Consider a product for which the average demand is 70 items per day (for 365 days per year) and the standard deviation of demand is 10 per day. The product value is $3, the order cost is $30 per order, and the inventory carrying cost is 20% per year. The stockout cost is $0.50 per unit short. The probability of being in stock is to be 99%. The supplier has an average lead time of 5 days with a standard deviation of 1.5 days.

a) Design a reorder point system using the 99% probability of being in stock and (i) state the policy (order size and when to order) and (ii) the total annual cost.

Policy (order size and when to order): ____________________________________

Total annual cost = ________

b) If the product must be ordered in multiples of 500 items, design a reorder point system using the 99% probability of being in stock and

(i) state the policy (order size and when to order),

(ii) the total annual cost,

(iii) the % increase from the cost in part a, and

(iv) how many units they are out of stock on average each year.

(i) Policy (order size and when to order): _________________________________

(ii) Total annual cost = _______

(iii) % increase from cost in part a = _______

(iv) Number of units out-of-stock on average each year = ________

c) Suppose the probability of being in stock can be changed (it does not need to be 99%) and any size order is possible. What is:

(i) the best probability of being in-stock (to minimize total cost),

(ii) the order policy (order size and when to order),

(iii) the total annual cost,

(iv) the number of units they are out of stock on average each year, and

(v) the % savings relative to the annual cost in part a).

(i) Best probability of being in-stock = ________

(ii) Policy (order size and when to order): _______________________________________

(iii) Total annual cost = _______

(iv) Number of units out-of-stock on average each year = ________

(v) % savings from cost in part a = _______

(4 pts.) d) Suppose now that new, more reliable suppliers are being sought. This will decrease the standard deviation of lead time below the 1.5 days in the original problem. How much could be saved ($ per year) compared to the situation in part c) with a supplier that is perfectly reliable (standard deviation = 0)? (Use the best probability of being in stock.)

Best probability of being in stock = _______

Annual cost savings = ________