Stateline Shipping and Transport Company
1. Formulation of the Problem
The Stateline Shipping and Transport Company wanted to transport industrial wastes from the 6 plants to the 3 waste disposable sites. The problem can be represented in as a Transportation table as shown below. Our problem is to find roots to disposable sites, such that the cost of transportation is minimized..
White water Los Canos Duras Availability (bbl)
Kingsport $12.00 $15.00 $17.00 35
Danville $14.00 $9.00 $10.00 26
Macon $13.00 $20.00 $11.00 42
Selma $17.00 $16.00 $19.00 53
Columbus $7.00 $14.00 $12.00 29
Allentown $22.00 $16.00 $18.00 38
Capacity (barrels) 65 80 105
Mathematical Formulation
Let Xij i=1,2,3,4,5,6; j =1,2,3 denote the quantity of waste transported from i-th plant to j-th waste disposal centre. Then the objective function Z representing the cost and different constraints of the problem can be written as
Minimize Z=12X11+15X12+17X13+14X21+9X22+10X23+13X31+20X32+11X33+17X41+16X42+19X43+7X51+14X52+12X53+22X61+16X62+18X63
Subject to
X11+X12+X13 = 35
X21+X22+X23 = 26
X31+X32+X33 = 42
X41+X42+X43 = 53
X51+X52+X53 = 29
X61+X62+X63 = 38
X11+X21+X31+X41+X51+X61 65
X12+X22+X32+X42+X52+X62 80
X13+X23+X33+X43+X53+X63 105
Xij 0, i=1,2,3,4,5,6; j=1,2,3.
2. The transportation problem described above can be solved mathematically using a computer package. The solution to the problem using excel solver are given in the following table.
Whitewater Los Canos Duras
Kingsport 35 ---- -----
Danville ---- ---- 26
Macon ----- ---- 42
Selma 1 52 -----
Columbus 29 ----- -----
Allentown ------ 28 10
Dummy ---- ----- 27
The above table can be explained, in the following way
(1) 35 bbl from Kingport, to the Whitewater waste disposal plant.
(2) 1 bbl from Selma to the Whitewater waste disposal plant.
(3) 29 bbl from Columbus to the Whitewater waste disposal plant.
(4) 52 bbl from Selma to Los Canos waste disposal plant.
(5) 28 bbl from Allentown to Los Canos waste disposal plant.
The Stateline Shipping and Transport Company wanted to transport industrial wastes from the 6 plants to the 3 waste disposable sites. The problem can be represented in as a Transportation table as shown below. Our problem is to find roots to disposable sites, such that the cost of transportation is minimized..
White water Los Canos Duras Availability (bbl)
Kingsport $12.00 $15.00 $17.00 35
Danville $14.00 $9.00 $10.00 26
Macon $13.00 $20.00 $11.00 42
Selma $17.00 $16.00 $19.00 53
Columbus $7.00 $14.00 $12.00 29
Allentown $22.00 $16.00 $18.00 38
Capacity (barrels) 65 80 105
Mathematical Formulation
Let Xij i=1,2,3,4,5,6; j =1,2,3 denote the quantity of waste transported from i-th plant to j-th waste disposal centre. Then the objective function Z representing the cost and different constraints of the problem can be written as
Minimize Z=12X11+15X12+17X13+14X21+9X22+10X23+13X31+20X32+11X33+17X41+16X42+19X43+7X51+14X52+12X53+22X61+16X62+18X63
Subject to
X11+X12+X13 = 35
X21+X22+X23 = 26
X31+X32+X33 = 42
X41+X42+X43 = 53
X51+X52+X53 = 29
X61+X62+X63 = 38
X11+X21+X31+X41+X51+X61 65
X12+X22+X32+X42+X52+X62 80
X13+X23+X33+X43+X53+X63 105
Xij 0, i=1,2,3,4,5,6; j=1,2,3.
2. The transportation problem described above can be solved mathematically using a computer package. The solution to the problem using excel solver are given in the following table.
Whitewater Los Canos Duras
Kingsport 35 ---- -----
Danville ---- ---- 26
Macon ----- ---- 42
Selma 1 52 -----
Columbus 29 ----- -----
Allentown ------ 28 10
Dummy ---- ----- 27
The above table can be explained, in the following way
(1) 35 bbl from Kingport, to the Whitewater waste disposal plant.
(2) 1 bbl from Selma to the Whitewater waste disposal plant.
(3) 29 bbl from Columbus to the Whitewater waste disposal plant.
(4) 52 bbl from Selma to Los Canos waste disposal plant.
(5) 28 bbl from Allentown to Los Canos waste disposal plant.