3. The reorder point [see equation (14.6)] is defined as the lead-time demand for an item. In cases of long lead times, the lead-time demand and thus the reorder point may exceed the economic order Q*. In such cases, the inventory position will not equal the inventory on hand when an order is placed, and the reorder point may be expressed in terms of either the inventory position or the inventory on hand. Consider the economic order quantity model with D = 5000, Co = $32, Ch = $2, and 250 working days per year. Identify the reorder point in terms for each of the following lead times:
a. 5 days
b. 15 days
c. 25 days
d. 45 days
5. The Metropolitan Bus Company (MBC) purchases diesel fuel from American Petroleum Supply. In addition to the fuel cost, American Petroleum Supply charges MBC $250 per order to cover the expenses of delivering and transferring the fuel to MBC's storage tanks. The lead time for a new shipment from American Petroleum is 10 days; the cost of holding a gallon of fuel in the storage tanks is $0.04 per month, or $0.48 per year; and annual fuel usage is 150,000 gallons. MBC buses operate 300 days a year.
a. What is the optimal quantity for MBC?
b. How frequently should MBC order to replenish the gasoline supply?
c. The MBC storage tanks have a capacity of 15,000 gallons. Should MBC consider expanding the capacity of its storage tank?
d. What is the reorder point?
9. Cress Electronic Products manufactures components used in the automotive industry. Cress purchases parts for use in its manufacturing operation from a variety of different suppliers. One particular supplier provides a part where the assumptions of the EOQ model are realistic. The annual demand is 5000 units, the ordering cost is $80 per order, and the annual holding cost rate is 25%.
a. If the cost of the part is $20 per unit, what is the economic order quantity?
b. Assume 250 days of operation per year. If the lead time for an order is 12 days, what is the reorder point?
c. If the lead time for the part is seven weeks (35 day), what is the reorder point?
d. What is the reorder point for part (c) if the reorder point is expressed in terms of the inventory on hand rather than the inventory position?
11. Assume that a production line operates such that the production lot size model of Section 14.2 is applicable. Given D = 6400 units per year, Co =$100 and Ch = $2 per unit per year, compute the minimum cost production lot size for each of the following production rates:
a. 8000 units per year
b. 10,000 units per year
c. 32,000 units per year
d. 100.000 units per year
19. The A&M Hobby Shop carries a line of radio-controlled model racing cars. Demand for the cars is assumed to be constant at a rate of 40 cars per month. The cars cost $60 each, and ordering costs are approximately $15 per order, regardless of the order size. The annual holding cost rate is 20%.
a. Determine the economic order quantity and total annual cost under the assumption that no backorders are permitted.
b. Using a $45 per-unit per-year backorder cost, determine the minimum cost inventory policy and total annual cost for the model racing costs.
c. What is the maximum number of days a customer would have to wait for a backorder under the policy in part (b)? Assume that the Hobby Shop is open for business 300 days per year.
d. Would you recommend a no-backorder or a backorder inventory policy for this product? Explain.
e. If the lead time is six days, what is the reorder point for both the no-backorder and backorder inventory policies?