Five departments, 1 to 5, are to be assigned to locations B - F in the grid below. For technical reasons, department 6 must be assigned to location A. Transportation cost is $2 per metre. The objective is to minimize total transportation cost. Information on from-to departmental work flows and distances between centres of locations is shown in the following tables. Create a weighted from-to diagram and a dimensionless block diagram showing a layout to meet the needs and evaluate the total transportation cost.

The distance when travelling from 1 to 2 is the same distance as travelling from 2 to 1. Forward and backward workflows are equivalent, in other words; ignore backwards workflows and only use forward workflows.

Example: The total number of trips between Dept 1 and Dept 2 is 90 + 35 = 125 trips. If Dept 1 is in position A and Dept 2 is in position B then each trip is 50 metres for a total distance of 125 x 50 = 6250 metres with a cost of 6250 metres x $2/metre = $12,500.

Distance between Centres of Location (metres)

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							-

From-To Departmental Workflows (number of trips per day)

From	To	1	2	3	4	5	6
1		-	90	25	23	11	18
2		35	-	8	5	10	16
3		37	2	-	1	0	7
4		41	12	1	-	4	0
5		14	16	0	9	-	3
6		32	38	13	2	2	-

A Dept. 6	B	C
D	E	F