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Assignment #4

Case Problem: Stateline Shipping and Transport Company

MAT540: Quantitative Methods

Vargha Azad

09/08/13

In Excel, or other suitable program, develop a model for shipping the waste directly from the 6 plants to the 3 waste disposal sites.

Solve the model you developed in #1 (above) and clearly describe the results. In Excel, or other suitable program. Develop a transshipment model in which each of the plants and disposal sites can be used as intermediate points.

6 Plants labeled 1 through 6, 3 waste facilities labeled A through C

Objective function:

Minimize Z = 1A(12) + 1B(15) + 1C(17) + 2A(14) + 2B(9) + 2C(10) + 3A(13) + 3B(20) + 3C(11) + 4A(17) + 4B(16) + 4C(19) + 5A(7) + 5B(14) + 5C(12) + 6A(22) + 6B(16) + 6C(18);

Subject to:

1A + 1B + 1C = 35

2A + 2B + 2C = 26

3A + 3B + 3C = 42

4A + 4B + 4C = 53

5A + 5B + 5C = 29

6A + 6B + 6C = 38

1A + 2A + 3A + 4A + 5A + 6A ≤ 65

1B + 2B + 3B + 4B + 5B + 6B ≤ 80

1C + 2C + 3C + 4C + 5C + 6C ≤ 105

All Combinations ≥ 0

Solver add-on solution in MS Excel yielded the following results:

35 bbl of wastes shipped from Kingsport to Whitewater,

26 bbl of waste shipped from Danville to Duras,

42 bbl of wastes shipped from Macon to Duras,

1 bbl of wastes shipped from Selma to Whitewater,

52 bbl of wastes shipped from Selma to Los Canos,

29 bbl of wastes shipped from Columbus to Whitewater,

28 bbl of wastes shipped from Allentown to Los Canos,

10 bbl of wastes shipped from Allentown to Duras.

Total Cost = $2,822

Rachel is considering using each of the plant and waste disposal sites as intermediate shipping points. Now, there is a possibility to reduce the transportation coat by utilizing alternative routes. For example, as per the given cost table,...

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...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 Is this essay helpful? Join OPPapers to read more and access more than 600,000 just like it! get better grades 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......

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...Stateline Shipping and Transport In the “Stateline Shipping and Transport Company” case there is the manager Rachel Sundusky of the South –Atlantic office of the Stateline Shipping and Transport Company. She is trying to negotiate a new shipping contract with Polychem where Stateline picks up and transport waste product form its six plants to three waste disposal sites. In this problem we are trying to determine the shipping routes the will minimize Stateline total cost. In the first part I set up the problem in excel showing the shipping to the waste directly from the six plants to the three waste disposal site. In the result I had a Z value which is the minimum cost of $3090.00 that Polychem will pay Stateline to transport their products. It also shows that Danville and Columbus is not safe to ship from because they cannot provide the supply that is needed. In the second part I develop a transshipment model in which each of the plants and disposal sites can be used as intermediate points. In the results it shows that I had a Z value which is the minimum cost of 2884.00 that Polychem will pay Stateline to transport their products. Also shows that Danville is not worth using to ship from because they cannot provide the supply that is needed. The overall results show that it is cheaper for Stateline to use the routes where the plants and disposal sites can be used as intermediate points. In both models it shows that Danville is not a good shipping site. Over all......

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...Stateline Shipping and Transport Company School of Business MAT 540 This paper was presented in submission for MAT 540 assignment four (Part 1 Only). Abstract This paper serves as a written response to the instructions and questions asked in assignment four. Assignment four instructed the writer to read the case problem Stateline Shipping and Transport Company from pages 273-274 in the text, Introduction to Management Science by Bernard W. Taylor. The assignment then directed the writer to Formulate and Solve and linear transportation programming model, this step was done in QM. The linear programming model is attached herein. Keywords: Linear Programming, Transportation, Shipping, Model Introduction This Case Problem, Stateline Shipping and Transport Company, is based on a girl named Rachel Sundusky who is a manager of the South-Atlantic office for Stateline Shipping and Transport (Taylor, 2010). Rachel is negotiating a contract with Polychem an industrial use chemical company (Taylor, 2010). Polychem has six sites that it would like for Stateline to pick up waste from (Taylor, 2010). Polychem would then like for Stateline to transport the waste for disposal to one of three sites (Taylor, 2010). Polychem has agreed to handle all of the waste at all sites therefore Stateline needs only transport the materials and incur costs for the same (Taylor, 2010). Rachel would like to see what the less costly shipping routes are (Taylor, 2010). Rachel will need all of......

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...• Assignment #4: Case Problem "Stateline Shipping and Transport Company" Read the 'Stateline Shipping and Transport Company" Case Problem on pages 273-274 of the text. Analyze this case, as follows: 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. 2. Solve the model you developed in #1 (above) and clearly describe the results. In Excel, or other suitable program, Develop a transshipment model in which each of the plants and disposal sites can be used as intermediate points. 3. Solve the model you developed in #3 (above) and clearly describe the results. 4. Interpret the results and draw conclusions that address the question posed in the case problem. What are the limits of the study? Write at least one paragraph. There are two deliverables for this Case Problem, the Excel spreadsheets and an accompanying written description/explanation. Please submit both of them electronically via the dropbox. The assignment will be graded using the associated rubric. |Outcome Assessed: |Develop solutions for transshipment problems. | | |Communicate issues in Management Science | |Grading Rubric for Stateline Shipping & Transport Case Problem ...

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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......

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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...

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