are157-homework-4 - ARE 157 ANALYSIS FOR PRODUCTION...

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Unformatted text preview: ARE 157 ANALYSIS FOR PRODUCTION MANAGEMENT Homework 4, due Wednesday, June 2nd in class Spring 2010 M.Whitney (10) 1. Karlberg=s produces and sells pewter platters, mugs and bowls. Its most popular item is its salad bowl. The firm is open for business 360 days per year, and sells 20 salad bowls each business day. The firm is capable of producing 100 bowls per day. The firm=s setup cost per production lot is $400. The annual holding cost to keep a bowl in inventory is $20. The wholesale value of each finished bowl is $65. The firm does not maintain any safety stock. a. What is the economic production lot-size? b. How many cycles will there be per year? How many business days will there be in each production phase, and in each drawdown or inventory depletion phase? What is the total number of business days per cycle? c. What is the maximum cycle inventory (maximum quantity of bowls in storage)? What is the average inventory quantity? What are the maximum and average levels of inventories, in terms of dollar value? d. What are the firm=s total annual setup costs? What are total annual holding costs? e. Sketch a diagram of production and inventories over a 2-cycle period, labeling output, maximum inventory level, average inventory level, production phase, and inventory depletion or drawdown phase. (10)2. Ken=s Music sells an average of 40 German saxophones per week. Weekly demand is distributed normally with a variance of 25. Lead time for ordering these saxophones is 4 weeks. The firm wants to choose a level of safety stock that will minimize its total costs of inventories and stockouts. The stocking cost per order is $1664, and the cost to hold one saxophone in inventory for a year is $40. The opportunity cost of each lost sale due to stockout is $39.90. a. b. c. d. e. f. What is the least number of saxophones Ken=s would expect to sell in a week? The average? The most? What is the firm=s economic order quantity? How many cycles per year will the firm experience? What is the firm=s optimal stockout probability P(D*)? What service level does this correspond to? Find σL and Z. What amount of safety stock should the firm maintain? What is the optimal reorder level? What is the firm=s average level of inventory? What are annual stocking costs and holding costs? About how many times per year will the firm stock out? 3. (5) Clients arrive at Donatelli=s Deli according to a Poisson distribution, with a mean arrival rate of 16 per hour. The firm has a single cash register, and can serve an average of 20 customers per hour. a. Sam works at the cash register. What percent of the time is he idle? b. On average, how many customers are in the queue, and in the system as a whole? c. Barbara is considering ordering a sandwich at this deli, but is in a hurry. What average wait time should she expect if she visits this firm? d. Mr. Donatelli, the owner, is concerned that the line might grow too long for the available standing room near the register. What is the probability that exactly 8 customers will be in the service area at any given time? 4. (15) A product structure tree for a toy train set is shown below: Level 0 0001 Deluxe toy train set | 1 wk. | Level 1 _________________________________________________________ | | | | | 1001 Carton 1002 Engine assembly 1003 Box car assembly (4) 1004 Track (12) 1 wk | 2 wks | 2 wks 3 wks | | Level 2 ____________________ _____________________ | | | | 2001 Engine body 2002 Wheel (4) 2003 Boxcar body 2002 Wheel (4) 2 wks 1 wk. 2 wks 1 wk. The firm also makes a standard toy train set. Its product structure tree is identical, except it includes only 2 box car assemblies, and 8 sections of track. The firm must produce the following output. Week Item 0001 Deluxe toy train 0002 Standard toy train 5 6 200 7 400 8 9 500 100 300 a. Develop an inventory status file for wheels (2002). Assume there are 1,000 wheels on hand initially, and that an order of 2000 is scheduled to be received in week three. Assume lot-for-lot ordering. (Hint: remember that there is only one status file for each input item, regardless of how many outputs it is used in). b. Develop an inventory status file for track (1004). Assume there are 4000 units on hand initially, and no orders have been scheduled yet. Assume track is sold in packages of 2000 units each, ...
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This note was uploaded on 10/06/2010 for the course ARE 51800 taught by Professor Whitney during the Spring '10 term at UC Davis.

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