Operations Management I Winter 2005 Odette School of Business University of Windsor

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1 Last Name First Name ID Operations Management I 7-1 Winter 005 Odette School of Business University of Windsor Midterm Exam II Solution Thursday, March 1 Last Name A-L: Room OB B0 Last Name M-Z: Room ED 11 Instructor: Mohammed Fazle Baki Aids Permitted: Calculator, straightedge, and a one-sided formula sheet. Time available: 1 hour 0 min Instructions: This solution has 6 pages including this cover page. Please be sure to put your name and student ID number on each odd numbered page. Show your work. State results up to four decimal places. It s not necessary to return tables and formula sheet. Grading: Question Marks: 1 /10 /1 /16 /1 5 /1 Total: /65

2 Question 1: (10 points) Circle the most appropriate answer 1.1 The fundamental problem of inventory management can be succinctly described by the two questions a. When should an order be placed and how much should be reorder point b. When should an order be placed and how much should be ordered c. When should an order be placed and how much should be inventory on hand d. When should an order be placed and how much should be salvaged 1. The basic EOQ model assumes the following a. Shortages are not permitted b. There is no order lead time c. Both d. None 1. For the all-units discount case, the following candidates for optimal order quantity are considered: a. All EOQ and all break points b. The largest realizable EOQ and all break points c. The largest realizable EOQ and all breakpoints less than the largest realizable EOQ d. The largest realizable EOQ and all breakpoints more than the largest realizable EOQ 1. The lead time is the length of time between a. placing and receiving order b. demand forecast and sales c. receiving raw material and producing finished goods d. receiving raw material and selling finished goods 1.5 If quantity ordered is more than EPQ a. the annual setup cost is more than the annual holding cost b. the annual setup cost is the same as the annual holding cost c. the annual setup cost is less than the annual holding cost d. quantity ordered is never more than EPQ 1.6 Rotation cycle policy a. is an assumption b. is an optimal policy c. requires every product to be produced once every month d. requires every product to be produced whenever demand for that product is high 1.7 A backorder cost is charged if a. the order is placed after inventory is counted b. the excess demand is backlogged and fulfilled in a future period c. a sale is lost when a customer order cannot be fulfilled and the customer purchases goods from elsewhere d. b and c

3 1.8 For which of the following products a single-period inventory model is the most suitable? a. Furniture b. Automobiles c. Books d. Fruits and Vegetables 1.9 Increase of which of the following causes the order size to increase? a. Underage cost b. Overage cost c. Holding cost d. Cost of item 1.10 In case of the EPQ model with a finite production rate a. the maximum inventory is more than the quantity ordered b. the maximum inventory is the same as the quantity ordered c. the maximum inventory is less than the quantity ordered d. the EPQ model does not assume a finite production rate Question : (1 points) A large national producer of canned foods plans to purchase a combine that will be customized for its needs. One of the parts used in the combine is a replaceable blade for harvesting corn. Spare blades can be purchased at the time the order is placed for $10 each, but will cost $1,00 each if purchased at a later time because a special production run will be required. It is estimated that the number of replacement blades required by the combine over its useful lifetime can be closely approximated by a normal distribution with mean 0 and standard deviation 5. The combine maker agrees to buy back unused blades for $0 each. How many spare blades should the company purchase with the combine? a. ( points) Compute the underage cost C The cost incurred when order < demand $90-0 $900 u b. ( points) Compute the overage cost C The cost incurred when order > demand $10-0 $100 o c. (5 points) How many spare blades should the company purchase with the combine? cu 900 p 0.90 cu + co From Table A-, 1. 8 F z z for ( ) 0 p. So, Q µ + zσ ( 5) d. ( points) How would you change your answer to part c if the company purchases combines? How many spare blades should the company purchase with combines? µ ' µ 0 80, σ ' σ 5 ( ) ( ) 10

4 So, Q µ ' + zσ ' ( 10) 9. 8

5 Question : (16 points) An automotive warehouse stocks a variety of parts that are sold at neighborhood stores. One particular part, a popular brand of oil filter, is purchased by the warehouse for $ each. It is estimated that the cost of order processing and receipt is $80 per order. The company uses an inventory carrying charge based on a 5 percent annual interest rate. The monthly demand for the filter follows a normal distribution with mean 00 and standard deviation 50. Order lead time is assumed to be three months. Assume that if a filter is demanded when the warehouse is out of stock, then the demand is back-ordered, and the cost assessed for each back-ordered demand is $ Determine the average annual cost of holding, setup, and stock-out associated with this item assuming Q 1000, R 95. c $, K $80, I 0.5, h Ic 0.5 ( ) λ 00 1,600, σ µ λτ Q 1000, R 95 ( ) , σ σ y ( ) , τ y 0.50, p $10 τ a. ( points) Compute the average annual holding cost. months /1 year 0.5 year hq Average annual holding cost + h( R µ ) ( ) ( ) b. ( points) Compute the average annual setup cost. Average annual setup cost Q Kλ ( 600) $88 c. ( points) Compute the average annual stock-out cost. R µ z 0.9 σ L ( Z ) n σ. L ( z ) ( 0.706).791units/cycl e Averageannual stock - out cost npλ Q ( )( 600) $85.5 d. ( points) Compute the probability(no stock-out) Probability(no stock-out) Φ( ) F( z) z from Table A-. e. ( points) Compute the fill rate (up to four decimal places) Fill rate 1 n / Q 1.791/

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7 Question : (1 points) The Wod Chemical Company produces a chemical compound that is used as a lawn fertilizer. The compound can be produced at a rate of 10,000 pounds per day. Annual demand for the compound is 0.60 million pounds per year. The fixed cost of setting up for a production run of chemical is $1,500, and the variable cost of production is $.00 per pound. The company uses an interest rate of 15 percent to account for the cost of capital, and the costs of storage and handling of the chemical amount to 10 percent of the value. Assume that there are 50 working days in a year. P 10,000pounds/day. 5millionpounds/year? 0. 6millionpounds/year K $1,500 c $.00, I 0.5, h Ic λ / P 1 h' h 0.60 / ( ) ( 1 λ / P) 1( 0.76) 0.76/pound/year $1.00/pound/yea r a. ( points) What is the optimal size of the production run for this particular compound? Q * Kλ h' ( )( 600,000) 1, ,666.pounds b. (5 points) What proportion of each cycle consists of uptime and what proportion consists of downtime? Q 8,666. Cycle time, T year days λ 600,000 Q 8,666. Uptime, T year days P,500,000 Downtime, T T T year days Proportionof uptime 0. % Proportionof downtime % c. ( points) What is the average annual cost of holding and setup attributed to this item? ( 8,666.) h' Q 0.76 Average annual holding cost Kλ 1, ,000 Average annual setup cost Q 8,666. ( ) $18,9. $18,9. 7

8 Question 5: (1 points) A large producer of household products purchases a glyceride used in one of its deodorant soaps from outside of the company. It uses the glyceride at a fairly steady rate of 50 pounds per month, and the company uses a 5 percent annual interest rate to compute holding costs. The chemical can be purchased from two suppliers, A and B. A offers the following all-units discount schedule: Order Size Price per Pound 0 Q 500 $ Q 1,000 $1.5 1,000 Q $1.5 Supplier B offers the following incremental discount schedule: $1.0 per pound for all orders less than or equal to 800 pounds and $1.0 per pound for all orders above 800 pounds. Assume that the cost of order processing for each case is $00. Which supplier should be used? λ 50 / month 600/ year, I 0.5, K $00 Offers from both suppliers can be merged as follows: i Order Size Best price $/pound 1 0 Q Q Q Q 1. 5 Start with the cheapest price, c $1. 5 EOQ EOQ Kλ h ( 00 )( 600 ) 0.15 Kλ h ( 00 )( 600 ) 0.5 Holding cost $/unit/year c Ic 0.5( 1.0) 0. 5 Company giving the best price h B 1 1 c Ic 0.5( 1.5) h A c Ic 0.5 ( 1.0 ) 0. 5 h B c Ic 0.5( 1.5) h A not feasible. So, Q 1, 000, Supplier A feasible. So, Q 859, Supplier B. Stop searching for Q. i ( ) 00( 600) hq Kλ TC + + λc Q 1000 ( ) $1,06. 5 ( 859 ) 00( 600) hq Kλ 0.5 TC + + λc Q 859 ( 1.0) $1, Thus, the best is to order 1000 units from Supplier A for total annual cost $1,06.5 8