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Chapter 17

Q. 17.5

Partial Automation
The company is considering replacing one of the current manual workstations with an automatic work head on a 10-station production line. The current line has six automatic stations and four manual stations. Current cycle time is 30 sec.
The limiting process time is at the manual station that is proposed for replacement.
Implementing the proposal would allow the cycle time to be reduced to 24 sec. The new station would cost $0.20/min. Other cost data: C_{w} = \$0.15/min, C_{as} = \$0.10/min, and C_{at} = \$0.12/min. Breakdowns occur at each automated station with a probability p = 0.01. The new automated station is expected to have the same frequency of breakdowns. Average downtime per occurrence T_{d} = 3.0 min, which will be unaffected by the new station. Material costs and tooling costs will be neglected in the analysis. It is desired to compare the current line with the proposed change on the basis of production rate and cost per piece. Assume a yield of 100% good product.


Verified Solution

For the current line, T_{c} = 30  sec = 0.50  min
T_{p} = 0.50 + 6(0.01)(3.0) = 0.68 min and R_{p} = 1/0.68 = 1.47  pc/min = 88.2  pc/hr


C_{o} = 0.12 + 4(0.15) + 6(0.10) = \$1.32/min and C_{pc} = 1.321(0.682) = \$0.898/pc
For the proposed line, T_{c} = 24  sec = 0.4  min

T_{p} = 0.40 + 7(0.01)(3.0) = 0.61 min and R_{p} = 1/0.61 = 1.64  pc/min = 98.4  pc/hr


C_{o} = 0.12 + 3(0.15) + 6(0.10) + 1(0.20) = \$1.37/min and C_{pc} = 1.37(0.61) = \$0.836/pc
Even though the line would be more expensive to operate per unit time, the proposed change would increase production rate and reduce piece cost.