21) The single milling machine at Fred\'s Manufacturing was severely overloaded
ID: 347820 • Letter: 2
Question
21) The single milling machine at Fred's Manufacturing was severely overloaded last year. The plant operates 8 hours per day, 5 days per week, and 50 weeks per year. Two major types of products are routed through the milling machine. The annual demand for product A is 5000 units and 4000 units for product B. The batch size for A is 20 units and 30 units for B. The standard processing time for A is 0.5 hours/unit and 0.8 for B. The standard setup time for product A is 2 hours and 8 hours for product B. How many additional milling machines are required if Fred's management is considering to have: a. 30 percent capacity cushion. b. 10 percent capacity cushion.Explanation / Answer
Total time available in an year = Hours per day*Days per week*Weeks per year = 8*5*50 = 2000 hours
Annual demand:
Product A = 5000
Product B = 4000
Processing time of A = 5000*0.5 = 2500 hours
Processing time of B = 4000*0.8 = 3200 hours
Set up time of A = Demand/Batch size*Setup time per batch = 5000/20*2 = 500 hours
Set up time of B = Demand/Batch size*Setup time per batch = 4000/30*8 = 1066.67 hours
Total time required = 2500+3200+500+1066.67 = 7266.67 hours
Required machine = Total time required/Time available = 7266.67/2000 = 4 machines (Round off)
a) Capacity cushion of 30%
Desired capacity = Total time required/(1-Capacity cushion) = 7266.67/(1-30%) = 10380.96 hours
Number of machines = 10380.96/Time available = 10380.96/2000 = 5.2 Hence, 6 machines
Additional = 6-4 = 2 machines
b) Capacity cushion of 10%
Desired capacity = Total time required/(1-Capacity cushion) = 7266.67/(1-10%) 8074.1 hours
Number of machines = 8074.1/Time available = 8074.1/2000 = 4.03 Hence, 5 machines
Additional = 5-4 = 1 machine
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