6. 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 8 per day. The order cost is $40 per order the inventory carrying cost is 20% per year and the product value is $30. The stockout cost is $10 per unit short. The probability of being in stock is to be 90%. The supplier has an average lead time of 4 days with a standard deviation of 1.5 days. (6 pts.) a) Design a reorder point system using the 90% probability of being in stock and () state the policy (order size and when to order) and (ii) the total annual cost. (1) Policy (order size and when to order): (11) Total annual cost= pts.) b) If the product must be ordered in multiples of 250 items, design a reorder point system using the 90% probability of being in stock and state the policy (order size and when to order), (i) 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. Policy (order size and when to order): (11) Total annual cost=. (111) % increase from cost in part a = (iv) Number of units out-of-stock on average each year= (3 pts.) c) 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 small of a standard deviation of lead time is needed to make the total cost with the best probability of being in-stock equal to $4,000/year? Standard deviation of lead time = 6. 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 8 per day. The order cost is $40 per order the inventory carrying cost is 20% per year and the product value is $30. The stockout cost is $10 per unit short. The probability of being in stock is to be 90%. The supplier has an average lead time of 4 days with a standard deviation of 1.5 days. (6 pts.) a) Design a reorder point system using the 90% probability of being in stock and () state the policy (order size and when to order) and (ii) the total annual cost. (1) Policy (order size and when to order): (11) Total annual cost= pts.) b) If the product must be ordered in multiples of 250 items, design a reorder point system using the 90% probability of being in stock and state the policy (order size and when to order), (i) 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. Policy (order size and when to order): (11) Total annual cost=. (111) % increase from cost in part a = (iv) Number of units out-of-stock on average each year= (3 pts.) c) 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 small of a standard deviation of lead time is needed to make the total cost with the best probability of being in-stock equal to $4,000/year? Standard deviation of lead time =
