Chapter 6, Problem 15P

Summary Introduction

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:

$\begin{array}{c}\text{Cost}=10\times 100\times 1\\ =\$1,000\end{array}$

Department 1-3:

$\begin{array}{c}\text{Cost}=5\times 120\times 1\\ =\$600\end{array}$

Department 1-4:

$\begin{array}{c}\text{Cost}=90\times 60\times 1\\ =\$5,400\end{array}$

Department 1-5:

$\begin{array}{c}\text{Cost}=370\times 40\times 1\\ =\$14,800\end{array}$

Department 1-6:

$\begin{array}{c}\text{Cost}=135\times 80\times 1\\ =\$10,800\end{array}$

Department 1-7:

$\begin{array}{c}\text{Cost}=125\times 40\times 1\\ =\$5,000\end{array}$

Department 2-3:

$\begin{array}{c}\text{Cost}=360\times 50\times 1\\ =\$18,000\end{array}$

Department 2-4:

$\begin{array}{c}\text{Cost}=120\times 40\times 1\\ =\$4,800\end{array}$

Department 2-5:

$\begin{array}{c}\text{Cost}=40\times 120\times 1\\ =\$4,800\end{array}$

Department 2-6:

$\begin{array}{c}\text{Cost}=115\times 40\times 1\\ =\$4,600\end{array}$

Department 2-7:

$\begin{array}{c}\text{Cost}=45\times 70\times 1\\ =\$3,150\end{array}$

Department 2-8:

$\begin{array}{c}\text{Cost}=120\times 40\times 1\\ =\$4,800\end{array}$

Department 3-4:

$\begin{array}{c}\text{Cost}=350\times 40\times 1\\ =\$14,000\end{array}$

Department 3-5:

$\begin{array}{c}\text{Cost}=110\times 60\times 1\\ =\$6,600\end{array}$

Department 3-6:

$\begin{array}{c}\text{Cost}=40\times 90\times 1\\ =\$3,600\end{array}$

Department 3-7:

$\begin{array}{c}\text{Cost}=20\times 85\times 1\\ =\$1,700\end{array}$

Department 3-8:

$\begin{array}{c}\text{Cost}=200\times 40\times 1\\ =\$8,000\end{array}$

Department 4-5:

$\begin{array}{c}\text{Cost}=190\times 40\times 1\\ =\$7,600\end{array}$

Department 4-6:

$\begin{array}{c}\text{Cost}=70\times 50\times 1\\ =\$3,500\end{array}$

Department 4-7:

$\begin{array}{c}\text{Cost}=50\times 45\times 1\\ =\$2,250\end{array}$

Department 4-8:

$\begin{array}{c}\text{Cost}=190\times 45\times 1\\ =\$8,550\end{array}$

Department 5-6:

$\begin{array}{c}\text{Cost}=10\times 140\times 1\\ =\$1,400\end{array}$

Department 5-7:

$\begin{array}{c}\text{Cost}=40\times 60\times 1\\ =\$2,400\end{array}$

Department 5-8:

$\begin{array}{c}\text{Cost}=10\times 130\times 1\\ =\$1,300\end{array}$

Department 6-7:

$\begin{array}{c}\text{Cost}=50\times 40\times 1\\ =\$2,000\end{array}$

Department 6-8:

$\begin{array}{c}\text{Cost}=20\times 60\times 1\\ =\$1,200\end{array}$

Department 7-8:

$\begin{array}{c}\text{Cost}=20\times 90\times 1\\ =\$1,800\end{array}$

Calculation of total cost:

The total cost is calculated by adding the cost of individual work center pairs.

$\begin{array}{c}\text{Cost}=1,000+600+5,400+14,800+10,800+5,000\\ +18,000+4,800+4,800+4,600+3,150+4,800\\ +14,000+6,600+3,600+1,700+8,000\\ +7,600+3,500+2,250+8,550\\ +1,400+2,400+1,300\\ +2,000+1,200\\ +1,800\\ =\$143,650\end{array}$

The total transportation cost for the arrangement is $143,650.