A retailer believes that the average demand for its most popular product is 15 units with a standard deviation 6 units. The retailer pre-stocks = 20 units of inventory. Let = infEmin(, ) be the lowest expected sales quantity, where is the inventory level and is the random demand.

a) (5 marks) Formulate an SIP model to compute Z.

b) (5 marks) Use a discrete state space = {0,1,2,3, ,45} and the SIP model for part a) to compute an approximate value of Z. Hint: Keep 2 decimal places for Z and 3 decimal places for shadow prices.

Q7) (10 marks) A retailer believes that the average demand for its most popular product is 15 units with a standard deviation 6 units. The retailer pre-stocks q = 20 units of inventory. Let Z = inf Emin(q,0) be the lowest expected sales quantity, where q is the inventory level and 0 is the random demand. a) (5 marks) Formulate an SIP model to compute Z. b) (5 marks) Use a discrete state space N' = {0,1,2,3,...,45} and the SIP model for part a) to compute an approximate value of Z. Hint: Keep 2 decimal places for Z and 3 decimal places for shadow prices. Q7) (10 marks) A retailer believes that the average demand for its most popular product is 15 units with a standard deviation 6 units. The retailer pre-stocks q = 20 units of inventory. Let Z = inf Emin(q,0) be the lowest expected sales quantity, where q is the inventory level and 0 is the random demand. a) (5 marks) Formulate an SIP model to compute Z. b) (5 marks) Use a discrete state space N' = {0,1,2,3,...,45} and the SIP model for part a) to compute an approximate value of Z. Hint: Keep 2 decimal places for Z and 3 decimal places for shadow prices