UNIVERSITY OF GUELPH Operations Management, FARE*3310 Winter 2013 Assignment 3

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1 UNIVERSITY OF GUELPH Operations Management, FARE*3310 Winter 2013 Assignment 3 A N S W E R LAST NAME K E Y FIRST NAME F A R E STUDENT ID NUMBER INSTRUCTIONS: 1. The due date for this assignment is Friday, March 22, 2011, beginning of the class.. Please note that late assignment will be given a zero grade. 2. This assignment contains FIVE questions. Total marks are out of 55. The point value is shown at the beginning of each question. You are required to answer all questions, and SHOW YOUR WORK FOR FULL CREDIT. 3. The assignment will count for 6.67 percent of your grade. 4. If you have to, make reasonable assumptions, but explain/justify any assumptions made in your answers. 5. Please round your calculations to THREE decimal places (e.g., 0.003) 6. If you have any queries, please contact the instructor or the GTAs. 7. PRINT your NAME on this page and attach it to your assignment. Question Maximum Score Grader Total 55

2 1) [Chapter 12](20 points 4 points each) Suppose a beer distributor finds that it sells on average 100 cases a week of regular10-oz. Budweiser. For this problem assume that demand occurs at a constant rate over a 50-week year. The distributor currently purchases beer every two weeks at a cost of $8 per case. The inventory related holding cost (i.e., capital, insurance, etc) for the distributor equals 25% of the dollar value of inventory per year. Each order placed with the supplier costs labour, forms, postage, etc.- the distributer $10. a. Assume the distributor can choose any order quantity it wishes. What order quantity minimizes the distributor s total inventory-related costs (holding and ordering)? For the next three parts, assume the distributor selects the order quantity specified in part (a). D = 100 * 50 = 5000 cases P = $8 per case (price per case) S = $10 per order H = 0.25 * $8 = $2 per case per year b. Given the answer in (a), how many times a year does the distributor place orders? What is the optimal interval (in weeks) between orders? c. What is the distributor s total order cost for one year? What is the distributor s total holding cost for one year? What is the distributor s inventory-related cost per case of beer sold? $ $ $0.090 d. Using an appropriately labelled diagram, graph setup cost, holding cost, and total inventory cost showing show the optimal order quantity and the minimum total inventory cost. Page 2

3 e. Assume the brewery is willing to give a 5% quantity discount if the distributor orders 600 cases or more at a time. If the distributor is interested in minimizing its total cost (i.e., purchases and inventory related costs), should the distributor begin ordering 600 or more cases at a time? P = $8 *(1-0.05) = $7.6 H= 0.25 *$7.6 = 1.9 Without discount: 224 $10 $2 $ $40, With discount: 600 $10 $1.9 $ $38, Order 600 cases as the total cost (inventory plus product cost) are lower with the discount. 2) [Chapter 12] ](10 points 2.5 each) Suppose a local green coffee distributor operates 200 days a year and sells an average of 75 pounds of Fair Trade Organic (FTO) beans a day. The daily demand for the Fair Trade Organic beans is assumed to be normally distributed with a standard deviation, d, of 15 pound per day. After ordering, the distributor always receives beans within exactly 4 days. Annual holding costs per pound for the beans are $3. The ordering cost is $16 per order. a. Determine the EOQ for the FTO beans. What are the total annual holding costs of stock for FTO beans? d = 75 lbs per day D = 75 * 200 = 15,000 lbs per year d = 15 lb per day (Variable demand) L = 4 days H = $3 per pound per year S = $16 per order Page 3

4 $3 $600 2 b. Assume that management has specified that no more than a 5% risk of stockout is acceptable. What is the safety stock needed to attain a 5% risk of stockout during lead time? What is the average demand during the lead time? What should the reorder point be? Risk of stockout = 0.05 Service level = = 0.95 or 95% Z = 1.65 Safety Stock: SS = Z * dlt = Z *sqrt(l)* dlt = 1.65* sqrt(4)*15 = 49.5 Average demand during lead time: d * L = 75 * 4 = 300 Reorder Point: ROP = d*l + SS = = c. What is the annual holding cost of maintaining the level of safety stock needed to support a 5% risk of stockout? SS = 49.5 HC(SS) = HC(49.5) = H*$3 = 49.5 * $3 = $ d. If management specified that a 10% risk of stockout during lead time would be acceptable, would the safety stock holding costs decrease or increase? Why? Service Level = = 0.9 or 90% Z = 1.28 SS = 1.28* sqrt(4)*15 = 38.4 HC(49.5) = 38.4 * $3 = $ The holding cost decreases from $ to $ as the probability of stockout increases from 5% to 10%. 3) [Chapter 16] ](7.5 points each) A firm has a repetitive manufacturing plant producing lamps. The following information has been collected. Currently, the firm operates 250 days per year. Annual demand, D 22,000 Daily demand, d 88 Daily production, p 250 Desired lot size (2 hours of production), Qp 63 Holding cost per unit per year, H $50 a. What is the setup cost, based on the desired lot size? Page 4

5 $ ,000 b. What is the setup time, based on $40 per hour setup labor? Setup time = $. $/ c. Suppose safety stock is half of daily production. Determine the number of kanbans needed ? 63 Not enough information. You need lead time to calculate the number of kanbans. An aside: suppose now L=5 days ) [Chapter 12] ](7.5 points) A local firm is considering the use of ABC analysis to focus on the most critical items in its inventory. For a random sample of eight items in its inventory, the following table shows the annual dollar usage. Item Dollar per unit Annual Usage volume (units) I001 $0.10 1,200 I002 $ ,000 I003 $ I004 $ ,000 I005 $ I006 $ I007 $ ,000 I008 $ a. Rank the items and assign them to the A, B, or C class. (4.5 points) Page 5

6 item price quantity Dollar I001 $0.10 x 1,200 = $120 I002 $0.05 x 120,000 = $6,000 I003 $1.45 x 100 = $145 I004 $0.75 x 40,000 = $30,000 I005 $4.50 x 900 = $4,050 I006 $1.00 x 350 = $350 I007 $0.20 x 70,000 = $14,000 I008 $1.50 x 200 = $300 Sort and calculate percentage: item price quantity dollar Class I004 $ ,000 $30, $30, % A I007 $ ,000 $14, $14, % 80.1% A I002 $ ,000 $6, $6, % B I005 $ $4, $4, % 18.3% B I006 $ $ $ % C I008 $ $ $ % C I003 $ $ $ % C I001 $0.10 1,200 $ $ % 1.7% C 232,750 $54, % A items B items C items Page 6 b. The management 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

7 counted semi-annually (every 120 working days). How many items need to be counted each day? (3 point) item price quantity Class I004 $ ,000 A I007 $ ,000 A 110,000 I002 $ ,000 B I005 $ B 120,900 I006 $ C I008 $ C I003 $ C I001 $0.10 1,200 C 1850 item price quantity Class Total units by class # of items counted I004 $ ,000 A I007 $ ,000 A 110, I002 $ ,000 B I005 $ B 120, I006 $ C I008 $ C I003 $ C I001 $0.10 1,200 C Class A: (40,000+70,000)/20 = 5500 items per day Class B: (120, ) /60 = 2015 items per day Class C: ( )/120 = 15 item per day items per day items per day + 15 items per day = 7,530 items per day. 5) [Chapter 7](10 points 2 each) An organization is considering three process configuration options. There are two different intermittent processes, as well as a repetitive focus. The smaller intermittent process has fixed costs of $3,000 per month, and variable costs of $10 per unit. The larger intermittent process has fixed costs of $12,000 per month and variable costs of $2 per unit. A repetitive focus plant has fixed costs of $50,000 and variable costs of $1 per unit. a. What is the crossover point between the two intermittent processes? What is the crossover point between the repetitive process and the larger intermittent process? Crossover two intermittent processes: Page 7

8 OR Crossover large intermittent and repetitive: , ,000 12, ,000 OR ,000 b. Using an appropriately labelled diagram, draw the three total cost lines on the same chart illustrating the crossover (or indifferent) points. $600,000 $400,000 Inter_small Inter_large $200,000 $ Page 8 c. At what output does the large intermittent process become cheaper than the small one? At what output does the repetitive process become cheaper than the larger intermittent process? The large intermittent process becomes cheaper than the small one when output is above 1125 units. The repetitive process becomes cheaper than the larger intermittent process when output is above 38,000 units. An aside: The large intermittent process is cheaper between 1125 and 38,000 units d. If the company produced 20,000 units, what would be its cost under each of the three choices? TC(IN1) = *20,000 = $203,000 TC(IN2) = *20,000 = $52,000 (low cost) TC(REP) = 50,000+ 1*20,000 = $70,000

9 e. Which process offers the lowest cost to produce 40,000 units? What is that cost? Based on (a-c)- repetitive process is low cost above 38,000 units, hence repetitive is low cost. TC(IN1) = *40,000 = $403,000 TC(IN2) = *40,000 = $92,000 TC(REP) = 50,000+ 1*40,000 = $90,000 Page 9