OM 24 WORKSHEET 9 - Inventory Models
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School
Amrita Vishwa Vidyapeetham**We aren't endorsed by this school
Course
MBA TERM 3
Subject
Industrial Engineering
Date
Dec 16, 2024
Pages
3
Uploaded by SargentOtterMaster3034
WORKSHEET 9 Inventory –Types / EOQ / EMQ 1.A part is produced in lots of 1,000 units. It is assembled from 2 components worth $50 total. The value added in production (for labor and variable overhead) is $60 per unit, bringing total costs per completed unit to $110. The average lead time for the part is 6 weeks and annual demand is 3,800 units, based on 50 business weeks per year. a.How many units of the part are held, on average, in cycle inventory? What is the dollar value of this inventory? b.How many units of the part are held, on average, in pipeline inventory? What is the dollar value of this inventory? 2.Prince Electronics, a manufacturer of consumer electronic goods, has five distribution centers in different regions of the country. For one of its products, a highspeed modem priced at $350 per unit, the average weekly demand at each distribution center is 75 units. Average shipment size to each distribution center is 400 units, and average lead time for delivery is 2 weeks. Each distribution center carries 2 weeks’ supply as safety stock but holds no anticipation inventory. a.On average, how many dollars of pipeline inventory will be in transit to each distribution center? b.How much total inventory (cycle, safety, and pipeline) does Prince hold for all five distribution centers? 3.At Dot Com, a large retailer of popular books, demand is constant at 32,000 books per year. The cost of placing an order to replenish stock is $10, and the annual cost of holding is $4 per book. Stock is received 5 working days after an order has been placed. No backordering is allowed. Assume 300 working days a year. a.What is Dot Com’s optimal order quantity?b.What is the optimal number of orders per year? c.What is the optimal interval (in working days) between orders? d.What is demand during the lead time? e.What is the reorder point? f.What is the inventory position immediately after an order has been placed? 4.A bakery buys flour in 25-pound bags. The bakery uses 1,215 bags a year. Ordering cost is $10 per order. Annual carrying cost is $75 per bag. a. Determine the economic order quantity. b. What is the average number of bags on hand? c. How many orders per year will there be? d. Compute the total cost of ordering and carrying flour. e. If holding costs were to increase by $9 per year, how much would that affect the minimum total annual cost? 5.A large law firm uses an average of 40 boxes of copier paper a day. The firm operates 260 days a year. Storage and handling costs for the paper are $30 a year per box, and it costs approximately $60 to order and receive a shipment of paper. a. What order size would minimize the sum of annual ordering and carrying costs? b. Compute the total annual cost using your order size from part a. c. Except for rounding, are annual ordering and carrying costs always equal at the EOQ? d. The office manager is currently using an order size of 200 boxes. The partners of the firm expect the office to be managed “in a cost-efficient manner.” Would you recommend that the office manager use the optimal order size instead of 200 boxes? Justify your answer. 6.A food processor uses approximately 27,000 glass jars a month for its fruit juice product. Because of storage limitations, a lot size of 4,000 jars has been used. Monthly holding cost is 18 cents per jar, and reordering cost is $60 per order. The company operates an average of 20 days a month. a. What penalty is the company incurring by its present order size?
b. The manager would prefer ordering 10 times each month but would have to justify any change in order size. One possibility is to simplify order processing to reduce the ordering cost. What ordering cost would enable the manager to justify ordering every other day (i.e., 10 times a month)? 7.Harley-Davidson has its engine assembly plant in Milwaukee and its motorcycle assembly plant in Pennsylvania. Engines are transported between the two plants using trucks, with each trip costing $1,000. The motorcycle plant assembles and sells 300 motorcycles each day. Each engine costs $500; Harley incurs a holding cost of 20 percent per year. How many engines should Harley load onto each truck? What is the cycle inventory of engines at Harley? 8.The Friendly Sausage Factory (FSF) can produce hot dogs at a rate of 5,000 per day. FSF supplies hot dogs to local restaurants at a steady rate of 250 per day. The cost to prepare the equipment for producing hot dogs is $66. Annual holding costs are 45 cents per hot dog. The factory operates 300 days a year. Find a. The optimal run size. b. The number of runs per year. c. How many days does it take to produce the optimal run quantity? 9.A chemical firm produces sodium bisulfate in 100-pound bags. Demand for this product is 20 tons per day. The capacity for producing the product is 50 tons per day. Setup costs $100, and storage and handling costs are $5 per ton a year. The firm operates 200 days a year. ( Note: 1 ton _ 2,000 pounds.) a. How many bags per run are optimal? b. What would the average inventory be for this lot size? c. Determine the approximate length of a production run, in days. d. About how many runs per year would there be? e. How much could the company save annually if the setup cost could be reduced to $25 per run? 10.A company manufactures hair dryers. It buys some of the components, but it makes the heating element, which it can produce at the rate of 800 per day. Hair dryers are assembled daily, 250 days a year, at a rate of 300 per day. Because of the disparity between the production and usage rates, the heating elements are periodically produced in batches of 2,000 units. a. Approximately how many batches of heating elements are produced annually? b. If production on a batch begins when there is no inventory of heating elements on hand, how much inventory will be on hand two days later? c. What is the average inventory of elements, assuming each production cycle begins when there are none on hand? d. The same equipment that is used to make the heating elements could also be used to make a component for another of the firm's products. That job would require four days, including setup. Setup time for making a batch of the heating elements is a half day. Is there enough time to do this job between production of batches of heating elements? Explain. 11.Sharpe Cutter is a small company that produces specialty knives for paper cutting machinery. The annual demand for a particular type of knife is 100,000 units. The demand is uniform over the 250 working days in a year. Sharpe Cutter produces this type of knife in lots and, on average, can produce 450 knives a day. The cost to set up a production lot is $300, and the annual holding cost is $1.20 per knife. a. Determine the economic production lot size (EMQ). b. Determine the total annual setup and inventory holding cost for this item. c. Determine the TBO, or cycle length, for the EMQ. d. Determine the production time per lot . 12.A manager receives a forecast for next year. Demand is projected to be 600 units for the first half of the year and 900 units for the second half. The monthly holding cost is $2 per unit, and it costs an estimated $55 to process an order. Assuming that monthly demand will be level during each of the six-month periods covered by the forecast (e.g., 100 per month for each of the first six months), determine an order size that will minimize the sum of ordering and carrying costs for each of the six-month periods. a.Why is it important to be able to assume that demand will be level during each six-month period?
b.If the vendor is willing to offer a discount of $10 per order for ordering in multiples of 50 units (e.g., 50, 100, 150), would you advise the manager to take advantage of the offer in either period? If so, what order size would you recommend? 13.All Good Computers, a US chain of computer hardware and software retail outlets, supplies educational and commercial customers with memory and storage devices. It currently faces the following ordering decision relating to purchases of very high-density disks: D = 36,000 disks, S = $25, H = $0.45, Purchase price =$0.85, and Discount price = $0.82, Quantity needed to qualify for the discount = 6,000 disks. Should the discount be taken? 14.Rocky Mountain Tire Center sells 20,000 go-cart tires per year. The ordering cost for each order is $40, and the holding cost is 20% of the purchase price of the tires per year. The purchase price is $20 per tire if fewer than 500 tires are ordered, $18 per tire if 500 or more—but fewer than 1,000—tires are ordered, and $17 per tire if 1,000 or more tires are ordered. How many tires should Rocky Mountain order each time it places an order? What is the total cost of this policy? 15.Cool Computers purchases integrated chips at $350 per chip. The holding cost is $35 per unit per year, the ordering cost is $120 per order, and sales are steady, at 400 per month. The company’s supplier, Hot Chip Manufacturing, Inc., decides to offer price concessions in order to attract larger orders. The price structure is shown below. Hot Chip’s Price Structure: (QUANTITY - PURCHASED PRICE/UNIT): 1–99 units - $350; 100–199 units - $325; 200 or more units -$300 a.What is the optimal order quantity and the minimum annual cost for Bell Computers to order, purchase, and hold these integrated chips? b.Cool Computers wishes to use a 10% holding cost rather than the fixed $35 holding cost in (a). What is the optimal order quantity, and what is the optimal annual cost? 16.The catering manager of La Vista Hotel, Lisa Ferguson, is disturbed by the amount of silverware she is losing every week. Last Friday night, when her crew tried to set up for a banquet for 500 people, they did not have enough knives. She decides she needs to order some more silverware but wants to take advantage of any quantity discounts her vendor will offer. For a small order (2,000 or fewer pieces), her vendor quotes a price of $1.80Ypiece. If she orders 2,001–5,000 pieces, the price drops to $1.60 per piece. 5,001–10,000 pieces bring the price to $1.40 per piece, and 10,001 and above reduces the price to $1.25 per piece. Lisa’s order costs are $200 per order, her annual holding costs are 5%, and the estimated annual demand is 45,000 pieces. For the best option: a.What is the optimal order quantity? b.What is the annual holding cost? c.What is the annual ordering (setup) cost?