Question

A factory that makes stamped parts has a painting operation. All parts must be painted to combat corrosion. The factory has 10 different parts, each of which have an annual demand of 500,000. Typically the factory sets up for one part per day and runs for the entire shift producing just that one part. To keep up with demand, the factory works a six-day work week and two 8-hour shifts, working 50 weeks per year. Each machine can paint 100 parts at a time and the standard cycle time is 15 minutes to paint and cure 100 parts. Approximately 5% of the parts painted must be scrapped due to paint flaws. At the beginning of the day, each paint machine requires 45 minutes to set up. After set up, it is run for the remainder of the 2 shifts (16 hours). Paint booths are notoriously unreliable (clogs, leaks, messes, machinery failures) and shutdowns are commonplace. The plant assumes 20% downtime for each machine to deal with in-process issues. Booths are 100% available for setup. Because it is a tiring job, worker efficiency is 90%. Calculate the number of paint booths required to meet annual demand.? ( ) machines

Answer 1

ANSWER

Total number of available days in a year = 6 days/ week x 50 weeks = 300 days

Total number of hours available in a day = 8 hour/ shift x 2 shifts = 16 hours

Since worker efficiency is 90%, actual number of hours a labour is available for activity on one machine = 0.9 x 16 =14.4 hours

Set up time per machine = 45 minutes =0.75 hours

Therefore,

Net available time for actual operation = 14.4 – 0.75 = 13.65 hours

Net available time for actual operation =13.65 hours

Thus 13.65 hours theoretically can be used for actual production per machine per day

However 20% of this time is wasted due to downtime

Therefore ,

up time per machine per day = 80% of 13.65 hours = 10.92 hours

up time per machine per day = 10.92 hours

It takes 15 minutes or 0.25 hours to produce 100 parts

Therefore, time taken for 1 part will be 0.0025 hours

Hence,

number of items which can be produced/ painted in 10.92 hours = 10.92/0.0025 = 4368

number of items which can be produced/ painted in 10.92 hours = 4368

Out of above numbers , 5% of the parts painted must be scrapped due to paint failure

Therefore, 95% of parts produced are of good quality .

Therefore ,

number of good quality parts which can be produced per day = 95% of 4368 = 4149.6

number of good quality parts which can be produced per day = 4149.6

Since there are 10 parts and only one part is produced per day, we can say that a cycle of production will consists of 10 days. Therefore, number of cycles in a year of 300 days will be 300/10 = 30 cycles .

Number of items per part per machine/ paint booth produced per cycle of 10 days = 4149.6

Therefore,

Number of items per part per machine produced in a year i.e. 30 cycles = 4149.6 x 30 = 124488

Hence ,

number of machines/paint booths required to produce 500,000 parts in 1 year i.e. 30 cycles = 500,000/124,488 = 4.016

number of machines/paint booths required to produce 500,000 parts in 1 year i.e. 30 cycles = 4.016 ( 5 rounded to next higher whole number )

Note : Providing only 4 machines/ paint booths will yield an output just short of 500,000 and hence not acceptable.

NUMBER OF PAINT BOOTHS REQUIRED TO MEET ANNUAL DEMAND = 5

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