Five departments are to be assigned to locations B–F in the grid. (For technical reasons, department 6 must be assigned to location A.) Transportation cost is $2 per foot. The objective is to minimize total transportation cost. Information on interdepartmental work flows and distances between

Question

Five departments are to be assigned to locations B–F in the grid. (For technical reasons, department 6 must be assigned to location A.) Transportation cost is $2 per foot. The objective is to minimize total transportation cost. Information on interdepartmental work flows and distances between locations is shown in the following tables. Assign departments with the greatest interdepartmental work flow first.

Accepted Answer

F irst either rank or arrange the work flows from high to low. Here they have been arranged from high to low.

From this, we can see that departments 1 and 2 have the greatest interdepartmental work flow, so they should be close, perhaps at B and E. Next, work flows for 1–3 and 1–4 are high. Note, though, that the work flow for 3–4 is low, suggesting that they need not be close. Instead, we would place them on either side of department 1. Note also that 3–4 is only 2, 3–5 is 0, while 3–6 is 20 and 4–5 is 13. Hence, place department 3 at location D, department 4 at location F, and department 5 at location C.

Total cost:

		DISTANCE BETWEEN LOCATIONS (FEET)
From	To	A	B	C	D	E	F
A		—	50	100	50	80	130
B			—	50	90	40	70
C				—	140	60	50
D					—	50	120
E						—	50
F							—

		NUMBER OF TRIPS PER DAY BETWEEN CENTERS
From	To	1	2	3	4	5	6
1		—	125	62	64	25	50
2			—	10	17	26	54
3				—	2	0	20
4					—	13	2
5						—	5
6							—

Dept.	Work Flow	Dept.	Work Flow
1–2	125	2–4	17
1–4	64	4–5	13
1–3	62	2–3	10
2–6	54	5–6	5
1–6	50	3–4	2
2–5	26	4–6	2
1–5	25	3–5	0
3–6	20

Trip	b Distance	c Frequency	(b × c × $2) Cost
1–2	(B–E) 40	125	$10,000
1–3	(D–E) 50	62	6,200
1–4	(F–E) 50	64	6,400
1–5	(E–C) 60	25	3,000
1–6	(A–E) 80	50	8,000
2–3	(B–D) 90	10	1,800
2–4	(B–F) 70	17	2,380
2–5	(B–C) 50	26	2,600
2–6	(A–B) 50	54	5,400
3–4	(F–D) 120	2	480
3–5	(D–C) 140	0	0
3–6	(A–D) 50	20	2,000
4–5	(C–F) 50	13	1,300
4–6	(A–F) 130	2	520
5–6	(A–C) 100	5	$\underline{\ \ \ \ \ 1,000}$
			$51,080

Question 6.P.3: Five departments are to be assigned to locations B–F in the ......

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