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# Operations Management TOM 301

CSU Pomona

GPA 3.52

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This 20 page Class Notes was uploaded by Hester Marquardt on Saturday October 3, 2015. The Class Notes belongs to TOM 301 at California State Polytechnic University taught by Wenge Zhu in Fall. Since its upload, it has received 33 views. For similar materials see /class/218246/tom-301-california-state-polytechnic-university in Management Sciences And Information Technology at California State Polytechnic University.

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Date Created: 10/03/15

The weekly output of a production process is shown below together with data for labor and material inputs The standard inventory value of the output is 125 per unit Overhead is charged weekly at the rate of 1500 plus 5 times direct labor cost Assume a 40hour week and an hourly wage of 16 Material cost is 10 per running foot What is the average multifactor productivity for this process We k 397 Output Workers 397 Material 151 1 412 2 354 5 2550 3 392 7 5 7 2720 4 408 5 2790 Answer 412125 51500 1 1444 64016 2840 10 564016 1500 35660 365125 45500 2 1431 54016 2550 10 554016 1500 31800 392125 49000 k 3 1463 54016 2720 10 554016 1500 33500 408125 51000 i 451 4 7 640 16 2790 10 56 40 16 1500 35160 Avg 1444 1431 1463 14514 57894 1447 Or 125412364392408 150040516406556164406556102840 2550 2720 2790 1 From http nanceyahoocom nd the quotes of a stock of your own choice tip use the symbol lookup beside the GET QUOTES button to nd stock symbol for the company for example LUV is symbol for Southwest Airline Once you enter the stock symbol click the historical prices from the left menu More on xxx under quotes example httn39 nance vahnn qhpsLUV Use 1 quot 39 smoothing method to forecast the Adj Close price rightmost one in the quotes table which means the stock price when the market is closed for the next date Please use Adj Close price from 6 Six previous business dates to get your forecast Start your forecast with na39139ve method for the Fifth previous date For example if you are working on this problem on Oct 01 you will be using data from 2151 24m 25m 26 27th and 283911 of September as 22quot 1 and 23ml are holiday You will start with a forecast for 24 h using na39139ve method to start your exponential smoothing forecast Please choose two different Alfa by yourself within 0 1 range Once you nished please also let me know what the real stock price is on the date you are trying to predict you have to wait at least until 4pm the next day to know the real price and which Alfa is better Answer skipped 2 A manager has been using a certain technique to forecast demand for gallons of ice cream for the past six periods Actual and predicted amounts are shown below Would a naive forecast have produced better results 0 22 22 18 21 22 F3 20 3022 720 206 F4 206 3018 7 206 1982 F5 1982 302171982 2017 F6 2017 3022 7 2017 2072 2075 t Y tY t2 1 220 220 1 2 245 490 4 3 280 840 9 4 275 1100 16 5 300 1500 25 6 310 1860 36 7 350 2450 49 8 360 2880 64 9 400 3600 81 10 380 3800 100 11 420 4620 121 12 450 5400 144 13 460 5980 169 14 475 6650 196 15 500 7500 225 16 510 8160 256 17 525 8925 289 18 21M 171 7001 75713 2109 ST 2 Y 7001 Z t 171 2 1f 2109 7 nxz an 7 z ax K 002er 02 b 7 1875713717170017165663 719 7 182109 7171Z 7 8721 7 Z 111 75713 b 7001 171 a 7 719 7 38894471995208444 18 18 Y 208 444 19 F 208444 1920 588444 F 208444 1921 607444 The forecasted demand for week 20 and 21 is 588444 and 607444 respectively 800 7 541 19 It would take approximately 14 more weeks Since we have just completed week 18 the loading volume is expected to reach 800 by week 32 18 14 1363 weeks The weekly output of a production process is shown below together with data for labor and material inputs The standard inventory value of the output is 125 per unit Overhead is charged weekly at the rate of 1500 plus 5 times direct labor cost Assume a 40hour week and an hourly wage of 16 Material cost is 10 per running foot What is the average multifactor productivity for this process We k 397 Output Workers 397 Material 151 1 412 2 354 5 2550 3 392 7 5 7 2720 4 408 5 2790 Answer 412125 51500 1 1444 64016 2840 10 564016 1500 35660 365125 45500 2 1431 54016 2550 10 554016 1500 31800 392125 49000 k 3 1463 54016 2720 10 554016 1500 33500 408125 51000 i 451 4 7 640 16 2790 10 56 40 16 1500 35160 Avg 1444 1431 1463 14514 57894 1447 Or 125412364392408 150040516406556164406556102840 2550 2720 2790 1 From http nanceyahoocom nd the quotes of a stock of your own choice tip use the symbol lookup beside the GET QUOTES button to nd stock symbol for the company for example LUV is symbol for Southwest Airline Once you enter the stock symbol click the historical prices from the left menu More on xxx under quotes example httn39 nance vahnn qhpsLUV Use 1 quot 39 smoothing method to forecast the Adj Close price rightmost one in the quotes table which means the stock price when the market is closed for the next date Please use Adj Close price from 6 Six previous business dates to get your forecast Start your forecast with na39139ve method for the Fifth previous date For example if you are working on this problem on Oct 01 you will be using data from 2151 24m 25m 26 27th and 283911 of September as 22quot 1 and 23ml are holiday You will start with a forecast for 24 h using na39139ve method to start your exponential smoothing forecast Please choose two different Alfa by yourself within 0 1 range Once you nished please also let me know what the real stock price is on the date you are trying to predict you have to wait at least until 4pm the next day to know the real price and which Alfa is better Answer skipped 2 A manager has been using a certain technique to forecast demand for gallons of ice cream for the past six periods Actual and predicted amounts are shown below Would a naive forecast have produced better results 0 22 22 18 21 22 F3 20 3022 720 206 F4 206 3018 7 206 1982 F5 1982 302171982 2017 F6 2017 3022 7 2017 2072 2075 t Y tY t2 1 220 220 1 2 245 490 4 3 280 840 9 4 275 1100 16 5 300 1500 25 6 310 1860 36 7 350 2450 49 8 360 2880 64 9 400 3600 81 10 380 3800 100 11 420 4620 121 12 450 5400 144 13 460 5980 169 14 475 6650 196 15 500 7500 225 16 510 8160 256 17 525 8925 289 18 21M 171 7001 75713 2109 ST 2 Y 7001 Z t 171 2 1f 2109 7 nxz an 7 z ax K 002er 02 b 7 1875713717170017165663 719 7 182109 7171Z 7 8721 7 Z 111 75713 b 7001 171 a 7 719 7 38894471995208444 18 18 Y 208 444 19 F 208444 1920 588444 F 208444 1921 607444 The forecasted demand for week 20 and 21 is 588444 and 607444 respectively 800 7 541 19 It would take approximately 14 more weeks Since we have just completed week 18 the loading volume is expected to reach 800 by week 32 18 14 1363 weeks Inventory Management 1 A car rental agency uses 96 boxes of staples a year The boxes cost 4 each It costs 10 to order staples and carrying costs are 080 per box on an annual basis Determine A the order quantity that will minimize the sum of ordering and holding boxes of staples B the annual cost of ordering and carrying the boxes of staples Answer D 96 boxesyear S 10 H 80 per boxyear A Qo V2DSH 2961080 49 boxes per order B TC H 33 801019601959 3919 2 Q0 2 49 2 A service garage uses 120 boxes of cleaning cloths a year The boxes cost 6 each LA Ordering cost is 3 and holding cost is 10 percent of purchase cost per unit on an annual basis Determine A The economic order quantity B The total cost of carrying the cloths excluding purchase price C The average inventory Answer D 120 boxes per year S 3 H 106 60 per boxyear A Qo 2DSH 2120360 35 B TC ampH 28 60g3 1050 1029 2079 2 Q0 2 35 C Average inventory 2 175 boxes Estimated demand for gold lled lockets at Sam39s Bargain Jewelry and Housewares is 2420 lockets a year Manager Veronica Winters has indicated that ordering cost is 45 and that the following price schedule applies 1 to 599 lockets 90 each 600 to 1199 lockets 80 each and 1200 or more 75 each What order size will minimize total cost in each of these cases A Carrying cost is 18 per locket on an annual basis 4 B Carrying cost is 20 percent of price on an annual basis Answer A D 2420 lockets per year S 45 H 18 per locket Q0 1 M21100 H 18 Since this quantity is in the range of feasibility for 80 per unit compare the total cost of 1100 80 each with the total cost of 1200 75 each TC1100 18 2 1100 TC1200 g 18 2 1200 45 242080 2134 45 242075 2014 Hence buy 1200 per order 13 H 20P Range Price i 1 599 90 18 600 1999 80 16 1200 75 15 Determine Qo for the lowest price s curve Q0 1205 Since this quantity is feasible at the lowest price it is optimum Suppose that you are the manager of a production department that uses 400 boxes of rivets per year The supplier quotes you a price of 850 per box for an order size of 199 boxes or less a price of 800 per box for orders of 200 to 999 boxes and a price of 750 per box for an order of 1000 or more boxes You assign a holding cost of 20 percent of the price to this inventory What order quantity would you use if the objective is to minimize total annual costs of holding purchasing and ordering Assume ordering cost is 80order Answer D 400 boxes per year S80 H 20P Range i H 320 1 199 850 170 200 999 800 160 200 1000 750 150 The lowest curve with its minimum in the feasible range is 800 where Q 200 Hence compare the total cost of 200 800 each and the total cost of 1000 750 each T0200 160 80 800400 3520 2 200 TC1000 150 750400 3782 Hence buy 200 per order 800 each The operator of a concession at a downtown location estimates that he will sell 400 bags of circus peanuts during a month Carrying costs are 17 percent of unit price and ordering cost is 22 The price schedule for bags of peanuts is 1 to 199 100 each 200 to 499 94 each and 500 or more 87 each What order size would be most economical Answer D 400 bags per year S 22 H 17P Range 2 H 32 1199 100 17 200 499 94 16 332 500 87 15 The lowest curve with a feasible EOQ is the 94 curve Hence compare total cost of 332 bags 94 each with the total cost of 500 87 each T0332 16 2294400 42907 2 332 T0500 120152287400 40310 Hence buy 500 per order 87 each 7 00 0 Suppose that usage of cooking oil at Harry39s Fish Fry is normally distributed with an average of 15 gallonsday and a standard deviation of two gallons day Hairy has just red the manager and taken over operating the restaurant himself Harry has asked you to help him decide how to reorder cooking oil in order to achieve a service level which is seven times the risk of stockout 78 Lead time is eight days A If cooking oil can be ordered as needed what reorder point should be used B If a xed interval of 30 days is speci ed how much safety stock should Harry carry Answer d 15 gallons per day 6d 2 gallons per day LT 8 days SL 78 875 Z 115 A ROP dLT leLTcd 158115 l82 12650 gallons B 01 30 days Safety stock zodVOI LT 115230 8 1418 gallons A bakery39s use of corn sweetener is normally distributed with a mean of 80 gallons per day and a standard deviation of four gallons per day Lead time for delivery of the corn sweetener is normal with a mean of siX days and a standard deviation of two days If the manager wants a service level of 99 percent what reorder point should be used Answer d 80 gallons per day LT 6 days 6d 4 gallons per day 6LT 2 days SL 99 percent Z 233 ROP 5 2 Had2 d ZGLTZ 806 2334 642 80222 85350 gallons A manager is reordering lubricant when the amount onhand reaches 422 pounds Average daily usage is 45 pounds which is normally distributed and has standard deviation of three pounds per day Lead time is nine days What is the risk of a stockout Answer d 45 lb per day 6d 3 lb per day LT 9 days ROP dLT Z4 LTO39 d Thus 422 459 z J93 Solvingfor z z 189 which implies a risk of 1 9706 0294 or about 3 percent The injection molding department of a company uses 40 pounds of a powder a day Inventory is reordered when the amount on hand is 240 pounds Lead time averages ve days It is normally distributed and has a standard deviation of two days What is the probability of a stockout during lead time Answer d 40 pounds day ROP 240 pounds ROP 7 dLT chT d 240 7 405 z240 Solving for z we obtain 2 50 From Appendix B Table B SL 6915 so risk is 1000 7 6915 3085 Answer 03085 The manager of a bakery orders three caketogo39 wedding cakes every Saturday to accommodate last minute purchases Demand for the cakes can be described by a Poisson distribution that has a mean of 2 The cakes cost 10 each to prepare and they sell for 26 each Any cakes that haven t been sold by the end of the day are sold for half price the next day Usually half of those are sold and the rest are tossed What stocking level would be appropriate Answer Cs 26 7 10 16 Ce 10 7 513 350 LCS 16 82 CsCe 16350 For Poisson with mean 20 this falls between 677 and 857 Therefore stock 3 cakes 14 A manager has just received a revised price schedule from a vendor What order quantity should the manager use in order to minimize total costs Annual Demand is 120 units ordering cost is 8 and annual carrying cost is 1 per unit Quantity Unit price 1 39 14 40 59 13 60 89 12 90 11 Answer D 120 units S 8 H 1unit Q m 438 or 44 Because this is in the 4059 range compare TC of 44 13 60 12 and 90 11 TC Q2H DQS PD TC44 160382 TC60 1486 TC90 137567 90 yields the lowest cost A firm stocks a seasonal item that it buys for 22unit and sells for 29 unit During the season daily demand can be described using a Poisson distribution with a mean of 24 Because of the nature of the item units remaining at the close of business each day must be removed at a cost of 2 each What is the optimum stocking level and what is the effective service level Answer Cs29227 Ce22224 LCS 7 226 CsCe 247 Referring to Appendix B Table C for a mean of 24 this falls between 0 and 1 Hence stock 1 unit At that level the effective service level is 308 17 A restaurant prepares Peking Duck daily at a cost of 18 per duck Each duck generates revenue of 47 if sold Demand for Peking Duck can be described by a Poisson distribution with a mean of 42 ducks per day Unsold ducks at the end of each day are converted to duck soup at an additional cost of 5 over and above the resulting value as soup How many ducks should be prepared each day What will be the effective service level Answer Cs 47 18 29 Cel8523 Mean 42 per day Poisson L 2 9 5577 29 23 Between three and four in Appendix B Table C hence stock four ducks with an effective service level of 59 19 A manager intends to order a new machine and must now decide on the number of spare parts to order along with the machine The parts cost 400 each and have no salvage value The manager has compiled a frequency distribution for the probable usage of spare parts as shown For what range of shortage costs would stocking one spare part constitute an optimal decision No of Spares Freguency 0 08 l 30 2 24 3 20 4 18 Answer Ce 400 Find range for Cs In order for a stocking level of one part to be optimal the service level must fall in the range 08 to 38 see frequency distribution Thus 008 36 53 038 CS C2 Setting the service level ratio equal to 08 yields Cs 34 78 Setting the service level ratio equal to 30 yields Cs 24516 Hence the range of shortage costs for a stocking level of one to be optimal is 3478 to 24516 Pm act Managemem HW 1 Apmj echs shuwed as fulluws a and But the mm path cme men h Fm Dunne duranun nuns men n and But the slack ume fur each 211th quota I anMFv Z Lhuse whth are un the mast path 3 The fullumngmfumanums fur m 7 DAf culty Medmm Answer Cnncal path ArDrFrH 372 In Brashmg ths prujeBL whth amvxtyxsthe 5mm bereduBed7 Dxf BLthy Medium swer ABusts SKEW D Busts S ll F Busts SIDED H Busts SIZIIEIEI ReduBe aBtzvrty D at mum 373 ms my Medium Answer 374 What is the tum Bust ufreduBmg ths pm eBtby m weeks7 Answer Tutal Bust 14 Dxf Bulty Medmm 375 Whats the ml Bust ufreduBmg the menu 18 weeks7 Answer Tutal Bust MELUUU Dxf Bulty Medmm 4 Gwen Lhanetwurk dngrzm abuvedetenn1ne each 1me fulluwmg A the emwues whmh are un me cnncal path B the expected pmject am Em c the pmba mhty that me prujed w111 be cumpleted m 29 weeks Dr less m V m m F r DAf culty Medmm Answer M Dmanun 5m Dev z 1 thahmu 1 i1 75 7 3 1 1 147 2 1 1457 5 m1 1 A Themucalpathu 1737577 B Expected pruject aurauems 25 weeks large values The prubab1l1ty ufmucal paih eemp1euen by week 2915 7111 The feuuvwngmfmmanums fees 1 575 571 Whats the estimated expected mean ume fur ammty E7 A 91 days B 99 days c Inn days 1 1111a s E 115 days Answer D Dif culty Medium 52 What is the estimated standard deviation in the time for activity E A 2 days B 3 days C 4 days D 16 days E 24 days Answer C Dif culty Medium 53 What is the estimated expected mean time for project completion A 100 days B 140 days C 199 days D 200 days E 440 days Answer D Dif culty Medium 54 What is the estimated slack time for actiVity A A 0 days B 20 days C 40 days D 60 days E 100 days Answer D Dif culty Hard 55 What is the probability that this project will be completed within 205 days A 06826 B 08413 C 09544 D 09772 E 09987 Answer B Dif culty Hard

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