Inventory Management and Inventory Pooling

  BADM 378 (Total Points: 100) 1. A firm procures a sub-assembly from a supplier. The daily demand for the product is fixed at 50 units. The cost of ordering is $4000 per order. The cost of inventory holding is $0.1 per unit per day. Lead time of delivery is zero. Answer the following questions: (5 + 5 + 10 + 5 = 25 points) a. What is the optimal order quantity that minimizes the cost of ordering and cost of holding jointly? b. What is the time between two consecutive orders? c. What is the daily holding cost and the daily ordering cost? d. Provide a rough diagram of the inventory cycle? 2. Now, in the problem 1, consider that the lead time of delivery is 3 days. (5 + 10 + 10 = 25 points) a. What is the reorder point? b. The procurement manager orders 200 units more per order than the optimal order quantity. What is the new ordering cost and holding cost per day? What is the increase in total inventory cost per day? c. If the manager ordered 200 units less than the optimal order quantity, what would have been the daily ordering cost, holding cost and total cost of inventory? 3. Consider a demand that is distributed normally with mean demand 300 and standard deviation of 50. The inventory ordering cost is $3000 per order and the holding cost is $0.1 per unit per day. The firm maintains a service level of 99% (z = 1.97). The lead time of delivery is 5 days. Answer the following questions. (5 + 5 + 5 + 5 + 5 = 25) a. Under the continuous review policy (Q, R), what is the optimal order quantity and reorder point? b. What is the expected cost of inventory holding per day? What is the expected ordering cost per day? c. Now if the company moves to a periodic review policy (base stock policy), where inventory status is reviewed every 10 days, what is the base stock level? d. What is the new holding cost and ordering cost per day under the base stock policy? e. What is the increase in safety stock under the base stock policy, compared that of the continuous review policy? 4. A firm sells a seasonal product with a demand that is estimated to be normally distributed with mean demand of 5,000 units, and a standard deviation of 500 units. The cost of producing the product is $30 and the selling price is $45. (10+15 = 25 points) a. How much should the firm stock for the upcoming selling season to jointly minimize the expected overstocking and understocking costs? b. If the firm is able to sell the unsold inventory at the end of the selling season at a discounted price of $15, how much should the firm stock to minimize the expected total cost?