Scenario 15.2 - The Hilltop
Gregory and his followers scavenge the countryside for anything of value and with minimal investment,make it ready to provide for any customer visiting their compound.Their average investment in a product is $3,and one popular product,body armor,is in high demand.Residents of The Kingdom and Alexandria in particular,are eager to procure The Hilltop's body armor for $65 and sell it to anyone left in the world at an average price of $650.The demand for the body armor is normally distributed,with a mean of 250 units and a standard deviation of 50.
-If The Kingdom and Alexandria are acting independently,what is their expected overstock quantity if they order the optimal quantity?

Question

Quizplus · Accepted Answer

The optimal order quantity in a newsvendor model is determined by the critical ratio, which is the probability that demand is less than or equal to the optimal order quantity. Given the demand is normally distributed with a mean of 250 units and a standard deviation of 50, and assuming The Kingdom and Alexandria aim to maximize expected profit without facing stockouts, they would order at the quantity where the probability of demand being less than or equal to this quantity equals the critical ratio. However, the expected overstock quantity is essentially the expected amount of unsold inventory, which can be calculated using the standard deviation and the properties of the normal distribution. Without the exact critical ratio or cost parameters provided, we cannot directly calculate the optimal order quantity or the expected overstock. However, given the choices and understanding that the expected overstock is a function of the standard deviation and the distribution of demand, we can infer that the correct answer must be related to the properties of the normal distribution and the standard deviation. The answer provided directly, without the necessary calculations or critical ratio, suggests an approximation or a typical scenario given the parameters of the problem.

Scenario 15.2 - the Hilltop