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.
- The annual demand for product B is 2000 units.
- The batch size for A is 20 units.
- The batch size for B is 40 units.
- The standard processing time for A is 0.5 hours/unit.
- The standard processing time for B is 0.8 hours/unit.
- The standard setup time for product A is 2 hours.
- The standard setup time for product B is 8 hours.

How many new milling machines are required if Stout does not resort to any short-term capacity options?

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).

CharlesBronson CharlesBronson · Answer 2 · 2024-04-09T08:54:07-04:00

Final answer:

Stout Manufacturing will need at least 3 new milling machines to meet the demand for products A and B, considering production and setup time as well as the desired capacity cushion.

Explanation:

To calculate the number of new milling machines required at Stout Manufacturing, we must first determine the total annual hours needed for both products and then compare this to the available machine hours per year, taking into account the desired capacity cushion.

First, let's calculate the total hours needed for production and setup for each product independently:

Annual hours for product A (production + setup) = (Annual demand / Batch size) * (Standard processing time * Batch size + Standard setup time) = (3000 / 20) * (0.5 * 20 + 2) = 150 * 12 = 1800 hours

Annual hours for product B (production + setup) = (2000 / 40) * (0.8 * 40 + 8) = 50 * 40 = 2000 hours

Combined annual hours for A and B = 1800 + 2000 = 3800 hours

The total available hours per year for one machine is calculated as follows:

Available hours per machine per year (with cushion) = Operating hours per day * Days per week * Weeks per year * (1 - capacity cushion) = 8 * 5 * 50 * (1 - 0.15) = 1700 hours

Now, we divide the combined annual hours by the available hours per machine to find the number of machines required:

Number of machines required = Total annual hours / Available hours per machine per year = 3800 / 1700 ≈ 2.24

Since you cannot have a fraction of a machine, Stout Manufacturing will need to round up, meaning they require at least 3 new milling machines to meet the demand without resorting to short-term capacity options.