Operations Management I Fall 2001 Faculty of Business Administration University of Windsor

Transcription

1 Name (print, please) ID Operations Management I 7- Fall 00 Faculty of Business Administration University of Windsor Midterm Exam II Solution Wednesday, November, 5:0 6:50 pm Instructor: Mohammed Fazle Baki Aids Permitted: Calculator, straightedge, and a one-sided formula sheet. Time available: hour 0 min Instructions: This exam has pages including this cover page and pages of tables. Please be sure to put your name and student ID number on each page. Show your work. Grading: Question Marks: /5 /0 /0 4 /0 5 /0 6 /0 Total: /75

2 Question : ( point 5 questions 5 points). The following are the two major inventory control decisions: a. how to count and when to count b. how much to order and when to order c. how to estimate holding/ordering/stock-out costs and when to compute EOQ d. how to estimate holding/ordering/stock-out costs and when to compute EPQ. The loss of profit resulting from ordering less than the demand is a part of a. holding cost b. ordering cost c. setup cost d. stock-out cost e. none of the above. The EOQ model assumes that the on-hand inventory level increases a. instantaneously from zero to Q at time t 0 b. at the rate P at time t 0 c. at the rate P at time t 0 d. at the rate P at time t 0.4 The EPQ model assumes that the on-hand inventory level increases a. instantaneously from zero to Q at time t 0 b. at the rate P at time t 0 c. at the rate P at time t 0 d. at the rate P at time t 0.5 The annual holding cost is the same as the annual ordering cost a. for any order quantity b. for Q EOQ, but not for Q EPQ c. for Q EPQ, but not for Q EOQ d. for Q EOQ and for Q EPQ.6 The total annual holding and setup costs are to changes in order quantity for Q EOQ a. sensitive b. insensitive c. none of the above.7 The total annual holding and setup costs are to changes in order quantity for Q EPQ a. sensitive b. insensitive c. none of the above

3 .8 The rotation cycle policy a. is applicable when the budget is limited b. is applicable when space is limited c. is assumed when several products are produced in a single facility.9 The rotation cycle policy a. assumes that in each production cycle there is only one setup for each product, and the products are produced in the same sequence in each production cycle Kii b. dictates that Qi for the i -th product when the space is limited h + θw i i c. dictates that Q i meoqi for the i -th product when the budget is limited.0 In a single-period inventory model it is assumed that the ending inventory a. is salvaged b. is salvaged and transferred to the next period c. of one period is the beginning inventory of the next period. In a multi-period inventory model it is assumed that the ending inventory a. is salvaged b. is salvaged and transferred to the next period c. of one period is the beginning inventory of the next period. If the shortages are back-ordered, then the annual number of units purchased does not depend on ( Q, R) a. True b. False. What is reorder level? a. The time between arrival of successive orders b. The time between placing order and arrival of the order c. The number of units ordered d. The number of units on hand when the order is placed.4 The standardized loss function is denoted by F z a. ( ) b. φ( z) c. L(z).5 The standardized loss function is used to compute a. the probability of not stocking out during the lead time b. the proportion of demands that are met from the stock

4 Question : (0 points) Suppose that Item A has a unit cost of $0.00, an ordering cost of $50, and a monthly demand of 5 units. It is estimated that cost of capital is approximately 5 percent per year. Storage cost amounts to percent and breakage to percent of the value of the each item. a. ( points) Compute holding cost per unit per year. I h Ic $ per unit per year ( ) b. ( points) Compute annual demand. ( 5 )( ) 00 units per year c. ( points) Compute EOQ of Item A. EOQ K h ( 50)( 00) 00units d. ( points) Suppose that both Items A and B should be purchased and there is only $800 available for buying Items A and B. The unit cost of Item B is $5 and the EOQ of Item B is 00 units. What is the optimal order quantity of Item A? Fund required by the EOQ order quantity of Item A 00(0) $000 Fund required by the EOQ order quantity of Item B 00(5) $000 Total fund required by the EOQ order quantities of Items A and B $,000 Fund available $,800 fund available,800 Hence, m fund required,000 Therefore, the optimal order quantity of Item A m EOQ A 0.90(00) 90 units 4

5 Question : (0 points) Suppose that Item A has a production rate of 400 items per year. The cost and demand information of Item A are the same as those stated in Question. That is, Item A has a unit cost of $0.00, an ordering cost of $50, and a monthly demand of 5 units. It is estimated that cost of capital is approximately 5 percent per year. Storage cost amounts to percent and breakage to percent of the value of the each item. a. ( points) Compute EPQ of Item A. EOQ K h' K h P ( 50)( 00) units b. ( points) What is the cycle time of Item A? T Q EPQ years 00 Item C has a production rate of 400 items per year, a unit cost of $0.00, an ordering cost of $75, and a monthly demand of 40 units. c. (4 points) What is the cycle time if both Items A and C are produced in a single facility? T K j h' j j [ K + K ] [ ] h' + h' h P + h P [ 50 75] [ 50 75] Ic P 400,400 [ ] ( 0.0)( 0) years ,04,59 d. ( point) What is the optimal order quantity of Item A? Q T ( 0.44)( 00) 94. units 5

6 Question 4: (0 points) Irwin sells a particular model of fan, with most of the sales being made in the summer months. Irwin makes a one-time purchase of the fans prior to each summer season at a cost of $0 each and sells each fan for $50. Any fans unsold at the end of summer season are marked down to $0 and sold in a special fall sale. a. ( points) What is the underage cost per unit? cu Selling price purchase price 50-0 $0/unit b. ( points) What is the overage cost per unit? co Purchase price salvage value 0-0 $0/unit c. ( points) If the demand is uniformly distributed between 00 and 800 units, find the optimal order quantity. cu 0 For the optimal order quantity Q, Probability(demand Q), p c + c Hence, Q a + p( b a) ( ) 600 units u o d. ( points) If the demand is normally distributed with a mean of 500 and a standard deviation of 00, find the optimal order quantity. cu 0 For the optimal order quantity Q, Probability(demand Q), p c + c Find the standard normal z -value for which cumulative area on the left, F ( z ) u o. Since Table A- gives area between z 0 and positive z -values, find z -value for which Table A- area is Hence, z 0. 4 Q µ + zσ units 6

7 Question 5: (0 points) Comptek Computers wants to reduce a large stock of personal computers it is discontinuing. It has offered the University Bookstore a quantity discount pricing schedule if the store will purchase the personal computers in volume, as follows: Quantity Price -9 $ The annual inventory holding cost is 0%, the ordering cost is $50, and annual demand for this particular model is estimated to be 0 units. Compute the optimal order size. First, consider the cheapest price level of c $900 per unit. h Ic $ 80/unit/year K ( 50)( 0) EOQ h units ( point for EOQ computation) Since the price level of c $900 is not available for an order quantity Q EOQ 4.4 units, EOQ is infeasible and a candidate for optimal order quantity is Q 50, because 50 is the minimum order quantity for the price level of c $900 Now, consider the next price level, c $90 per unit. h Ic $ 84 K ( 50)( 0) EOQ h /unit/year Since the price level of c $90 is available for an order quantity Q EOQ.988 units, EOQ is feasible and a candidate for optimal order quantity is Q It s not necessary to consider the other price level. Now, compute total cost for each candidate for optimal order quantity: j Candidate Q j Q 50 Holding cost h j Q j ,500 Ordering cost K Q j Cost of item c j Total cost Holding cost + Ordering cost + Cost of item , 000 $, Q , , 400 $,97.7, Conclusion: The total cost is minimum, $,860 for Q 50. Therefore, an optimal order quantity is Q 50. 7

8 Question 6: (0 points) The home appliance department of a large department store is using a lot size-reorder point system to control the replenishment of a particular model of FM table radio. The store sells an average of 600 radios each year. The annual demand follows a normal distribution with a standard deviation of 50. The store pays $5 for each radio, which it sells for $70. The holding cost is 0 percent per year. Fixed costs of replenishment amount to $50. If a customer demands the radio when it is out of stock, the customer will generally go elsewhere. Loss-of-goodwill costs are estimated to be about $5 per radio. Replenishment lead time is three months. Currently, the store is using Q 0 and R 90. Compute a. ( points) the mean and standard deviation of the lead time demand τ 0.5 years, µ τ units, σ σ τ 50 5 units b. the annual holding cost per unit h Ic 0. 5 $7.5 per unit per year c. the stock-out cost per unit p loss of profit + good will (70-5) +5 $60 per unit d. the safety stock R µ units e. ( points) the expected number of units stock-out per cycle z R µ.6 σ 5 L ( z) 0. 0 n σl z ( ) 5 ( 0.0) units per cycle (Continued ) 8

9 f. ( points) the annual holding cost hq + h R µ ( ) + 7.5( 90 50) $, ( point for each part) g. ( points) the annual ordering cost K Q $ h. ( points) the annual stock-out cost np Q $ i. the total annual holding, ordering and stock-out cost, $,90. j. ( points) the probability of not stocking out during the lead time z R µ.6 σ 5 Table A-4: The probability of not stocking out during the lead time F( z.6) Table A-: The probability of not stocking out during the lead time the area on the left of z. 6 P( z.6) P( z 0) + P( 0 z.6) ( 0 z.6) P k. ( points) the fill rate, up to four decimal places n 0.58 β % Q 0 9