Departments A, B, C, and D need to be assigned to four rooms 1, 2, 3, and 4. The
ID: 362216 • Letter: D
Question
Departments A, B, C, and D need to be assigned to four rooms 1, 2, 3, and 4. These rooms are arranged in a row, in that order, with 20 meters between each. The departmental work flows are contained in the table below.
(a) What is the material handling total of assigning A-1, B-2, C-3, D-4?
(b) What is the material handling total of assigning A-1, B-3, C-4, D-2?
Flow Matrix
Dept. A
Dept. B
Dept. C
Dept. D
Dept. A
0
30
5
20
Dept. B
5
0
40
20
Dept. C
0
10
0
40
Dept. D
10
5
0
0
Flow Matrix
Dept. A
Dept. B
Dept. C
Dept. D
Dept. A
0
30
5
20
Dept. B
5
0
40
20
Dept. C
0
10
0
40
Dept. D
10
5
0
0
Explanation / Answer
a - The material handling total of the assignment of the A-1, B-2, C-3 and D-4 is 5500.
Solution in detail
1-2 (A-B) :- 20*30+20*5=700
1-3 (A-C):- 40*5+40*0=800
1-4 (A-D): -60*20+60*10=1800
2-3(B-C):- 20*40+20*10=1000
2-4 (B-D):- 40*20+40*5=1000
3-4 (C-D) :- 20*40+20*0=800
hence the sum of all above factors is 700+200+1800+1000+1000+800=5500
b - The material handling total of the assignment of the A-1, B-2, C-3 and D-4 is 5400.
Solution in detail
1-2 (A-D): - 20*20+20*10=600
1-3 (A-B):- 40*30+40*5=1400
1-4(A-C): 60*5+60*0=300
2-3(B-D) :- 20*20+20*5=500
2-4 (C-D):- 40*40+40*0=1600
3-4 (B-C):- 20*40+20*10=1000
hence the sum of all above factors is 600+1400+300+500+1600+1000=5400, and this the optimum soultion for the assignments total material handling.
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