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 queuing system. Products arrive at the operation at an average rate of 30 per hour, and the present average production rate is 33 products per hour. Management wants products to be at the operation an average of only .1 hour. What is the new average production rate at the operation? The answer is 40 products per hour. I need to know what the formula is and an illustration of how to find the answer part two of this question which is . In problem 1, how much would the average work-in-progress (WIP) inventory be reduced with the new production rate?

Explanation / Answer

Mean arrival rate 30 products/hour production rate 33 products/hour (also the mean service rate in this problem) a) avg time spent on the operation = 1 / ( production rate - mean arrival rate) Given: avg time spent on the operation = 0.1 hour mean arrival rate = 30 products/hour new average production rate at the operation = 40 products/hour b) how much would the average work-in-progress (WIP) inventory be reduced with the new production rate? production rate 33 products/hour avg no on the operation = mean arrival rate / ( production rate - mean arrival rate) avg work-in-progress (WIP) inventory 10 products production rate 40 products/hour avg work-in-progress (WIP) inventory 3 products Hence, the average work-in-progress (WIP) inventory reduction is of 7 products

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