Question

A company is currently producing a carpet shampooer that sells about 4,000 units per year. It takes 2 hours to produce the unit, but 8 hours to set up the line for that process. This device is produced in batches of 100. Management is considering producing a second type of shampooer, for which it estimates that demand would 2,000 units per year, processing time would be 2.8 hours per unit, with a setup time of 16 hours per batch, and batches of 200.

There are currently two machines dedicated to the first product, which could also be used by the new one. The plant works two eight-hour shifts per day for 250 days per year, and frowns on overtime. Because of uncertainties in the introduction of the new product, the company would like to reserve a capacity cushion of 10%.

If management decides to go with the new product, how do you recommend that they expand to meet expected demand?

Answer 1

Carpet shampooer

Annual demand = 4000 units

Processing time = 2 hours

Setup time = 8 hours

Batch size = 100 units

Second type of shampooer

Annual demand = 2000 units

Processing time = 2.8 hours

Setup time = 16 hours

Batch size = 200 units

--------------------------------

Number of machines = 2

Number of shifts per day = 2

Hours per day = 8

Days per year = 250

Capacity cushion = 10%

Total capacity of each machine = Days per year * Number of shifts per day * 8 hours per day

= 250*2*8

= 4,000 hours

Available time per machine net of capacity cushion = 4000*(1-10%) = 3,600 hours

--------------------------------

Total time required for carpet shampooer = Processing time of both products + Setup time of both products

= 4000*2+(4000/100)*8

= 8,320 hours

Total time required for second type of shampooer = Processing time of both products + Setup time of both products

= 2000*2.8+(2000/200)*16

= 5,760 hours

Total time required for both types of shampooers = 8320+5760

= 14,080 hours

--------------------------------

Total number of machines required = 14080 / 3600

= 3.91

~ 4 machines

There are currently 2 machines. Therefore, in order to meet expected demand, it is recommended that management should add two more machines.