The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Products 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 new plant in one or more of the following alles: Detroit, Toledo, Denver, or Kansas City. The estimated annual foxed cost and the annual capacity for the four proposed plants are as follows: Annual Capacity Plant Number Proposed Plant Annual Fixed Cost 1 Detroit $150,000 10,000 Toledo $275,000 20,000 3 Denver $350.000 30,000 Kansas City $525,000 40,000 The company long-range planning group developed forecasts of the antipated annual demand at the distribution centers as follows Distribution Center Number Distribution Center Annual Demand 1 Boston 20,000 2 Atlanta 30,000 3 Houston 30,000 The shipping cost per unit from each plant to each distribution center is as follows Distribution Centers Plant Site Boston Atlanta Houston Detroit 5 2 The shipping cost per unit from each plant to each distribution center is as follows Distribution Centers Plant Site Boston Atlanta Houston Detroit 5 2 3 Toledo 4 3 4 Denver 9 7 5 10 4 Kansas City 2 St. Louis 8 4 3 (a) Formulate a mixed-integer programming model that could be used to help Merlin Beck determine which w plant or plan to open in order to satisfy anticipated demand and minime total cost in thousands of dollars). (Lety - units shipped in thousands from plant/ to distribution center with the exhing plant in St. Louis being plant number, et Yi - 1a plant is constructed in Detroit and if not, ya 1 plant constructed in Toledo and or not, plant is constructed in Denver and it notandy plant is constructed in Kansas City and if not.) Min Detroit Capacity Toledo Capacity Denver Capacity Wamenei s.t. Detroit Capacity Toledo Capacity Denver Capacity Kansas City Capacity St. Louis Capacity Boston Demand Atlanta Demand Houston Demand X;> 0 for all i and j and Y 11 Y21 Y 31 Y4 binary (b) Solve the model you formulated in part (a). What is the optimal cost (in $)? $ What is the optimal set of plants to open? (Select all that apply.) Detroit Toledo Atlanta Demand Houston Demand ya o for all and and yg. Yyx binary (b) Solve the model you formulated in part (a). What is the optimal cost (in $>> What is the optimal set of plants to open? (Select all that apply.) Detroit Toledo B Denver Kansas City (4) Using equation (13.1). (Sum of variables in the set o) - (sum of variables in the set ) (number of variables. In the set o) - where is the set of binary variables in our original optimal solution set to one and is the set of those set to zero, find a second best solution. What is the increase in cost in ) versus the best solution from part()? The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Products 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 new plant in one or more of the following alles: Detroit, Toledo, Denver, or Kansas City. The estimated annual foxed cost and the annual capacity for the four proposed plants are as follows: Annual Capacity Plant Number Proposed Plant Annual Fixed Cost 1 Detroit $150,000 10,000 Toledo $275,000 20,000 3 Denver $350.000 30,000 Kansas City $525,000 40,000 The company long-range planning group developed forecasts of the antipated annual demand at the distribution centers as follows Distribution Center Number Distribution Center Annual Demand 1 Boston 20,000 2 Atlanta 30,000 3 Houston 30,000 The shipping cost per unit from each plant to each distribution center is as follows Distribution Centers Plant Site Boston Atlanta Houston Detroit 5 2 The shipping cost per unit from each plant to each distribution center is as follows Distribution Centers Plant Site Boston Atlanta Houston Detroit 5 2 3 Toledo 4 3 4 Denver 9 7 5 10 4 Kansas City 2 St. Louis 8 4 3 (a) Formulate a mixed-integer programming model that could be used to help Merlin Beck determine which w plant or plan to open in order to satisfy anticipated demand and minime total cost in thousands of dollars). (Lety - units shipped in thousands from plant/ to distribution center with the exhing plant in St. Louis being plant number, et Yi - 1a plant is constructed in Detroit and if not, ya 1 plant constructed in Toledo and or not, plant is constructed in Denver and it notandy plant is constructed in Kansas City and if not.) Min Detroit Capacity Toledo Capacity Denver Capacity Wamenei s.t. Detroit Capacity Toledo Capacity Denver Capacity Kansas City Capacity St. Louis Capacity Boston Demand Atlanta Demand Houston Demand X;> 0 for all i and j and Y 11 Y21 Y 31 Y4 binary (b) Solve the model you formulated in part (a). What is the optimal cost (in $)? $ What is the optimal set of plants to open? (Select all that apply.) Detroit Toledo Atlanta Demand Houston Demand ya o for all and and yg. Yyx binary (b) Solve the model you formulated in part (a). What is the optimal cost (in $>> What is the optimal set of plants to open? (Select all that apply.) Detroit Toledo B Denver Kansas City (4) Using equation (13.1). (Sum of variables in the set o) - (sum of variables in the set ) (number of variables. In the set o) - where is the set of binary variables in our original optimal solution set to one and is the set of those set to zero, find a second best solution. What is the increase in cost in ) versus the best solution from part()
