Solved Problems Virtual Office October 7, 2020 postadmin Post in Uncategorized Solved Problems Virtual Office Hours help is available at www.myomlab.com Solved Problem 12.1 David Alexander has compiled the following table of six items in inventory at Angelo Products, along with the unit cost and the annual demand in units: Use ABC analysis to determine which item(s) should be carefully controlled using a quantitative inventory technique and which item(s) should not be closely controlled. Solution The item that needs strict control is 33CP, so it is an A item. Items that do not need to be strictly controlled are 3CPO, R2D2, and RMS; these are C items. The B items will be XX1 and B66. 70% of Total cost = $100, 516.56 total cost = $70, 347.92 Page 2 of 9 12/11/2016https://jigsaw.vitalsource.com/api/v0/books/9780133558203/print?from=505&to=506 Solved Problem 12.2 The Warren W. Fisher Computer Corporation purchases 8,000 transistors each year as components in minicomputers. The unit cost of each transistor is $10, and the cost of carrying one transistor in inventory for a year is $3. Ordering cost is $30 per order. What are (a) the optimal order quantity, (b) the expected number of orders placed each year, and (c) the expected time between orders? Assume that Fisher operates on a 200-day working year. Solution a. b. c. With 20 orders placed each year, an order for 400 transistors is placed every 10 working days. PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted. = = = 400 unitsQ∗ 2DS H − −−√ 2(8,000) (30)3 − −−−−−−−√ N = = = 20 ordersD Q∗ 8,000 400 Time between orders = T = = = 10 working dNumber of working days N 200 20 Page 3 of 9 12/11/2016https://jigsaw.vitalsource.com/api/v0/books/9780133558203/print?from=505&to=506 Solved Problem 12.3 Annual demand for notebook binders at Meyer’s Stationery Shop is 10,000 units. Brad Meyer operates his business 300 days per year and finds that deliveries from his supplier generally take 5 working days. Calculate the reorder point for the notebook binders. Solution Thus, Brad should reorder when his stock reaches 167 units. Solved Problem 12.4 Leonard Presby, Inc., has an annual demand rate of 1,000 units but can produce at an average production rate of 2,000 units. Setup cost is $10; carrying cost is $1. What is the optimal number of units to be produced each time? Solution L d ROP = = = 5 days = 33.3 units per day10,000300 d × L = (33.3 units per day)(5 days) = 166.7 units = =Q∗p 2DS H(1− )Annual demand rate Annual production rate − −−−−−−−−−−−−−√ 2(1,000) (10)1[1−(1,000/2,000)] − −−−−−−−−−−√ = = = 200 units20,000 1/2 − −−−√ 40, 000− −−−−−√ Page 4 of 9 12/11/2016https://jigsaw.vitalsource.com/api/v0/books/9780133558203/print?from=505&to=506 Solved Problem 12.5 Whole Nature Foods sells a gluten-free product for which the annual demand is 5,000 boxes. At the moment, it is paying $6.40 for each box; carrying cost is 25% of the unit cost; ordering costs are $25. A new supplier has offered to sell the same item for $6.00 if Whole Nature Foods buys at least 3,000 boxes per order. Should the firm stick with the old supplier, or take advantage of the new quantity discount? Page 5 of 9 12/11/2016https://jigsaw.vitalsource.com/api/v0/books/9780133558203/print?from=505&to=506 Solution Under the present price of $6.40 per box: Economic order quantity, using Equation (12-10) : where Note: Order and carrying costs are rounded. Under the quantity discount price of $6.00 per box: We compute which is below the required order level of 3,000 boxes. So Q* is adjusted to 3,000. Q∗ Q∗ = = = 2DS IP − −−√ 2(5,000) (25) (0.25) (6.40) − −−−−−−−√ 395.3, or 395 boxes D S P I H = = = = = period demand ordering cost price per box holding cost as percent holding cost = IP Total cost = Order cost + Holding cost + Purchase cost = + H + PDDS Q Q 2 = + + (6.40) (5, 000)(5,000) (25)395 (395) (0.25) (6.40) 2 = 316 + 316 + 32, 000 = $ 32, 632 = 408.25,Q∗ = + H + PDDS Q Q 2 = + + (6.00) (5, 000)(5,000) (25)3,000 (3,000) (0.25) (6.00) 2 = 42 + 2, 250 + 30, 000 = $32, 292 Page 6 of 9 12/11/2016https://jigsaw.vitalsource.com/api/v0/books/9780133558203/print?from=505&to=506 Therefore, the new supplier with which Whole Nature Foods would incur a total cost of $32,292 is preferable, but not by a large amount. If buying 3,000 boxes at a time raises problems of storage or freshness, the company may very well wish to stay with the current supplier. Solved Problem 12.6 Children’s art sets are ordered once each year by Ashok Kumar, Inc., and the reorder point, without safety stock (dL), is 100 art sets. Inventory carrying cost is $10 per set per year, and the cost of a stockout is $50 per set per year. Given the following demand probabilities during the lead time, how much safety stock should be carried? Solution The safety stock that minimizes total incremental cost is 50 sets. The reorder point then becomes or 150 sets. PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted. 100 sets + 50 sets, Page 7 of 9 12/11/2016https://jigsaw.vitalsource.com/api/v0/books/9780133558203/print?from=505&to=506 Solved Problem 12.7 What safety stock should Ron Satterfield Corporation maintain if mean sales are 80 during the reorder period, the standard deviation is 7, and Ron can tolerate stockouts 10% of the time? Solution From Appendix I , Z at an area of and Equation (12-14) : . 9 (or 1 − . 10) = 1.28, Safety stock = = ZσdLT 1.28(7) = 8.96 units, or 9 units Page 8 of 9 12/11/2016https://jigsaw.vitalsource.com/api/v0/books/9780133558203/print?from=505&to=506 Solved Problem 12.8 The daily demand for 52ʺ flat-screen TVs at Sarah’s Discount Emporium is normally distributed, with an average of 5 and a standard deviation of 2 units. The lead time for receiving a shipment of new TVs is 10 days and is fairly constant. Determine the reorder point and safety stock for a 95% service level. Solution The ROP for this variable demand and constant lead time model uses Equation (12-15) : where So, with The safety stock is 10.4, which can be rounded up to 11 TVs. Solved Problem 12.9 The demand at Arnold Palmer Hospital for a specialized surgery pack is 60 per week, virtually every week. The lead time from McKesson, its main supplier, is normally distributed, with a mean of 6 weeks for this product and a standard deviation of 2 weeks. A 90% weekly service level is desired. Find the ROP. ROP = (Average daily demand × Lead time in days) + ZσdLT =σdLT σd Lead time − −−−−−−−√ Z = 1.65, ROP = = (5 × 10) + 1.65(2) 10−−√ 50 + 10.4 = 60.4 ≅60 TVs, or rounded up to 61 TVs PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted. Page 9 of 9 12/11/2016https://jigsaw.vitalsource.com/api/v0/books/9780133558203/print?from=505&to=506 Page 1 of 10 12/11/2016https://jigsaw.vitalsource.com/api/v0/books/9780133558203/print?from=508&to=509 Problems Note: means the problem may be solved with POM for Windows and/or Excel OM. • • 12.1 L. Houts Plastics is a large manufacturer of injection-molded plastics in North Carolina. An investigation of the company’s manufacturing facility in Charlotte yields the information presented in the table below. How would the plant classify these items according to an ABC classification system? L. Houts Plastics’ Charlotte Inventory Levels • • 12.2 Boreki Enterprises has the following 10 items in inventory. Theodore Boreki asks you, a recent OM graduate, to divide these items into ABC classifications. a. Develop an ABC classification system for the 10 items. b. How can Boreki use this information? c. Boreki reviews the classification and then places item A2 into the A category. Why might he do so? • • 12.3 Jean-Marie Bourjolly’s restaurant has the following inventory items that it orders on a weekly basis: a. Which is the most expensive item, using annual dollar volume? b. Which are C items? c. What is the annual dollar volume for all 20 items? • 12.4 Lindsay Electronics, a small manufacturer of electronic research equipment, has approximately 7,000 items in its inventory and has hired Joan Blasco-Paul to manage its inventory. Joan has determined that 10% of the items in inventory are A items, 35% are B items, and 55% are C items. She would like to set up a system in which all A items are counted monthly (every 20 working days), all B items are counted quarterly (every 60 working days), and all C items are counted semiannually (every 120 working days). How many items need to be counted each day? Page 2 of 10 12/11/2016https://jigsaw.vitalsource.com/api/v0/books/9780133558203/print?from=508&to=509 • 12.5 William Beville’s computer training school, in Richmond, stocks workbooks with the following characteristics: Calculate the EOQ for the workbooks. b. What are the annual holding costs for the workbooks? c. What are the annual ordering costs? • 12.6 If per month, per order, and per unit per month, a. What is the economic order quantity? b. How does your answer change if the holding cost doubles? c. What if the holding cost drops in half? • • 12.7 Henry Crouch’s law office has traditionally ordered ink refills 60 units at a time. The firm estimates that carrying cost is 40% of the $10 unit cost and that annual demand is about 240 units per year. The assumptions of the basic EOQ model are thought to apply. a. For what value of ordering cost would its action be optimal? b. If the true ordering cost turns out to be much greater than your answer to (a), what is the impact on the firm’s ordering policy? • 12.8 Matthew Liotine’s Dream Store sells beds and assorted supplies. His best-selling bed has an annual demand of 400 units. Ordering cost is $40; holding cost is $5 per unit per year. a. To minimize the total cost, how many units should be ordered each time an order is placed? Demand D = 19, 500 units/year Ordering cost S = $25/order Holding cost H = $4/unit/year a. PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted. D = 8, 000 S = $45 H = $2 Page 3 of 10 12/11/2016https://jigsaw.vitalsource.com/api/v0/books/9780133558203/print?from=508&to=509 b. If the holding cost per unit was $6 instead of $5, what would be the optimal order quantity? • 12.9 Southeastern Bell stocks a certain switch connector at its central warehouse for supplying field service offices. The yearly demand for these connectors is 15,000 units. Southeastern estimates its annual holding cost for this item to be $25 per unit. The cost to place and process an order from the supplier is $75. The company operates 300 days per year, and the lead time to receive an order from the supplier is 2 working days. a. Find the economic order quantity. b. Find the annual holding costs. c. Find the annual ordering costs. d. What is the reorder point? • 12.10 Lead time for one of your fastest-moving products is 21 days. Demand during this period averages 100 units per day. a. What would be an appropriate reorder point? b. How does your answer change if demand during lead time doubles? c. How does your answer change if demand during lead time drops in half? • 12.11 Annual demand for the notebook binders at Duncan’s Stationery Shop is 10,000 units. Dana Duncan operates her business 300 days per year and finds that deliveries from her supplier generally take 5 working days. a. Calculate the reorder point for the notebook binders that she stocks. b. Why is this number important to Duncan? • • 12.12 Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation. Thomas’s fastest-moving inventory item has a demand of 6,000 units per year. The cost of each unit is $100, and the Page 4 of 10 12/11/2016https://jigsaw.vitalsource.com/api/v0/books/9780133558203/print?from=508&to=509 inventory carrying cost is $10 per unit per year. The average ordering cost is $30 per order. It takes about 5 days for an order to arrive, and the demand for 1 week is 120 units. (This is a corporate operation, and there are 250 working days per year.) a. What is the EOQ? b. What is the average inventory if the EOQ is used? c. What is the optimal number of orders per year? d. What is the optimal number of days in between any two orders? e. What is the annual cost of ordering and holding inventory? f. What is the total annual inventory cost, including the cost of the 6,000 units? • • 12.13 Joe Henry’s machine shop uses 2,500 brackets during the course of a year. These brackets are purchased from a supplier 90 miles away. The following information is known about the brackets: a. Given the above information, what would be the economic order quantity (EOQ)? b. Given the EOQ, what would be the average inventory? What would be the annual inventory holding cost? c. Given the EOQ, how many orders would be made each year? What would be the annual order cost? d. Given the EOQ, what is the total annual cost of managing the inventory? e. What is the time between orders? f. What is the reorder point (ROP)? • • 12.14 Abey Kuruvilla, of Parkside Plumbing, uses 1,200 of a certain spare part that costs $25 for each order, with an annual holding cost of $24. a. Calculate the total cost for order sizes of 25, 40, 50, 60, and 100. b. Identify the economic order quantity and consider the implications for making an error in calculating economic order quantity.