The Makonsel Company is a fully integrated company that both produces goods and sells them at its retail outlets. After production, the goods are stored in the company's two warehouses until needed by the retail outlets. Trucks are used to transport the goods from the two plants to the warehouses, and then from the warehouses to the three retail outlets. Using units of full truckloads, the following table shows each plant's monthly output, its shipping cost per truckload sent to each warehouse, and the maximum amount that it can ship per month to each warehouse. To Unit Shipping Cost Shipping Capacity From Warehouse 1 Warehouse 2 Warehouse 1 Warehouse 2 Output Plant 1 $425 $560 125 150 200 Plant 2 $510 $600 175 200 300 For each retail outlet (RO), the next table shows its monthly demand, its shipping cost per truckload from each warehouse, and the maximum amount that can be shipping per month from each warehouse. To Unit Shipping Cost Shipping Capacity From RO1 RO2 RO3 RO1 RO2 RO3 Warehouse 1 $470 $505 $490 100 150 100 Warehouse 2 $390 $410 $440 125 150 75 Demand 150 200 150 150 200 150 Management now wants to determine a distribution plan (number of truckloads shipped per month from each plant to each warehouse and from each warehouse to each retail outlet) that will minimize the total shipping cost. (a) Draw a network that depicts the company's distribution network. Identify the supply nodes, transshipment nodes, and demand nodes in this network. (b) Formulate this problem as a minimum cost flow problem by inserting all the necessary data into this network (c) Use Excel Solve to solve this problem
The Makonsel Company is a fully integrated company that both produces goods and sells them at its retail outlets. After production, the goods are stored in the company's two warehouses until needed by the retail outlets. Trucks are used to transport the goods from the two plants to the warehouses, and then from the warehouses to the three retail outlets. Using units of full truckloads, the following table shows each plant's monthly output, its shipping cost per truckload sent to each warehouse, and the maximum amount that it can ship per month to each warehouse. To Unit Shipping Cost Shipping Capacity From Warehouse 1 Warehouse 2 Warehouse 1 Warehouse 2 Output Plant 1 $425 $560 125 150 200 Plant 2 $510 $600 175 200 300 For each retail outlet (RO), the next table shows its monthly demand, its shipping cost per truckload from each warehouse, and the maximum amount that can be shipping per month from each warehouse. To Unit Shipping Cost Shipping Capacity From RO1 RO2 RO3 RO1 RO2 RO3 Warehouse 1 $470 $505 $490 100 150 100 Warehouse 2 $390 $410 $440 125 150 75 Demand 150 200 150 150 200 150 Management now wants to determine a distribution plan (number of truckloads shipped per month from each plant to each warehouse and from each warehouse to each retail outlet) that will minimize the total shipping cost. (a) Draw a network that depicts the company's distribution network. Identify the supply nodes, transshipment nodes, and demand nodes in this network. (b) Formulate this problem as a minimum cost flow problem by inserting all the necessary data into this network (c) Use Excel Solve to solve this problem.
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