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 Gregory and a single retailer - say Alexandria - act as a vertically integrated supply chain,what is their expected overstock quantity if Alexandria orders optimally?

Question

Quizplus · Accepted Answer

To find the expected overstock quantity, we need to calculate the optimal order quantity for Alexandria. 
Using the formula for the economic order quantity (EOQ), 
EOQ = sqrt[(2DS)/H] 
where D = Demand per year = 250 units, 
S = Setup cost = $3 (investment per unit), 
H = Holding cost per unit per year = cost of product * holding cost rate = $65 * 0.25 = $16.25

Plugging in the values, 
EOQ = sqrt[(2*250*3)/16.25] = 81 
So, Alexandria should order 81 units of body armor from The Hilltop.

The expected overstock quantity can then be calculated as the difference between the optimal order quantity and the mean demand: 
Expected overstock quantity = EOQ - mean demand = 81 - 250 = -169

However, negative overstock does not make sense, so we can assume that the overstock quantity is zero in this case. Therefore, the best choice is Option B, 130 (since 81 is not given as an option).

Scenario 15.2 - the Hilltop