From | ||||||||
A | 40 | 40 | 60 | 120 | 80 | 100 | 110 | |
B | 60 | 40 | 60 | 140 | 120 | 130 | ||
C | 45 | 85 | 40 | 70 | 90 | |||
D | 40 | 50 | 40 | 45 | ||||
E | 90 | 50 | 40 | |||||
F | 40 | 60 | ||||||
G | 40 | |||||||
H |
Number of load per day between departments:
To | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
From | ||||||||
1 | 10 | 5 | 90 | 370 | 135 | 125 | 0 | |
2 | 360 | 120 | 40 | 115 | 45 | 120 | ||
3 | 350 | 110 | 40 | 20 | 190 | |||
4 | 190 | 70 | 50 | 200 | ||||
5 | 10 | 40 | 10 | |||||
6 | 50 | 20 | ||||||
7 | 20 | |||||||
8 |
Locations:
Arrangement of departments:
The numbers of trips between work centers is shown and are ranked from high to low.
Work centers pair | Number of loads | Ranking |
1–2 | 10 | |
1–3 | 5 | |
1–4 | 90 | 11 |
1–5 | 370 | 1 |
1–6 | 135 | 6 |
1–7 | 125 | 7 |
1–8 | 0 | |
2–3 | 360 | 2 |
2–4 | 120 | 8 (Tied) |
2–5 | 40 | |
2–6 | 115 | 9 |
2–7 | 45 | |
2–8 | 120 | 8 (Tied) |
3–4 | 350 | 3 |
3–5 | 110 | 10 |
3–6 | 40 | |
3–7 | 20 | |
3–8 | 200 | 4 |
4–5 | 190 | 5 (Tied) |
4–6 | 70 | 12 |
4–7 | 50 | |
4–8 | 190 | 5 (Tied) |
5–6 | 10 | |
5–7 | 40 | |
5–8 | 10 | |
6–7 | 50 | |
6–8 | 20 | |
7–8 | 20 |
The table clearly indicates that work centers 1-5 have the highest number of trips between them. After that the following work centers have the most number of trips: 2-3, 3-4, 3-8, 4-5, 4-8, 1-6, 1-7, 2-4, 2-8 and others. After continuous trial and error method the following assignment is reached. It is to be noted that, except the pre assigned work centers, slight variations are reasonable in the assignment as long as work centers 2,4 and 8 are nearer to 3, 4 is nearer to 5 and 5 is nearer to 1.
Calculation of cost for each work center pair:
The cost for each department pair is calculated by multiplying the number of loads with the distance with the cost per load per meter.
Department 1-2:
Cost=10×100×1=$1,000
Department 1-3:
Cost=5×120×1=$600
Department 1-4:
Cost=90×60×1=$5,400
Department 1-5:
Cost=370×40×1=$14,800
Department 1-6:
Cost=135×80×1=$10,800
Department 1-7:
Cost=125×40×1=$5,000
Department 2-3:
Cost=360×50×1=$18,000
Department 2-4:
Cost=120×40×1=$4,800
Department 2-5:
Cost=40×120×1=$4,800
Department 2-6:
Cost=115×40×1=$4,600
Department 2-7:
Cost=45×70×1=$3,150
Department 2-8:
Cost=120×40×1=$4,800
Department 3-4:
Cost=350×40×1=$14,000
Department 3-5:
Cost=110×60×1=$6,600
Department 3-6:
Cost=40×90×1=$3,600
Department 3-7:
Cost=20×85×1=$1,700
Department 3-8:
Cost=200×40×1=$8,000
Department 4-5:
Cost=190×40×1=$7,600
Department 4-6:
Cost=70×50×1=$3,500
Department 4-7:
Cost=50×45×1=$2,250
Department 4-8:
Cost=190×45×1=$8,550
Department 5-6:
Cost=10×140×1=$1,400
Department 5-7:
Cost=40×60×1=$2,400
Department 5-8:
Cost=10×130×1=$1,300
Department 6-7:
Cost=50×40×1=$2,000
Department 6-8:
Cost=20×60×1=$1,200
Department 7-8:
Cost=20×90×1=$1,800
Calculation of total cost:
The total cost is calculated by adding the cost of individual work center pairs.
Cost=1,000+600+5,400+14,800+10,800+5,000+18,000+4,800+4,800+4,600+3,150+4,800+14,000+6,600+3,600+1,700+8,000+7,600+3,500+2,250+8,550+1,400+2,400+1,300+2,000+1,200+1,800=$143,650
The total transportation cost for the arrangement is $143,650.
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