As part of their vaccine distribution, Pharma Inc. needs to determine where to warehouse the vaccines...

  

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As part of their vaccine distribution, Pharma Inc. needs to determine where to warehouse the vaccines to distribute to the Midwest market. Each of the Midwest states can warehouse the vaccines, but only have enough doses to fulfill the demand of only three states. Pharma Inc.'s government contract stipulates that the company will open five warehouses in the Midwest for distribution to these states. Unfortunately, due to the fact that the vaccine must be transported at -80 degrees Celsius, the vaccines cannot take more than six hours to reach their destination. A table with the travel time between locations is provided below. Because speed is the top priority, identify which states to open up the five warehouses such that the warehouse is within six hours of the destination, each state receives delivery of the vaccine, and each warehouse fulfills no more than 3 states. Develop an integer optimization model that finds the minimum time to ship the vaccine. Note: Solver has an artificially imposed constraint of no more than 100 constraints. To address this, you can either use OpenSolver OR transform the time in hours table such that any time above the defined threshold is exceptionally large (i.e. 999) - such that the model would not select it. Time In Hours Springfield, Illinois Indianapolis, Indiana Des Moines, lowa Topeka, Kansas Lansing, Michigan Saint Paul, Minnesota Jefferson City, Missouri Lincoln, Nebraska Bismarck, North Dakota Columbus, Ohio Pierre, South Dakota Madison, Wisconsin Springfield, Illinois 0.00 3.09 4.73 5.88 5.78 7.49 3.32 6.70 13.26 5.53 11.59 4.27 Indianapolis, Indiana Des Moines, Iowa 4.73 6.67 0.00 3.95 7.63 3.41 3.09 0.00 6.67 7.99 3.63 8.70 5.28 9.30 14.61 2.58 14.36 5.33 4.60 2.67 9.47 9.11 6.95 4.49 Topeka, Kansas 5.88 7.99 3.95 0.00 11.54 7.26 3.46 3.16 11.23 10.40 8.14 8.33 Warehouse Location Lansing, Michigan Saint Paul, Minnesot Jefferson City, Misso Lincoln, Nebraska 5.78 3.63 7.49 3.32 8.70 7.63 3.41 11.54 7.26 0.00 9.13 8.86 10.27 15.03 3.84 14.55 5.76 9.13 0.00 7.88 6.57 6.06 11.19 7.23 3.76 5.28 4.60 3.46 8.86 7.88 0.00 5.21 12.80 7.67 10.27 7.17 6.70 9.30 2.67 3.16 10.27 6.57 5.21 0.00 9.16 12.20 6.31 7.07 Bismarck, North Dak Columbus, Ohio 13.26 14.61 9.47 11.23 15.03 6.06 12.80 9.16 0.00 17.07 3.41 9.66 5.53 2.58 9.11 10.40 3.84 11.19 7.67 12.20 17.07 0.00 16.00 7.73 Pierre, South Dakota Madison, Wisconsin 11.59 14.36 6.95 8.14 14.55 7.23 10.27 6.31 3.41 16.00 0.00 10.31 4.27 5.33 4.49 8.33 5.76 3.76 7.17 7.07 9.66 7.73 10.31 0.00 1) (5 points) Where should the company place their five warehouses? (Order ascending by state name) 2) (12 points) For each state, which warehouse will the vaccines be shipped from? Destination Warehouse Springfield, Illinois Indianapolis, Indiana Des Moines, lowa Topeka, Kansas Lansing, Michigan Saint Paul, Minnesota Jefferson City, Missouri Lincoln, Nebraska Bismarck, North Dakota Columbus, Ohio Pierre, South Dakota Madison, Wisconsin 3) (3 points) What is the minimum total time to ship the vaccines to all of the states from the five warehouses? hours As part of their vaccine distribution, Pharma Inc. needs to determine where to warehouse the vaccines to distribute to the Midwest market. Each of the Midwest states can warehouse the vaccines, but only have enough doses to fulfill the demand of only three states. Pharma Inc.'s government contract stipulates that the company will open five warehouses in the Midwest for distribution to these states. Unfortunately, due to the fact that the vaccine must be transported at -80 degrees Celsius, the vaccines cannot take more than six hours to reach their destination. A table with the travel time between locations is provided below. Because speed is the top priority, identify which states to open up the five warehouses such that the warehouse is within six hours of the destination, each state receives delivery of the vaccine, and each warehouse fulfills no more than 3 states. Develop an integer optimization model that finds the minimum time to ship the vaccine. Note: Solver has an artificially imposed constraint of no more than 100 constraints. To address this, you can either use OpenSolver OR transform the time in hours table such that any time above the defined threshold is exceptionally large (i.e. 999) - such that the model would not select it. Time In Hours Springfield, Illinois Indianapolis, Indiana Des Moines, lowa Topeka, Kansas Lansing, Michigan Saint Paul, Minnesota Jefferson City, Missouri Lincoln, Nebraska Bismarck, North Dakota Columbus, Ohio Pierre, South Dakota Madison, Wisconsin Springfield, Illinois 0.00 3.09 4.73 5.88 5.78 7.49 3.32 6.70 13.26 5.53 11.59 4.27 Indianapolis, Indiana Des Moines, Iowa 4.73 6.67 0.00 3.95 7.63 3.41 3.09 0.00 6.67 7.99 3.63 8.70 5.28 9.30 14.61 2.58 14.36 5.33 4.60 2.67 9.47 9.11 6.95 4.49 Topeka, Kansas 5.88 7.99 3.95 0.00 11.54 7.26 3.46 3.16 11.23 10.40 8.14 8.33 Warehouse Location Lansing, Michigan Saint Paul, Minnesot Jefferson City, Misso Lincoln, Nebraska 5.78 3.63 7.49 3.32 8.70 7.63 3.41 11.54 7.26 0.00 9.13 8.86 10.27 15.03 3.84 14.55 5.76 9.13 0.00 7.88 6.57 6.06 11.19 7.23 3.76 5.28 4.60 3.46 8.86 7.88 0.00 5.21 12.80 7.67 10.27 7.17 6.70 9.30 2.67 3.16 10.27 6.57 5.21 0.00 9.16 12.20 6.31 7.07 Bismarck, North Dak Columbus, Ohio 13.26 14.61 9.47 11.23 15.03 6.06 12.80 9.16 0.00 17.07 3.41 9.66 5.53 2.58 9.11 10.40 3.84 11.19 7.67 12.20 17.07 0.00 16.00 7.73 Pierre, South Dakota Madison, Wisconsin 11.59 14.36 6.95 8.14 14.55 7.23 10.27 6.31 3.41 16.00 0.00 10.31 4.27 5.33 4.49 8.33 5.76 3.76 7.17 7.07 9.66 7.73 10.31 0.00 1) (5 points) Where should the company place their five warehouses? (Order ascending by state name) 2) (12 points) For each state, which warehouse will the vaccines be shipped from? Destination Warehouse Springfield, Illinois Indianapolis, Indiana Des Moines, lowa Topeka, Kansas Lansing, Michigan Saint Paul, Minnesota Jefferson City, Missouri Lincoln, Nebraska Bismarck, North Dakota Columbus, Ohio Pierre, South Dakota Madison, Wisconsin 3) (3 points) What is the minimum total time to ship the vaccines to all of the states from the five warehouses? hours