The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units....

 

       

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The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin- Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Proposed Plant Annual Fixed Cost Annual Capacity Detroit $175,000 10,000 Toledo $300,000 20,000 Denver $375,000 30,000 Kansas City $500,000 40,000 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Annual Demand Boston 30,000 Atlanta 20,000 Houston 20,000 The shipping cost per unit from each plant to each distribution center is shown in table below. SHIPPING COST PER UNIT FOR THE MARTIN-BECK SUPPLY CHAIN Distribution Centers ETTT Plant Site Boston Atlanta Houston Detroit 2 3 Toledo Denver 4 3 7 4 5 Kansas City St. Louis 10 8. 4 4 2 3 A network representation of the potential Martin-Beck supply chain is shown in figure below. THE NETWORK REPRESENTATION OF THE MARTIN-BECK COMPANY SUPPLY CHAIN DESIGN PROBLEM 10 Detroit Distribution Centers 30 Boston 4 20 Toledo 3. 4 9 7 30 Denver 5 Atlanta 20 10 4. 40 Kansas City 8. Houston 20 3. 30 St. Louis Сараcities Distribution Routes Demands - Each potential plant location is shown; capacities and demands are shown in thousands of units. This network representation is for a transportation problem with a plant at St. Louis and at all four proposed sites. However, the decision has not yet been made as to which new plant or plants will be constructed. a. Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that a plant must be located either in Detroit or in Toledo, but not both. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Let y1 = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not Xij = the units shipped in thousands from plant i to distribution center j i= 1,2,3,4,5, and j = 1,2,3 Min X11+ X12 + X13 + X21 + X22+ X23 + X31 + X32 + X33 + X41+ X42 + X43 + X51+ X52 + X53+ Y2 + y3 + y4 + Min X11+ X12+ X13 + X21 + X22 + X23+ X31 + X32+ X33 + X41+ X42 X43 + X51+ X52 + X53 + yi + y2 y3 y4 s.t. X11 + X12 + X13 + y1 X21 + X22 X23 + y2 X31 X32 X33 y3 y4 X41 + X42 + X43 X51 + X52 + X53 X11 X21 +1 X31 + X41 + X51 X12 + X22 X42 X52 + X32 + + X13 X23 X33 + X43 X53 Xij 2 for all i i and j; y1 , Y2 , УЗ , Y1 + y2 + + + b. Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that no more than two plants can be located in Denver, Kansas City, and St. Louis. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Let yi = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not Xij the units shipped in thousands from plant i to distribution center j %3D i= 1,2,3,4,5, and j = 1,2,3 Min X11+ X12 + X13 + X21+ X22+ X23 + X31 + X32 + X33 + X41 + X42 X43 + X51+ X52 + X53 + y1 y2 y3 + Numeric field + + y4 s.t. X11 X12 X13 + X21 X22 X23 + y2 X31 + X32 X33 y3 X41 X42 +1 X43 y4 X51 + X52 + X53 X11 X21 X31 X41 X51 X12 + X22 X32 X42 X52 X13 + X23 X33 X43 X53 Xij 2 for all i and j; y1 , Y2 , Уз , Уз + у4 + + + + + + + + + + + + The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin- Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Proposed Plant Annual Fixed Cost Annual Capacity Detroit $175,000 10,000 Toledo $300,000 20,000 Denver $375,000 30,000 Kansas City $500,000 40,000 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Annual Demand Boston 30,000 Atlanta 20,000 Houston 20,000 The shipping cost per unit from each plant to each distribution center is shown in table below. SHIPPING COST PER UNIT FOR THE MARTIN-BECK SUPPLY CHAIN Distribution Centers ETTT Plant Site Boston Atlanta Houston Detroit 2 3 Toledo Denver 4 3 7 4 5 Kansas City St. Louis 10 8. 4 4 2 3 A network representation of the potential Martin-Beck supply chain is shown in figure below. THE NETWORK REPRESENTATION OF THE MARTIN-BECK COMPANY SUPPLY CHAIN DESIGN PROBLEM 10 Detroit Distribution Centers 30 Boston 4 20 Toledo 3. 4 9 7 30 Denver 5 Atlanta 20 10 4. 40 Kansas City 8. Houston 20 3. 30 St. Louis Сараcities Distribution Routes Demands - Each potential plant location is shown; capacities and demands are shown in thousands of units. This network representation is for a transportation problem with a plant at St. Louis and at all four proposed sites. However, the decision has not yet been made as to which new plant or plants will be constructed. a. Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that a plant must be located either in Detroit or in Toledo, but not both. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Let y1 = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not Xij = the units shipped in thousands from plant i to distribution center j i= 1,2,3,4,5, and j = 1,2,3 Min X11+ X12 + X13 + X21 + X22+ X23 + X31 + X32 + X33 + X41+ X42 + X43 + X51+ X52 + X53+ Y2 + y3 + y4 + Min X11+ X12+ X13 + X21 + X22 + X23+ X31 + X32+ X33 + X41+ X42 X43 + X51+ X52 + X53 + yi + y2 y3 y4 s.t. X11 + X12 + X13 + y1 X21 + X22 X23 + y2 X31 X32 X33 y3 y4 X41 + X42 + X43 X51 + X52 + X53 X11 X21 +1 X31 + X41 + X51 X12 + X22 X42 X52 + X32 + + X13 X23 X33 + X43 X53 Xij 2 for all i i and j; y1 , Y2 , УЗ , Y1 + y2 + + + b. Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that no more than two plants can be located in Denver, Kansas City, and St. Louis. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Let yi = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not Xij the units shipped in thousands from plant i to distribution center j %3D i= 1,2,3,4,5, and j = 1,2,3 Min X11+ X12 + X13 + X21+ X22+ X23 + X31 + X32 + X33 + X41 + X42 X43 + X51+ X52 + X53 + y1 y2 y3 + Numeric field + + y4 s.t. X11 X12 X13 + X21 X22 X23 + y2 X31 + X32 X33 y3 X41 X42 +1 X43 y4 X51 + X52 + X53 X11 X21 X31 X41 X51 X12 + X22 X32 X42 X52 X13 + X23 X33 X43 X53 Xij 2 for all i and j; y1 , Y2 , Уз , Уз + у4 + + + + + + + + + + + + The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin- Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Proposed Plant Annual Fixed Cost Annual Capacity Detroit $175,000 10,000 Toledo $300,000 20,000 Denver $375,000 30,000 Kansas City $500,000 40,000 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Annual Demand Boston 30,000 Atlanta 20,000 Houston 20,000 The shipping cost per unit from each plant to each distribution center is shown in table below. SHIPPING COST PER UNIT FOR THE MARTIN-BECK SUPPLY CHAIN Distribution Centers ETTT Plant Site Boston Atlanta Houston Detroit 2 3 Toledo Denver 4 3 7 4 5 Kansas City St. Louis 10 8. 4 4 2 3 A network representation of the potential Martin-Beck supply chain is shown in figure below. THE NETWORK REPRESENTATION OF THE MARTIN-BECK COMPANY SUPPLY CHAIN DESIGN PROBLEM 10 Detroit Distribution Centers 30 Boston 4 20 Toledo 3. 4 9 7 30 Denver 5 Atlanta 20 10 4. 40 Kansas City 8. Houston 20 3. 30 St. Louis Сараcities Distribution Routes Demands - Each potential plant location is shown; capacities and demands are shown in thousands of units. This network representation is for a transportation problem with a plant at St. Louis and at all four proposed sites. However, the decision has not yet been made as to which new plant or plants will be constructed. a. Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that a plant must be located either in Detroit or in Toledo, but not both. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Let y1 = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not Xij = the units shipped in thousands from plant i to distribution center j i= 1,2,3,4,5, and j = 1,2,3 Min X11+ X12 + X13 + X21 + X22+ X23 + X31 + X32 + X33 + X41+ X42 + X43 + X51+ X52 + X53+ Y2 + y3 + y4 + Min X11+ X12+ X13 + X21 + X22 + X23+ X31 + X32+ X33 + X41+ X42 X43 + X51+ X52 + X53 + yi + y2 y3 y4 s.t. X11 + X12 + X13 + y1 X21 + X22 X23 + y2 X31 X32 X33 y3 y4 X41 + X42 + X43 X51 + X52 + X53 X11 X21 +1 X31 + X41 + X51 X12 + X22 X42 X52 + X32 + + X13 X23 X33 + X43 X53 Xij 2 for all i i and j; y1 , Y2 , УЗ , Y1 + y2 + + + b. Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that no more than two plants can be located in Denver, Kansas City, and St. Louis. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Let yi = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not Xij the units shipped in thousands from plant i to distribution center j %3D i= 1,2,3,4,5, and j = 1,2,3 Min X11+ X12 + X13 + X21+ X22+ X23 + X31 + X32 + X33 + X41 + X42 X43 + X51+ X52 + X53 + y1 y2 y3 + Numeric field + + y4 s.t. X11 X12 X13 + X21 X22 X23 + y2 X31 + X32 X33 y3 X41 X42 +1 X43 y4 X51 + X52 + X53 X11 X21 X31 X41 X51 X12 + X22 X32 X42 X52 X13 + X23 X33 X43 X53 Xij 2 for all i and j; y1 , Y2 , Уз , Уз + у4 + + + + + + + + + + + + The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin- Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Proposed Plant Annual Fixed Cost Annual Capacity Detroit $175,000 10,000 Toledo $300,000 20,000 Denver $375,000 30,000 Kansas City $500,000 40,000 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Annual Demand Boston 30,000 Atlanta 20,000 Houston 20,000 The shipping cost per unit from each plant to each distribution center is shown in table below. SHIPPING COST PER UNIT FOR THE MARTIN-BECK SUPPLY CHAIN Distribution Centers ETTT Plant Site Boston Atlanta Houston Detroit 2 3 Toledo Denver 4 3 7 4 5 Kansas City St. Louis 10 8. 4 4 2 3 A network representation of the potential Martin-Beck supply chain is shown in figure below. THE NETWORK REPRESENTATION OF THE MARTIN-BECK COMPANY SUPPLY CHAIN DESIGN PROBLEM 10 Detroit Distribution Centers 30 Boston 4 20 Toledo 3. 4 9 7 30 Denver 5 Atlanta 20 10 4. 40 Kansas City 8. Houston 20 3. 30 St. Louis Сараcities Distribution Routes Demands - Each potential plant location is shown; capacities and demands are shown in thousands of units. This network representation is for a transportation problem with a plant at St. Louis and at all four proposed sites. However, the decision has not yet been made as to which new plant or plants will be constructed. a. Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that a plant must be located either in Detroit or in Toledo, but not both. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Let y1 = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not Xij = the units shipped in thousands from plant i to distribution center j i= 1,2,3,4,5, and j = 1,2,3 Min X11+ X12 + X13 + X21 + X22+ X23 + X31 + X32 + X33 + X41+ X42 + X43 + X51+ X52 + X53+ Y2 + y3 + y4 + Min X11+ X12+ X13 + X21 + X22 + X23+ X31 + X32+ X33 + X41+ X42 X43 + X51+ X52 + X53 + yi + y2 y3 y4 s.t. X11 + X12 + X13 + y1 X21 + X22 X23 + y2 X31 X32 X33 y3 y4 X41 + X42 + X43 X51 + X52 + X53 X11 X21 +1 X31 + X41 + X51 X12 + X22 X42 X52 + X32 + + X13 X23 X33 + X43 X53 Xij 2 for all i i and j; y1 , Y2 , УЗ , Y1 + y2 + + + b. Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that no more than two plants can be located in Denver, Kansas City, and St. Louis. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Let yi = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not Xij the units shipped in thousands from plant i to distribution center j %3D i= 1,2,3,4,5, and j = 1,2,3 Min X11+ X12 + X13 + X21+ X22+ X23 + X31 + X32 + X33 + X41 + X42 X43 + X51+ X52 + X53 + y1 y2 y3 + Numeric field + + y4 s.t. X11 X12 X13 + X21 X22 X23 + y2 X31 + X32 X33 y3 X41 X42 +1 X43 y4 X51 + X52 + X53 X11 X21 X31 X41 X51 X12 + X22 X32 X42 X52 X13 + X23 X33 X43 X53 Xij 2 for all i and j; y1 , Y2 , Уз , Уз + у4 + + + + + + + + + + + + The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin- Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Proposed Plant Annual Fixed Cost Annual Capacity Detroit $175,000 10,000 Toledo $300,000 20,000 Denver $375,000 30,000 Kansas City $500,000 40,000 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Annual Demand Boston 30,000 Atlanta 20,000 Houston 20,000 The shipping cost per unit from each plant to each distribution center is shown in table below. SHIPPING COST PER UNIT FOR THE MARTIN-BECK SUPPLY CHAIN Distribution Centers ETTT Plant Site Boston Atlanta Houston Detroit 2 3 Toledo Denver 4 3 7 4 5 Kansas City St. Louis 10 8. 4 4 2 3 A network representation of the potential Martin-Beck supply chain is shown in figure below. THE NETWORK REPRESENTATION OF THE MARTIN-BECK COMPANY SUPPLY CHAIN DESIGN PROBLEM 10 Detroit Distribution Centers 30 Boston 4 20 Toledo 3. 4 9 7 30 Denver 5 Atlanta 20 10 4. 40 Kansas City 8. Houston 20 3. 30 St. Louis Сараcities Distribution Routes Demands - Each potential plant location is shown; capacities and demands are shown in thousands of units. This network representation is for a transportation problem with a plant at St. Louis and at all four proposed sites. However, the decision has not yet been made as to which new plant or plants will be constructed. a. Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that a plant must be located either in Detroit or in Toledo, but not both. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Let y1 = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not Xij = the units shipped in thousands from plant i to distribution center j i= 1,2,3,4,5, and j = 1,2,3 Min X11+ X12 + X13 + X21 + X22+ X23 + X31 + X32 + X33 + X41+ X42 + X43 + X51+ X52 + X53+ Y2 + y3 + y4 + Min X11+ X12+ X13 + X21 + X22 + X23+ X31 + X32+ X33 + X41+ X42 X43 + X51+ X52 + X53 + yi + y2 y3 y4 s.t. X11 + X12 + X13 + y1 X21 + X22 X23 + y2 X31 X32 X33 y3 y4 X41 + X42 + X43 X51 + X52 + X53 X11 X21 +1 X31 + X41 + X51 X12 + X22 X42 X52 + X32 + + X13 X23 X33 + X43 X53 Xij 2 for all i i and j; y1 , Y2 , УЗ , Y1 + y2 + + + b. Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that no more than two plants can be located in Denver, Kansas City, and St. Louis. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Let yi = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not Xij the units shipped in thousands from plant i to distribution center j %3D i= 1,2,3,4,5, and j = 1,2,3 Min X11+ X12 + X13 + X21+ X22+ X23 + X31 + X32 + X33 + X41 + X42 X43 + X51+ X52 + X53 + y1 y2 y3 + Numeric field + + y4 s.t. X11 X12 X13 + X21 X22 X23 + y2 X31 + X32 X33 y3 X41 X42 +1 X43 y4 X51 + X52 + X53 X11 X21 X31 X41 X51 X12 + X22 X32 X42 X52 X13 + X23 X33 X43 X53 Xij 2 for all i and j; y1 , Y2 , Уз , Уз + у4 + + + + + + + + + + + + The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin- Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Proposed Plant Annual Fixed Cost Annual Capacity Detroit $175,000 10,000 Toledo $300,000 20,000 Denver $375,000 30,000 Kansas City $500,000 40,000 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Annual Demand Boston 30,000 Atlanta 20,000 Houston 20,000 The shipping cost per unit from each plant to each distribution center is shown in table below. SHIPPING COST PER UNIT FOR THE MARTIN-BECK SUPPLY CHAIN Distribution Centers ETTT Plant Site Boston Atlanta Houston Detroit 2 3 Toledo Denver 4 3 7 4 5 Kansas City St. Louis 10 8. 4 4 2 3 A network representation of the potential Martin-Beck supply chain is shown in figure below. THE NETWORK REPRESENTATION OF THE MARTIN-BECK COMPANY SUPPLY CHAIN DESIGN PROBLEM 10 Detroit Distribution Centers 30 Boston 4 20 Toledo 3. 4 9 7 30 Denver 5 Atlanta 20 10 4. 40 Kansas City 8. Houston 20 3. 30 St. Louis Сараcities Distribution Routes Demands - Each potential plant location is shown; capacities and demands are shown in thousands of units. This network representation is for a transportation problem with a plant at St. Louis and at all four proposed sites. However, the decision has not yet been made as to which new plant or plants will be constructed. a. Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that a plant must be located either in Detroit or in Toledo, but not both. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Let y1 = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not Xij = the units shipped in thousands from plant i to distribution center j i= 1,2,3,4,5, and j = 1,2,3 Min X11+ X12 + X13 + X21 + X22+ X23 + X31 + X32 + X33 + X41+ X42 + X43 + X51+ X52 + X53+ Y2 + y3 + y4 + Min X11+ X12+ X13 + X21 + X22 + X23+ X31 + X32+ X33 + X41+ X42 X43 + X51+ X52 + X53 + yi + y2 y3 y4 s.t. X11 + X12 + X13 + y1 X21 + X22 X23 + y2 X31 X32 X33 y3 y4 X41 + X42 + X43 X51 + X52 + X53 X11 X21 +1 X31 + X41 + X51 X12 + X22 X42 X52 + X32 + + X13 X23 X33 + X43 X53 Xij 2 for all i i and j; y1 , Y2 , УЗ , Y1 + y2 + + + b. Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that no more than two plants can be located in Denver, Kansas City, and St. Louis. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Let yi = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not Xij the units shipped in thousands from plant i to distribution center j %3D i= 1,2,3,4,5, and j = 1,2,3 Min X11+ X12 + X13 + X21+ X22+ X23 + X31 + X32 + X33 + X41 + X42 X43 + X51+ X52 + X53 + y1 y2 y3 + Numeric field + + y4 s.t. X11 X12 X13 + X21 X22 X23 + y2 X31 + X32 X33 y3 X41 X42 +1 X43 y4 X51 + X52 + X53 X11 X21 X31 X41 X51 X12 + X22 X32 X42 X52 X13 + X23 X33 X43 X53 Xij 2 for all i and j; y1 , Y2 , Уз , Уз + у4 + + + + + + + + + + + + The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin- Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Proposed Plant Annual Fixed Cost Annual Capacity Detroit $175,000 10,000 Toledo $300,000 20,000 Denver $375,000 30,000 Kansas City $500,000 40,000 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Annual Demand Boston 30,000 Atlanta 20,000 Houston 20,000 The shipping cost per unit from each plant to each distribution center is shown in table below. SHIPPING COST PER UNIT FOR THE MARTIN-BECK SUPPLY CHAIN Distribution Centers ETTT Plant Site Boston Atlanta Houston Detroit 2 3 Toledo Denver 4 3 7 4 5 Kansas City St. Louis 10 8. 4 4 2 3 A network representation of the potential Martin-Beck supply chain is shown in figure below. THE NETWORK REPRESENTATION OF THE MARTIN-BECK COMPANY SUPPLY CHAIN DESIGN PROBLEM 10 Detroit Distribution Centers 30 Boston 4 20 Toledo 3. 4 9 7 30 Denver 5 Atlanta 20 10 4. 40 Kansas City 8. Houston 20 3. 30 St. Louis Сараcities Distribution Routes Demands - Each potential plant location is shown; capacities and demands are shown in thousands of units. This network representation is for a transportation problem with a plant at St. Louis and at all four proposed sites. However, the decision has not yet been made as to which new plant or plants will be constructed. a. Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that a plant must be located either in Detroit or in Toledo, but not both. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Let y1 = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not Xij = the units shipped in thousands from plant i to distribution center j i= 1,2,3,4,5, and j = 1,2,3 Min X11+ X12 + X13 + X21 + X22+ X23 + X31 + X32 + X33 + X41+ X42 + X43 + X51+ X52 + X53+ Y2 + y3 + y4 + Min X11+ X12+ X13 + X21 + X22 + X23+ X31 + X32+ X33 + X41+ X42 X43 + X51+ X52 + X53 + yi + y2 y3 y4 s.t. X11 + X12 + X13 + y1 X21 + X22 X23 + y2 X31 X32 X33 y3 y4 X41 + X42 + X43 X51 + X52 + X53 X11 X21 +1 X31 + X41 + X51 X12 + X22 X42 X52 + X32 + + X13 X23 X33 + X43 X53 Xij 2 for all i i and j; y1 , Y2 , УЗ , Y1 + y2 + + + b. Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that no more than two plants can be located in Denver, Kansas City, and St. Louis. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Let yi = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not Xij the units shipped in thousands from plant i to distribution center j %3D i= 1,2,3,4,5, and j = 1,2,3 Min X11+ X12 + X13 + X21+ X22+ X23 + X31 + X32 + X33 + X41 + X42 X43 + X51+ X52 + X53 + y1 y2 y3 + Numeric field + + y4 s.t. X11 X12 X13 + X21 X22 X23 + y2 X31 + X32 X33 y3 X41 X42 +1 X43 y4 X51 + X52 + X53 X11 X21 X31 X41 X51 X12 + X22 X32 X42 X52 X13 + X23 X33 X43 X53 Xij 2 for all i and j; y1 , Y2 , Уз , Уз + у4 + + + + + + + + + + + + The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin- Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Proposed Plant Annual Fixed Cost Annual Capacity Detroit $175,000 10,000 Toledo $300,000 20,000 Denver $375,000 30,000 Kansas City $500,000 40,000 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Annual Demand Boston 30,000 Atlanta 20,000 Houston 20,000 The shipping cost per unit from each plant to each distribution center is shown in table below. SHIPPING COST PER UNIT FOR THE MARTIN-BECK SUPPLY CHAIN Distribution Centers ETTT Plant Site Boston Atlanta Houston Detroit 2 3 Toledo Denver 4 3 7 4 5 Kansas City St. Louis 10 8. 4 4 2 3 A network representation of the potential Martin-Beck supply chain is shown in figure below. THE NETWORK REPRESENTATION OF THE MARTIN-BECK COMPANY SUPPLY CHAIN DESIGN PROBLEM 10 Detroit Distribution Centers 30 Boston 4 20 Toledo 3. 4 9 7 30 Denver 5 Atlanta 20 10 4. 40 Kansas City 8. Houston 20 3. 30 St. Louis Сараcities Distribution Routes Demands - Each potential plant location is shown; capacities and demands are shown in thousands of units. This network representation is for a transportation problem with a plant at St. Louis and at all four proposed sites. However, the decision has not yet been made as to which new plant or plants will be constructed. a. Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that a plant must be located either in Detroit or in Toledo, but not both. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Let y1 = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not Xij = the units shipped in thousands from plant i to distribution center j i= 1,2,3,4,5, and j = 1,2,3 Min X11+ X12 + X13 + X21 + X22+ X23 + X31 + X32 + X33 + X41+ X42 + X43 + X51+ X52 + X53+ Y2 + y3 + y4 + Min X11+ X12+ X13 + X21 + X22 + X23+ X31 + X32+ X33 + X41+ X42 X43 + X51+ X52 + X53 + yi + y2 y3 y4 s.t. X11 + X12 + X13 + y1 X21 + X22 X23 + y2 X31 X32 X33 y3 y4 X41 + X42 + X43 X51 + X52 + X53 X11 X21 +1 X31 + X41 + X51 X12 + X22 X42 X52 + X32 + + X13 X23 X33 + X43 X53 Xij 2 for all i i and j; y1 , Y2 , УЗ , Y1 + y2 + + + b. Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that no more than two plants can be located in Denver, Kansas City, and St. Louis. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Let yi = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not Xij the units shipped in thousands from plant i to distribution center j %3D i= 1,2,3,4,5, and j = 1,2,3 Min X11+ X12 + X13 + X21+ X22+ X23 + X31 + X32 + X33 + X41 + X42 X43 + X51+ X52 + X53 + y1 y2 y3 + Numeric field + + y4 s.t. X11 X12 X13 + X21 X22 X23 + y2 X31 + X32 X33 y3 X41 X42 +1 X43 y4 X51 + X52 + X53 X11 X21 X31 X41 X51 X12 + X22 X32 X42 X52 X13 + X23 X33 X43 X53 Xij 2 for all i and j; y1 , Y2 , Уз , Уз + у4 + + + + + + + + + + + +

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