Balanced plant and why "fat" is required in a system

1. About idle man power: Is it good to have excess unused capacity in the plant. Conventional wisdom is that the people should be utilized as much as possible for the plant's capacity to increase. But this results in excess inventory because people may be producing inventory which is not used immidiately. Thus tying money in WIP.

Balanced plant: Managers should aim at running balanced plant (which is easier said than done).
To balance a plant: Operational expense has to be reduced, while decreasing inventory and increasing throughput.

Managers of different divisions tend to focus on the performance of their units - for example operational personel might be most concerned about reducing the costs of operations - thus laying off people when there is excess capacity. This niehther brings in more sales or decreases inventory. There is no balance achieved. Only one factor is taken care of.

It can be proved mathematically that if capacity is balanced with marketing demand, then the inventory will go through the roof and throughput will decrease. This happens because of two mathematical phonomena:
Dependant events in combination with Statistical fluctuation.
The mathematical model can be understood from one of the simpler queuing models where

W = A / (2P(P-A))
where
W is the wait time in Queue
A is the rate of arrival of jobs to be processed
P is the rate of service of those jobs.

There fore, if rate of arrival of orders and rate of servicing them is same, the wait time will become infinity.