## Answers

Use the newsboy/newsvendor model for single period inventory

a)

The cost of overstaffing (Co) = 150

The cost of under staffing (Cu) = 240

The critical ratio = Cu/(Cu+Co) = 240/(150+240) = 0.6153

This means the probability of facing understaffing or overtime charges are 0.6153. Thus it is better to staff more than less. Based on this, the z value is 0.29

The optimal number is given by mean + z*standard deviation

This means the optimal number is 50 + 10*0.29 = 52.9 or 53 officers

b)

With the current solution, the possibility that we will still face shortage and overtime is 1-0.6153 = 0.3847 or 38.47% probability.

c)

If the probability of facing overtime needs to be reduced to 25% then we need to consider a critical ratio of 0.75. That means z = 0.675

This would means the optimal staffing be 50 + 0.675*10 = 56.75 or 57 officers

This is an increase of 4 officers.

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