A production operation is a single-channel, single-phase, unlimited-queue-length

Question

A production operation is a single-channel, single-phase, unlimited-queue-length queing system. Products arrive at the operation at an average rate of 90 per hour, and theautomated operation produces products at a constant rate of 95 products per hour. Engineering can modify the machinery at the operation to increase the production capacity to a constant rate of 105 products per hour. How much would the average lead time be reduced? How much would the average WIP be reduced with the improvements in the lead time?

Explanation / Answer

y=90

u1=95

u2=105

Lead time = y/[2u(u-y)] + 1/u

Lead time 1 = 90/950 + 1/95 = 0.1052631 hour = 6.3158 min

Lead time 2 = 90/3150 + 1/105 = 0.0381 hour = 2.2857 min

So lead time reduction is 4.03 minutes

WIP 1= y*lead time = .1052631*90= 9.474

WIP 1= y*lead time = .0381*90= 3.429

So WIP reduced by 6.025 units or 64%

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