# Mathematics and Time

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• Published : December 1, 2010

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1) Calculation of Labour Utilization:
No. of total employees = 22
No. of assistant supervisors = 4
Time used by assistant supervisors for production process = 100% -10% = 90% Therefore, the total available labour = 18 + 0.9*4 = 21.6

Maximum labour hours/ month =
No. of days*labour hrs available/day*total available labour = 20*8*21.6 = 3456 hrs Actual labour hours used = 1531.7 hrs
Capacity Utilization = Actual labour hours used/ Maximum labour hours available = (1531.7/3456) * 100 = 44.32%

This figure does not include the time taken by labour to rework on the parts rejected or returned by the customer. Hence, the actual labour utilization would be more than the above calculated figure. However, we believe that the above time signifies the actual time spent by labour in producing or working on new parts.

2) Profile operation (Fabrication) - Break even analysis: Let the optimal order size be N boards
a) Using Punch Press:
Total Operating Time = Setup time + Cycle Time*N = 50 + 1*N = 50 + N b) Using CNC router:
Operating Time = Setup time + Cycle time*N = 150 + 0.5*N= 150 + 0.5N We would use the CNC router when its operating time is less than that of the punch press. i.e. 150 + 0.5*N ≤ 50 + N
=> 0.5*N ≥ 100
=> N ≥ 200
=> N ≥ 200 boards
Thus, for orders above 200 boards, the CNC router should be used as it will take less time and hence, would produce more number of boards.

3) Drilling Operation (Image Tranfer) – Break Even Analysis Let the optimal order size be N boards
a) Using Manual drill:
Total Operation Time = Setup time + Run time = 15 + 0.08*500*N = 15 + 40N b) Using CNC drill:
Total Operation Time = Setup time + Run time = 240 + 0.004*500*N = 240 + 2*N We would use the CNC drill when its operating time is less than that of the punch press. i.e. 240 + 2*N ≤ 15 + 40*N
=> 38*N ≥ 225
=> N ≥ 5.92
=> N ≥ 6 boards
Therefore, for orders with size above 6 boards or more, CNC drill should be used as it will take less...