Kriegland is a specialty store that specializes in home theater systems. They ha

Question

Kriegland is a specialty store that specializes in home theater systems. They have decided to make an attempt to always stock their best-selling projector. One of the manager’s biggest problems is to decide on an appropriate inventory policy for stocking these projectors. On the one hand, s/he wants to have enough in stock so that customers receive their request right away, but on the other hand, s/he does not want to tie up too much money in inventory. Most of the difficulty results from the unpredictability of customer demand. If this demand were constant, the manager could decide on an appropriate inventory policy fairly easily. But the demand varies widely from month to month in a random manner. All the manager knows is that the historical average demand per month is approximately 9.

a.) What is the probability that the sales during any particular month would be less than 5 units?

p = _________            

b.) Starting a new month with 12 units, what is the likelihood that the store would run out of units during that month (assuming that no new shipments are coming in)?
p = _________          
                        

c.) Starting a new month with 12 units, what is the likelihood that the store would have back orders1 (assuming that no new shipments are coming in)? 1. A back order is a customer order that has not been fulfilled; a product that has been ordered but not sent to the customer because it is not yet available. A back order generally indicates that customer demand for a product or service exceeds a company's capacity to supply it.

p = _________                                        

Explanation / Answer

here we use poisson distribution with mean=9

answer a) P(x<5)=P(x=0)+P(x=1)+p(x=2)+p(x=4)=0.000123+0.001111+0.004998+0.014994+0.033737=0.5496

answer b) required probability=P(x<=12)-P(x<=9)=0.7277-0.1318=0.5959

answer c)requied probability=P(x<=13)-P(x<=12)=0.9261-0.8758=0.0503

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