The company produces broccoli at three plants, which are delivered to two customers via two warehouses....

 

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The company produces broccoli at three plants, which are delivered to two customers via two warehouses. Shipments between plants are allowed after the packaging has been completed. This also applies to between the warehouses and between the customers. The cost of producing the broccoli at each plant is different. As a result, the company is concerned with both production and shipping costs while meeting customer demands. The production capacity of each plant (in tonnes per year), the product cost at each plant (in dollars per tonnes), and the customer demand (in tonnes per year) are summarised in the table below: Plant Plant 1 Plant 2 Plant 3 From node Plant 1 Plant 2 Plant 3 Warehouse 1 Warehouse 2 Capacity 275 Customer 1 Customer 2 The cost (in thousands of dollars) of shipping a tonne of the product between each pair of locations is listed in the table below where a blank indicates that the company cannot ship on that route: To node Plant 1 300 350 0.5 0.5 Cost $1,550 $1,415 $1,375 Plant 2 Plant 3 0.5 0.5 0.5 0.5 Warehouse 1 2 2.5 4 Customer Customer 1 Customer 2 1 Warehouse 2 3 4 2 1 Customer 1 4 6 Demand 375 450 2 Customer 2 5 3 2 The management has set the maximum flow for each route to be 250 tonnes. Since sometimes the demands are fluctuated, the company plans to have safety stock of 50 and 25 tonnes at Warehouses 1 and 2 respectively. Based on the information above, the management wants you to design a network flow solution for their strategic plan to minimise the total costs that can meet the demands. Any change in the current scenario (e.g. plant capacities or route capacities) can be proposed if it is reasonable and based on the findings in your analysis (e.g. optimal solution, sensitivity analysis, and alternative optimal solutions). The company produces broccoli at three plants, which are delivered to two customers via two warehouses. Shipments between plants are allowed after the packaging has been completed. This also applies to between the warehouses and between the customers. The cost of producing the broccoli at each plant is different. As a result, the company is concerned with both production and shipping costs while meeting customer demands. The production capacity of each plant (in tonnes per year), the product cost at each plant (in dollars per tonnes), and the customer demand (in tonnes per year) are summarised in the table below: Plant Plant 1 Plant 2 Plant 3 From node Plant 1 Plant 2 Plant 3 Warehouse 1 Warehouse 2 Capacity 275 Customer 1 Customer 2 The cost (in thousands of dollars) of shipping a tonne of the product between each pair of locations is listed in the table below where a blank indicates that the company cannot ship on that route: To node Plant 1 300 350 0.5 0.5 Cost $1,550 $1,415 $1,375 Plant 2 Plant 3 0.5 0.5 0.5 0.5 Warehouse 1 2 2.5 4 Customer Customer 1 Customer 2 1 Warehouse 2 3 4 2 1 Customer 1 4 6 Demand 375 450 2 Customer 2 5 3 2 The management has set the maximum flow for each route to be 250 tonnes. Since sometimes the demands are fluctuated, the company plans to have safety stock of 50 and 25 tonnes at Warehouses 1 and 2 respectively. Based on the information above, the management wants you to design a network flow solution for their strategic plan to minimise the total costs that can meet the demands. Any change in the current scenario (e.g. plant capacities or route capacities) can be proposed if it is reasonable and based on the findings in your analysis (e.g. optimal solution, sensitivity analysis, and alternative optimal solutions).