Question

Decreasing the processing time at a step that has a setup, but is not the bottleneck,...

Decreasing the processing time at a step that has a setup, but is not the bottleneck, and holding everything else constant, _______ the average inventory. How?

The formula is average inventory is 1/2 Batch Size ( 1- Flow Rate * Processing Time)  

The answer is decrease. I do not understand how

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Answer #1

Irrespective whether a process is done in batch or not, the overall inventory buildup can be defined by Little’s law. The law states

L = λW

Here L denotes the length of the queue or the inventory buildup. In effect the average inventory value is dependent on this value. The flow rate is denoted by λ and the overall time in the system is denoted by W. Now, a component of W is also the processing time. This means if we reduce processing time the value of W reduces. If we keep λ constant and reduce the value of W, then the value of L reduces as well. This means the inventory buildup reduces. This reduces the average inventory.

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