Question

The single milling machine at Stout Manufacturing was severely overloaded last year. The plant operates eight hours per day, five days per week, and 50 weeks per year. Management prefers a capacity cushion of 15 percent. Two major types of products are routed through the milling machine. The annual demand for product A is 3000 units and 2000 units for product B. The batch size for A is 20 units and 40 units for B. The standard processing time for A is 0.5 hours/unit and 0.8 hours/unit for B. The standard setup time for product A is 2 hours and 8 hours for product B. How many new milling machines are required if Stout does not resort to any short-term capacity options

Answer 1

If we assumes we setup machine for product A x times, and B y times, the total hours required is 0.5*3000 + 0.8*2000+ 2*x + 8 *y = 3100+2x+8y. Notice that due to the capacity restriction x has to be no smaller than 150 hours (3000/20) and y has to be no smaller than 50 hours (2000/40). so total required hours must exceed 3100+2*150+8*50=3800. The management prefer a 15% capacity cushion, which means the total duration prepared for the processing should be at least 3800*(1+15%)=4370 hours.

If one machine operates eight hours per day, five days per week and 50 weeks a year, it operates 5*8*50 = 2000 hours in total.

That's why we need 2 more machines ( 3 machines in total since 4370 > 2*2000).