Question 5: SPECTRUMS BRANDS INC. AGAIN... (12 points) You have been moved to the Paper Products division of Spectrums Brands Inc. (SBI) to support operations for a certain B2B product line. Specifically, you have two major business customers, Goggle and Faceblock, who have firm contracts for your product each month of 1000 and 600 units, respectively. SBI has three different production plants that can produce the product, one in Scranton, PA, one in Utica, NY, and one in Stamford, CT. However, each of the plants is limited on how much they can produce during regular time. Additionally, each plant has a different cost (not including labor) to produce one unit of the product. The transportation costs to ship the product from each plant to each customer is also different. All of these details are provided in Table 3. Table 3: Plant informations and relevant costs Plant Costs per unit ($) Transportation Max capacity (units) Manufacture Goggle Faceblock 908 465 105 14 18 570 115 24 20 505 Scranton Utica Stamford If overtime is used, then each plant has an additional capacity of 100 units per month. The cost for overtime (not including labor) is 1.5 times the regular time cost. Given your previous success at determining workforce levels, SBI has also decided to ask you to deal with the labor options available to this operations group. There are two sources of labor: certified specialists (100 available in the area available at $2000 per month) and generalists (200 available in the area at $1700 per month). You do not have to hire all of the workers. The specialists are able to produce 12 units of product each month, whereas the generalists only produce 10 units per month. SBI must provide transportation for all workers to the plants. The cost per month of transporting a worker to Scranton is $300, to Utica is $250, and to Stamford is $275. Create a network flow formulation of this problem and solve to minimize costs while meeting demand. Hint: you may need to consider the generalized network flow model. Question 5: SPECTRUMS BRANDS INC. AGAIN... (12 points) You have been moved to the Paper Products division of Spectrums Brands Inc. (SBI) to support operations for a certain B2B product line. Specifically, you have two major business customers, Goggle and Faceblock, who have firm contracts for your product each month of 1000 and 600 units, respectively. SBI has three different production plants that can produce the product, one in Scranton, PA, one in Utica, NY, and one in Stamford, CT. However, each of the plants is limited on how much they can produce during regular time. Additionally, each plant has a different cost (not including labor) to produce one unit of the product. The transportation costs to ship the product from each plant to each customer is also different. All of these details are provided in Table 3. Table 3: Plant informations and relevant costs Plant Costs per unit ($) Transportation Max capacity (units) Manufacture Goggle Faceblock 908 465 105 14 18 570 115 24 20 505 Scranton Utica Stamford If overtime is used, then each plant has an additional capacity of 100 units per month. The cost for overtime (not including labor) is 1.5 times the regular time cost. Given your previous success at determining workforce levels, SBI has also decided to ask you to deal with the labor options available to this operations group. There are two sources of labor: certified specialists (100 available in the area available at $2000 per month) and generalists (200 available in the area at $1700 per month). You do not have to hire all of the workers. The specialists are able to produce 12 units of product each month, whereas the generalists only produce 10 units per month. SBI must provide transportation for all workers to the plants. The cost per month of transporting a worker to Scranton is $300, to Utica is $250, and to Stamford is $275. Create a network flow formulation of this problem and solve to minimize costs while meeting demand. Hint: you may need to consider the generalized network flow model
