Assignment4

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Assignment #4: Case Problem “Stateline Shipping and Transport Company” 1. In Excel, or other suitable program, develop a model for shipping the waste directly from the 6 plants to the 3 waste disposal sites. White water Los Canos Duras Availability

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 65 80 105 223
The objective of the problem is to develop a shipping schedule that minimizes the total cost of transportation. Suppose Xij denotes the number of barrels of wastes to be transported from the “i” plant to “j” site. Then the total cost of transportation is:

Z = 12 X11 + 15 X12 + 17 X13 + 14 X21 + 9 X22 + 10 X23 + 13 X31 + 20 X32 + 11 X33 + 17 X41+ 16 X42 + 19 X43 + 7 X51 + 14 X52+ 12 X53 + 22 X61 + 16 X62 + 18 X63. Thus the objective function of the problem is to minimize

Z = 12 X11 + 15 X12 + 17 X13 + 14 X21 + 9 X22 + 10 X23 + 13 X31 + 20 X32 + 11 X33 + 17 X41+ 16 X42 + 19 X43 + 7 X51 + 14 X52+ 12 X53 + 22 X61 + 16 X62 + 18 X63. Constraints
Availability in plants:
X11 + X12 + X13 = 35
X21 + X22 + X23 = 26
X31 + X32 + X33 = 42
X41 + X42 + X43 = 53
X51 + X52 + X53 = 29
X61 + X62 + X63 = 38
: Capacity of the sites
X11 + X21+ X31+X41 + X51 + X61 ≤ 65
X12 + X22+ X32+X42 + X52 + X62 ≤ 80
X13 + X23+ X33+X43 + X53 + X63 ≤ 105
Non- Negativity restrictions
Xij ≥ 0 , i = 1,2,3,4,5,6 ; j = 1,2,3.
2. Solve the model you developed in #1 (above) and clearly describe the results Target Cell (Min)
Cell Name Original Value Final Value
$B$22 Objective Function (Total cost) White water 2822 2822
Adjustable Cells
Cell Name Original Value Final Value
$B$13 Kingsport White water 35.00 35.00
$C$13 Kingsport Los Canos 0.00 0.00
$D$13 Kingsport Duras 0.00 0.00
$B$14 Danville White water 0.00 0.00
$C$14 Danville Los Canos 0.00 0.00
$D$14 Danville Duras 26.00...
Test
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Case: Stateline Shipping And Transport Company
Rachel Sundusky is the manager of the South-America office of the Stateline Shipping and Transport Company. She is in the process of negotiating a new a new shipping contract with Polychem, a company that manufactures chemicals for industrial use. Polychem wants Stateline to pick up and transport waste products from its six plants to three waste disposal sites. Rachel is very concerned about this proposed arrangement. The chemical wastes that will be hauled can be hazardous to humans and the environment if they leak. In addition, a number of towns and communities in the region where the plants are located prohibit hazardous materials from being shipped through their municipal limits. Thus, not only will the shipments have to handled carefully and transported at reduced speeds, they will also have to traverse circuitous routes in many cases. Rachel has estimated the cost of shipping a barrel of waste from each of the six plants to each of the three waste disposal sites as shown in the following table:

Plants
Waste Disposal Site
Whitewater Los Canos Duras
Kingsport $12 $15 $17
Danville 14 9 10
Macon 13 20 11
Selma 17 16 19
Columbus 7 14 12
Allentown 22 16 18
The plants generate the following amounts of waste products each week: Plant Waste per Week (bbl)
Kingsport 35
Danville 26
Macon 42
Selma 53
Columbus 29
Allentown 38
The three waste disposal sites at Whitewater, Los Canos, and Duras can accommodate a maximum of 65, 80, and 105 barrels per week, respectively.
In addition to shipping directly from each of the six plants to one of the three waste disposal sites, Rachel is also considering using each of the plants and waste disposal sites as intermediate shipping points. Trucks would be able to drop a load at a plant or disposal site to be picked up and carried on to the final...
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