Three cities (A, B, and C) bring in refuse of 100 tons/day, 50 tons/day, and 30 tons/day, respectively. The refuse can be shipped in several directions, including to each other, or to two transfer stations D and E, using local trucks. Once the refuse is shipped to the transfer stations at D or E, it is transferred to highway trucks and shipped to one of three landfills F, G, or H. The landfills have the following maximum capacities per day: F = 100 tons/day, G = 50 tons/day, and H = 60 tons/day.
The following unit costs per ton are charged for any and all refuse that comes into, through, or to the cities, transfer stations, or landfills. It is a “handling” charge applied to any material transported through the node:
|
City A |
$4/ton |
|
City B |
$6/ton |
|
City C |
$4/ton |
|
Transfer Station D |
$3/ton |
|
Transfer Station E |
$4/ton |
|
Land Fill F |
$8/ton |
|
Land Fill G |
$12/ton |
|
Land Fill H |
$7/ton |
Thus, the 100 tons/day entering City A will incur a $400 charge, simply because the refuse entered City A.
The costs to transport material between locations are as listed:
|
A |
B |
C |
D |
E |
F |
G |
H |
|
|
City A |
– |
$2/ton |
– |
$3/ton |
$4/ton |
– |
– |
– |
|
City B |
$2/ton |
– |
$3/ton |
$5/ton |
$4/ton |
– |
– |
– |
|
City C |
– |
$3/ton |
– |
$7/ton |
$9/ton |
– |
– |
– |
|
Transfer Station D |
– |
– |
– |
– |
$3/ton |
$10/ton |
$8/ton |
$12/ton |
|
Transfer Station E |
– |
– |
– |
$3/ton |
– |
$6/ton |
$4/ton |
$13/ton |
SEE TABLE ABOVE FOR THE NUMBERS SHOWN ON THE MAP BELOW
Total hauling costs per ton are shown in the table, and on the schematic above. Set up and solve the LP solution to determine the least cost way to get the refuse from the cities to the landfills. Note that it is possible to haul refuse between the cities as shown, and also between the transfer stations if that proves to be more economical.