Last Name First Name ID Operations Management I 7-1 Winter 00 Odette Scool of Business University of Windsor Midterm Exam II Solution Wednesday, Marc 7, 10:00 11:0 am Instructor: Moammed Fazle Baki Aids Permitted: Calculator, straigtedge, and a one-sided formula seet. Time available: 1 our 0 min Instructions: Tis exam as 17 pages including tis cover page and 8 pages of tables. Please be sure to put your name and student ID number on eac page. Sow your work. Grading: Question Marks: 1 /10 /10 /10 4 /10 5 /10 6 /15 Total: /65
Question 1: (10 points) 1.1 Te annual olding cost equals near EOQ a. te annual ordering cost b. te annual stock-out cost 1. Te total cost curve is flat near a. EOQ b. EPQ c. Bot d. None 1. In a rotation cycle policy te products are produced a. once in eac production cycle b. in te same sequence in eac production cycle c. bot d. none 1.4 In a single-period model, te items unsold at te end of te period is over to te next period. a. carried b. not carried 1.5 Wen te demand is uncertain, te reorder point, R includes a. te expected demand during te lead time b. safety stock c. bot d. none 1.6 Te standardized loss function is used to compute a. te probability of stocking out during te lead time b. te proportion of demands tat are met from te stock c. bot d. none 1.7 Storage cost is a part of a. olding cost b. ordering cost c. setup cost d. stock-out cost e. none of te above 1.8 In a multi-period inventory model it is assumed tat te ending inventory a. is salvaged b. is salvaged and transferred to te next period c. of one period is te beginning inventory of te next period
1.9 Te fact tat te EOQ cost curve is flat near te optimal order quantity implies tat a. if tere are some managerial reasons to order Q units suc tat Q EOQ, but Qis near EOQ, ten one may order Q units witout causing a large increase in inventory cost b. inventory cost is not sensitive to te cost of buying items 1.10 If te sortages are back-ordered, ten te annual number of units purcased equals te annual demand a. True b. False
Question : (10 points) Montgomery Associates produces switces for scientific equipment and as gatered information about te production of its 6-1 switces: Annual production rate,000 units Annual demand rate 1,800 units Cost per switc $1 Annual olding cost 5% Setup cost $10 a. (4 points) Find te optimal size of eac production run. EPQ Kλ ' Kλ λ 1 P ( )(,000) 10 1,800 1( 0.5) 1,000 600units b. ( points) Find te optimal cycle time. 600 Cycle time Q 0. years λ 1,800 c. ( points) Compute te uptime and downtime in eac cycle. Q 600 Uptime 0. 0 years P,000 Downtime Cycle time up time 0. 0.000 0.1 years Q λ 600 1,800 Or, downtime 1 1 0. 1 years λ P 1,800,000 d. ( points) Wat is te maximum dollar amount invested in te inventory? λ 1,800 Maximum inventory Q 1 600 1 40 units P,000 Cost of maximum inventory 40 1 $,880 4
Question : (10 points) Harold Gwynne is considering starting a sandwic-making business from is dormitory room to earn some extra income. However, e as only a limited budget of $1600 to make is initial purcase. Harold divides is needs into tree areas: bread, meats and ceeses, and condiments. He estimates tat e will be able to use all of te products e purcases before tey spoil, so perisability is not an issue. Te demand and cost parameters are given below: Breads Meats and Ceeses Condiments Weekly demand 0 packages 5 packages 10 pounds Cost per unit $1.5 $5 $ Fixed order cost $0 $0 $5 Te coice of tese fixed costs is based on te fact tat tese items are purcased at different locations in town. Tey include te cost of Harold s time in making te purcase. Assume tat olding costs are based on an annual interest rate of 0 percent. Find te optimal quantities tat Harold sould purcase of eac type of product so tat e does not exceed is budget. EOQ B EOQ M EOQ C Kλ Kλ Kλ ( 0)( 0 5) 1.5 0.0 ( 0)( 5 5) 5 0.0 ( 5)( 10 5) 0.0 456.07 units 186.19 units 169.97 units Fund required 1.5 456.07 + 5 186.19 + 169.97 $,14.96 Fund available $1,600 < $,14.96 Fund required Hence, order quantities are obtained by reducing te EOQ values proportionately 1,600 Compute m 0. 75,14.96 QB QB QB ( 456.07) 4. 4 0.75 ( ) 140. 0 0.75 186.19 ( ) 17. 99 0.75 169.97 units units units 5
Question 4: (10 points) Irwin sells a particular model of fan, wit most of te sales being made in te summer monts. Irwin makes a one-time purcase of te fans prior to eac summer season at a cost of $50 eac and sells eac fan for $100. Any fans unsold at te end of summer season are marked down to $0 and sold in a special fall sale. a. ( points) Wat is te underage cost per unit? cu Selling price purcase price 100-50 $50/unit b. ( points) Wat is te overage cost per unit? co Purcase price salvage value 50-0 $0/unit c. ( points) If te demand is uniformly distributed between 00 and 900 units, find te optimal order quantity. For te optimal order quantity Q, Probability(demand cu 50 Q), p 0. 65(1 point) c + c 50+ 0 u o * Hence, Q a + p( b a) 00 + 0.65( 900 00) 00 + 75 675 units ( points) d. ( points) If te demand is normally distributed wit a mean of 600 and a standard deviation of 10, find te optimal order quantity. cu 50 For te optimal order quantity Q, Probability(demand Q), p 0. 65 c + c 50+ 0 Find te standard normal z -value for wic cumulative area on te left, ( z ) 0. 65 u o F. Since Table A-1 gives area between z 0 and positive z -values, find z -value for wic Table A-1 area is 0.65-0.50 0.15. Hence, z 0. (1 point) Q * µ + zσ 600 + 0. 10 68.4units ( points) 6
Question 5: (10 points) Comptek Computers wants to reduce a large stock of personal computers it is discontinuing. It as offered te University Bookstore a quantity discount pricing scedule if te store will purcase te personal computers in volume, as follows: Quantity Price 1-9 $1800 10-49 1500 50+ 100 Te annual inventory olding cost is 40%, te ordering cost is $00, and annual demand for tis particular model is estimated to be 16 units. Compute te optimal order size. First, consider te ceapest price level of c $1,00 per unit. (1 point) Ic 0.40 1,00 $480 /unit/year Kλ ( 00)( 16) EOQ 0.40( 1,00) 1.4 units (1 point) Since te price level of c $1,00 is not available for an order quantity Q EOQ 1.4 units, EOQ is infeasible and a candidate for optimal order quantity is Q 50, because 50 is te minimum order quantity for te price level of c $1,00. (1 point) Now, consider te next price level, c $1,500 per unit. (1 point) Ic 0.40 1,500 $600/unit/year Kλ ( 00)( 16) EOQ 600 1 (1 point) Since te price level of c $90 is available for an order quantity Q EOQ 1 units, EOQ is feasible and a candidate for optimal order quantity is Q 1. (1 point) It s not necessary to consider te oter price level. Now, compute total cost for eac candidate for optimal order quantity: j (1 point) Candidate Q j Holding cost Q j j Ordering cost Kλ Q j Cost of item λc j Total cost Holding cost + Ordering cost + Cost of item Q 50 48 50 1, 00 00 16 1,00 16 59, 00 $7,064 864 50 (1 point) Q 1 600 1, 600 00 16 1,500 16 4, 000 $1,00,600 1 (1 point) Conclusion: Te total cost is minimum, $7,064 for Q 50. Terefore, an optimal order quantity is Q 50. (1 point) 7
Question 6: (15 points) Te ome appliance department of a large department store is using a lot size-reorder point system to control te replenisment of a particular model of FM table radio. Te store sells an average of 1,00 radios eac year. Te annual demand follows a normal distribution wit a standard deviation of 100. Te store pays $40 for eac radio, wic it sells for $80. Te olding cost is 0 percent per year. Fixed costs of replenisment amount to $98. If a customer demands te radio wen it is out of stock, te customer will generally go elsewere. Loss-of-goodwill costs are estimated to be about $15 per radio. Replenisment lead time is one mont. Currently, te store is using Q 150 and R 140. Compute a. ( points) te mean and standard deviation of te lead time demand 1 1 τ 0.08 years, µ λτ 100 100 units, (1 point) 1 1 1 σ σ τ 100 8.87 units (1 point) 1 b. (1 point) te annual olding cost per unit Ic 0. 40 $1 per unit per year c. (1 point) te stock-out cost per unit p loss of profit + good will (80-40) +15 $55 per unit d. (1 point) te safety stock R µ 140 100 40 units e. (1 point) te expected number of units stock-out per cycle 140 100 z R µ 1.855 σ 8.87 0.08+ 0.075 L ( z) 0. 079 (since ( z) 0. 08 n σl z ( ) 8.87( 0.079) 1. 09 f. ( points) te annual olding cost units per cycle L for 1. 8 8 z and ( z) 0. 075 L for z 1. 9 ) (Continued )
Q + R µ 1 150 ( ) + 1( 140 100) 900 + 480 $1, 80 (1 point for eac part) g. ( points) te annual ordering cost Kλ Q 98 1,00 $784 150. ( points) te annual stock-out cost npλ Q 1.09 55 1,00 $479.6 150 i. (1 point) te total annual olding, ordering and stock-out cost 1,80 + 784 + 479.6 $,64.6 j. (1 point) te probability of not stocking out during te lead time 140 100 z R µ 1.855 σ 8.86 Table A-4: Te probability of not stocking out during te lead time F( z 1.855) 0.916 + 0.9177 0.91695 (since ( z ) 0. 916 F for 1. 8 Table A-1: Te probability of not stocking out during te lead time te area on te left of z 1. 855 P( z 1.855) P( z 0) + P( 0 z 1.855) 0.50 + P( 0 z 1.855) 0.5+ 0.41695 0. 91695 z and ( z ) 0. 9177 F for z 1. 9 ) k. (1 point) te fill rate, up to four decimal places n 1.09 β 1 1 0.997 99.7% Q 150 9