MEDIAL Inc. is a company manufacturing medical equipment such as mechanical ventilators (MV), non-invasive ventilators (NIV), nebulizers (N) and kidney machines (KM). The company has just signed a contract with the Turkish Ministry of Health to supply NIVs to be distributed to 3 city hospitals; Ankara, Adana, and Bursa. Based on the number of Covid-19 patients with milder symptoms in the past months and experts' opinion, supply amounts have been estimated for the next four months as shown in Table 1. MEDIAL Inc. must meet this delivery schedule. Table 1. Delivery requirements for non-invasive ventilators for the next four months Months December January February March Supply Amounts 200 280 275 210 MEDIAL's factory in Polatl can produce NIVs at a cost of $25 per unit(labor cost is not included). To produce a NIV, 10 hours of labor are required and there are 12 workers available at the plant at the beginning of December. Each worker can work 180 hours per month in regular hours with a rate of $1.6 per hour, and 100 hours in overtime per month with a rate of $2.5. It is possible to hire new workers or to lay off some of the existing workers at the beginning of a month. A one-time additional cost for hiring and layoff of a worker is $500 and $1200, respectively. Note that it is possible to have non-integer number of workers and NIVs. It is also possible to subcontract some of the NIVs to another factory at a cost of $60 each, but the subcontractor has a production capacity of 10 units per month. NIVs can be carried in inventory to meet the requirement of a future month, but this costs $8 per unit per month, but the storage has a capacity of 25 units. Backordering is also allowed with a cost of $10 per unit per month. Part 1: Formulate MEDIAL Inc.'s problem as a linear programming model. Find the optimal decisions using Excel Solver. Report your findings. Part 2: Answer the following questions and interpret the results without resolving the model. a. How much should the subcontractor lower its price to become favorable in period 4? b. How much lower does the inventory carrying cost need to be for carrying inventory in period 2? c. In which months would the company consider hiring new workers if the hiring cost was reduced to $300 per worker? d. At what lay off cost would the company consider laying off workers? Discuss for each month. e. If MEDIAL Inc. could negotiate to lower the demand in some period, which period would they do so? f. Why does not the company consider overtime in period 1? How much lower does the overtime cost need to be for overtiming be favorable in period 1 ? MEDIAL Inc. is a company manufacturing medical equipment such as mechanical ventilators (MV), non-invasive ventilators (NIV), nebulizers (N) and kidney machines (KM). The company has just signed a contract with the Turkish Ministry of Health to supply NIVs to be distributed to 3 city hospitals; Ankara, Adana, and Bursa. Based on the number of Covid-19 patients with milder symptoms in the past months and experts' opinion, supply amounts have been estimated for the next four months as shown in Table 1. MEDIAL Inc. must meet this delivery schedule. Table 1. Delivery requirements for non-invasive ventilators for the next four months Months December January February March Supply Amounts 200 280 275 210 MEDIAL's factory in Polatl can produce NIVs at a cost of $25 per unit(labor cost is not included). To produce a NIV, 10 hours of labor are required and there are 12 workers available at the plant at the beginning of December. Each worker can work 180 hours per month in regular hours with a rate of $1.6 per hour, and 100 hours in overtime per month with a rate of $2.5. It is possible to hire new workers or to lay off some of the existing workers at the beginning of a month. A one-time additional cost for hiring and layoff of a worker is $500 and $1200, respectively. Note that it is possible to have non-integer number of workers and NIVs. It is also possible to subcontract some of the NIVs to another factory at a cost of $60 each, but the subcontractor has a production capacity of 10 units per month. NIVs can be carried in inventory to meet the requirement of a future month, but this costs $8 per unit per month, but the storage has a capacity of 25 units. Backordering is also allowed with a cost of $10 per unit per month. Part 1: Formulate MEDIAL Inc.'s problem as a linear programming model. Find the optimal decisions using Excel Solver. Report your findings. Part 2: Answer the following questions and interpret the results without resolving the model. a. How much should the subcontractor lower its price to become favorable in period 4? b. How much lower does the inventory carrying cost need to be for carrying inventory in period 2? c. In which months would the company consider hiring new workers if the hiring cost was reduced to $300 per worker? d. At what lay off cost would the company consider laying off workers? Discuss for each month. e. If MEDIAL Inc. could negotiate to lower the demand in some period, which period would they do so? f. Why does not the company consider overtime in period 1? How much lower does the overtime cost need to be for overtiming be favorable in period 1
