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6 Pages
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Course: BEN-ISRAEL 386, Fall 2008School: Rutgers
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Word Count: 275
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1 11666663.xls A 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 B C D E F WidgetCo Project Scheduling (AON) Requires C -----1 -C -----26 -26 Code A B C D E F G Code A B C D E F G Activity Train Workers Purchase RM Make SA 1 Make SA 2 Inspect SA 2 Assemble Safety Report Start Time 0 0 18 9 16 26 32 Duration 6 9 8 7 10 12 6 End Time 6 9 26 16 26 38 38 End Time 38 A --1 1 ---A --6 6 ---6 B --1...
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1 11666663.xls
A 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
B
C
D
E
F
WidgetCo Project Scheduling (AON) Requires C -----1 -C -----26 -26
Code A B C D E F G Code A B C D E F G
Activity Train Workers Purchase RM Make SA 1 Make SA 2 Inspect SA 2 Assemble Safety Report Start Time 0 0 18 9 16 26 32
Duration 6 9 8 7 10 12 6 End Time 6 9 26 16 26 38 38 End Time 38
A --1 1 ---A --6 6 ---6
B --1 1 ---B --9 9 ---9
Project End
VALUES
11666663.xls
G 1 2 3 Requires 4 D 5 -6 -7 -8 -9 1 10 -11 -12 13 D 14 -15 -16 -17 -18 16 19 -20 -21 16 22 23
H
I
J
E -----1 1 E -----26 26 26
FG -- --- --- --- --- --- --- -F -------38 G -------38
VALUES
11666663.xls
A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
B
C
D
E
WidgetCo Project Scheduling Code (AON)
Requir A B C D E F G Code A B C D E F G Activity Duration Train Workers 6 Purchase RM 9 Make SA 1 8 Make SA 2 7 Inspect SA 2 10 Assemble 12 Safety Report 6 Start Time End Time 0 6 0 9 18 26 9 16 16 26 26 38 32 38 End Time Project End 38 A --1 1 ---A --6 6 ---6 B --1 1 ---B --9 9 ---9
FORMULAS
11666663.xls
A 24 25 26
B
C
D
E
Decision variables
All constrained cell Each <= C23 entry in
FORMULAS
11666663.xls
F 1 2 3 4 5 6 7 8 9 10 11 12 13 ...
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Rutgers - BEN-ISRAEL - 386
11666670.xlsA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22BCDEWidgetCo Project Scheduling (AON)-SIMPLE vRequiresCode A B C D E F G Code A B C D E F GActivity Train Workers Purchase RM Make SA 1 Make SA 2 Inspect SA 2 Asse
Rutgers - BEN-ISRAEL - 386
Rutgers - BEN-ISRAEL - 386
11527167.xls1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22A B C D WidgetCo Project with Crashing (AON)E F Deadline 25GHIJKCode A B C D E FActivity Train Workers Purchase RM Make SA 1 Make SA 2 Inspect SA 2 AssembleDura
Rutgers - BEN-ISRAEL - 386
11666606.xlsABCDEFG1 WidgetCo Project with Crashing Deadline 2 3 Cost/Day Max Days 4 Code Activity Duration to Crash Crash 5 A Train Workers 6 $10.00 5 6 B Purchase RM 9 $20.00 5 7 C Make SA 1 8 $3.00 5 8 D Make SA 2 7 $30.00 5 9 E In
Rutgers - BEN-ISRAEL - 386
11666540.xlsA 1 2 3 4 5 6 7 8 9 10 11BCDEFGStockco Capital Budgeting Problem1 1 $19,000 $7,000 $50,000 Investment 2 1 $21,000 $9,000 3 0 4 1 $10,000 Total cost $5,000 $21,000 <=Investment level Total Net Return Investment cost Tota
Rutgers - BEN-ISRAEL - 386
ValuesA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21BCDEPlane Loading Problem Item Weight 1 4,000 2 800 3 2,000 4 1,500 Capacity 30,000 Cost/Unit $0.05 Item 1 2 3 4 Take 3 10 1 5 Weight 29,500 Weight $1,475Alternative Ship Volu
Rutgers - BEN-ISRAEL - 386
11527132.xlsA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22BCDEFGHIMachinco Assignment of Jobs to Machines Problem Costs to perform jobs on various machines Job 1 2 3 4 Machine 1 14 5 8 7 2 2 12 6 5 3 7 8 3 9 4 2 4 6 10
Rutgers - BEN-ISRAEL - 386
11666672.xlsA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28BCDEFGHIJKLMAn assignment problem with 8 persons and 8 jobs Costs of assinging persons to jobs 1 2 1 6 2 11 6 3 12 2 1 4 10 7 12 1 3 1
Rutgers - BEN-ISRAEL - 386
milkemA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24BCDEFGProblem 5.4 - "Boris Milkem" Data on selling prices of assets (in $millions) Asset 1 Asset 2 Asset 3 Asset 4 Asset 5 Asset 6 Sold in year 1 15 16 22 10 17 19
Rutgers - BEN-ISRAEL - 386
11527124.xlsA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17BCDEFGHIJKLMNWestern Airlines Set Covering ProblemCities Potential hub Covered AT BO CH DE HO LA NO NY AT 1 0 1 0 1 0 1 1 BO 0 1 0 0 0 0 0 1 CH 1 0 1 0 0 0 1 1 DE 0
Rutgers - BEN-ISRAEL - 386
A B C D E 1 Crew Assignment Problem: SmallTime Airlines 2 3 Duty Plan Cost 101 102 103 4 5 6 7 8 9 10 11 12 13 14 15 16 Covered: 17 18 Total Cost 19FGHIJKLMNOP201Flights Covered 202 203 401 402403501502503Use?A B
Rutgers - BEN-ISRAEL - 386
11666654.xlsA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16BCDEProblem 5.5 Data on pitchers Righty? (1 if yes, 0 if not) Cost (in $millions) Victories added Pitchers to sign (1 if signed, 0 if not) RS 1 Budget constraint (in $millions) Spent $11
Rutgers - BEN-ISRAEL - 386
ValuesA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31BCDGandy Fixed Charge Clothing ProblemInput data Shirts 3 4 40 $12 $6 $200 Product Shorts 2 3 53.33 $8 $4 $150 Pants 6 4 25 $15 $8 $100Labor hours
Rutgers - BEN-ISRAEL - 386
11666537.xlsA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25BCDPower Plant Problem (5.17) Boiler Min Steam 1 500 2 300 3 400 Turbine Min Steam 1 300 2 500 3 600 Run Boiler? 1 2 3 Total: Run Turbine? 1 2 3 0 1 1 0 1 1 Max
Rutgers - BEN-ISRAEL - 386
11666659.xlsA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26BCDEFGHIJKLMNOHiring Students Min Shifts Initials CM FI GR HS JD JE SR TR Availability Mon Tue Wed Thu Fri Profit/Shift AM PM AM PM AM P
Rutgers - BEN-ISRAEL - 386
ValuesA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46BCDEFGHIJKHuntco Plant/Warehouse Location Problem Plant to warehouse unit production, ship
Rutgers - BEN-ISRAEL - 386
LOGICAL CONSTRAINTS AND BINARY VARIABLESADI BEN-ISRAELLet A, B, C, denote some actions, and let A , B , C , be the corresponding decisions, i.e., X = 1, if action X is taken; 0, otherwise.We express logical conditions on the actions by con
Rutgers - BEN-ISRAEL - 386
Buying widgetsThe XYZ Corp. has a budget of $500,000, which it intends to use for buying widgets. There are three vendors, each with unlimited supply, who offered the following terms. Vendor 1 stipulates that an order must be no less than 4,000 widg
Rutgers - BEN-ISRAEL - 386
Tossing a CoinA coin shows "1" and "0" with probabilities p, 1-pp 0.4 Value Probability 0 0.6 1 0.4Simulated value #Rolling a dieA die shows "1", , "6" with given probabilitiesValue Probability 1 0.166667 2 0.166667 3 0.166667 4 0.166667 5 0
Rutgers - BEN-ISRAEL - 386
A Guessing GameThrow two dice and guess a number from 2 to 12 Your opponent always chooses the number in cell C10 If your number is closer to to the sum of the dice you win 1 point. If your opponent is closer you w There are 11 scenarios. Find the
Rutgers - BEN-ISRAEL - 386
11666634.xlsTranslator Hiring Problem Chance of Overtime Availability Fixed Cost per Translator Regular Order Cost Overtime Order Cost Revenue per Filled Order Translators Hired Actual Demand Overtime Translators Available Regular Orders Filled Ove
Rutgers - BEN-ISRAEL - 386
11666639.xlsA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25BCDETranslator Hiring Problem Chance of Overtime Availability Fixed Cost per Translator Regular Order Cost Overtime Order Cost Revenue per Filled Order Transla
Rutgers - BEN-ISRAEL - 386
0.25 0.24 0.23 0.22 0.21 0.2 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20200.25 0.24 0.23 0.22 0.21 0.2 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.1
Rutgers - BEN-ISRAEL - 386
11666627.xlsA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19BCDEOverbooking ModelTicket Price Penalty Seats Expected Demand Probability of Coming Overbooking Demand Tickets Sold Passengers Arrived Passengers Seated Passengers Not Seated
Rutgers - BEN-ISRAEL - 386
An illustration of the Central Limit TheoremWe generate 100 independent RV's in D17:D116, simulate their sum in D118, and compare its distribution with the "corresponding" normal distribution. Each RV is uniformly distributed on [0,a] where the a's
Rutgers - BEN-ISRAEL - 386
11666600.xls1 2 3 4 5 6 7 8 9 10 11 12 13 14 15A Classic 3-Door "Paradox" Door with car Door we pick at first Door Has car Is the door we picked Is a door Monty can show Random value Shown by Monty Door we would switch to Get car if don't switch
Rutgers - BEN-ISRAEL - 386
PROJECT DURATIONA project has 8 activities, see diagram below. The activity durations are random, with triangular distribution and Min, Mode, Max as given. Simulate: (a) The project duration (b) For each path, the probability that it is critical.A
Rutgers - BEN-ISRAEL - 386
A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25BCDEPower SupplyCost per kWh Selling price per kWh Startup Cost ($1000's) Capacity (MW) Expected Municipal Demand (MW) Standard Deviation of Municipal Demand (MW) Minimum I
Rutgers - BEN-ISRAEL - 386
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17A Insurance Reserve Capital ProblemBCDE1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17A B Insurance Reserve Capital ProblemCDEYASAI Simulation Output Workbook Sheet Start Date Start Time Run Ti
Rutgers - BEN-ISRAEL - 386
11527204.xls1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18A B Inventory Simulation Mean demand Fixed order cost Unit cost Sales price Holding cost Salvage value Beginning inventory Reorder point Reorder quantityCDEFGHIJ400 $600 $1
Rutgers - BEN-ISRAEL - 386
11666558.xls1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82
Rutgers - BEN-ISRAEL - 386
11527142.xlsA B C D E F 1 Westland Wranglers 2 Average Horses Captured per Day 4 3 Average Sales Demand per Day 4.1 4 Sales Price Per Horse $150.00 5 "Salvage" Value of Horses in Corral at End $130.00 6 Cost per Day of Keeping Horse in Corral $8.00
Rutgers - BEN-ISRAEL - 386
11666561.xlsA B C D E F G H I J 1 Truck Service Facility Expansion 2 Average arrival rate 3.8 Daily Operation Cost $425 per occupied bay per day 3 4 Number of Bays #NAME? 5 6 7 8 5 Incremental Daily Cost #NAME? $175 $325 $475 6 7 First Second Third
Rutgers - BEN-ISRAEL - 386
The St Petersburg ParadoxTwo players A & B, and a coin The coin gives H with probability in Cell B12 The coin is tossed until first H appears If this happens in Trial n, B pays A the amount 2^(n-1) To make the game fair, A pays B the value of the ga
Rutgers - BEN-ISRAEL - 386
BUFFON'S NEEDLE PROBLEMA needle of length L = #NAME? is dropped on equally spaced parallel lines a distance D = 1 apart. The probability that the needle will cross a line is 2 L / Pi D This formula makes sense fo L< Pi D/2 for otherwise it gives val
Rutgers - BEN-ISRAEL - 386
The Birthday ProblemAssume that birthday are equally likely on any day of the year. Given a random sample of n people what is the probability of at least one common birthday? How large must n be, in order that the probability of a common birthday wi
Rutgers - BEN-ISRAEL - 386
Simulation of PiyThe area of the unit circle is Pi A point in a square of side 2 is generated at random. The coordinates of the point are in K11:L11 Is the point in the unit circle? YES =1, NO = 0, in M11 The mean of M11, sample = 10^5, is in OUTP
Rutgers - BEN-ISRAEL - 386
A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102B
Rutgers - BEN-ISRAEL - 386
11666632.xlsA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 120 121 122 123BCDEFGBelt Replacement Simulation Scheduled Replace Cost Min Emergency Replace Cost Max Emergency Replace Cost $450 $1,000 $2,000Day o
Rutgers - BEN-ISRAEL - 386
11666566.xlsA B C D E F G H 1 Discrete Event Queueing Simulation 2 3 Server Server 4 Arrival Rate 1 1 2 Average Number #NAME? Min Service #NAME? 0.4 0.3 Average Wait #NAME? 5 Max Service #NAME? 1.4 1.1 6 7 8 Time Limit 120 9 10 15 11 12 13 14 15 10
Rutgers - BEN-ISRAEL - 386
Rutgers University, Business School/Undergraduate New Brunswick Operations Management (33:623:386:03) Spring 2008; Instructor: Adi Ben-IsraelMidterm Exam February 20, 2008You have 80 minutes to complete this examination. The exam has 6 pages. Ple
Rutgers - BEN-ISRAEL - 386
OPERATIONS MANAGEMENT 33:623:386:03,10MIDTERM EXAM # 2 MARCH 31, 2008SOLUTION OF PROBLEM 1Variables T =project duration, For activity X (X = A, , G) tX = the earliest time activity X can be started, yX = the number of days to crash from X, X
Rutgers - BEN-ISRAEL - 386
Rutgers University, Business School/Undergraduate New Brunswick Operations Management (33:623:386:03) Spring 2008; Instructor: Adi Ben-IsraelHourly Exam 3 April 23, 2008You have 80 minutes to complete this examination. The exam has 12 pages (the
Rutgers - BEN-ISRAEL - 386
Question 2: Yasai SpreadsheetA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34BCDEFGHIJQuestion 1Mean No. of Visitors Probability that a visitor is a buyer Probability that a buyer w
Rutgers - BEN-ISRAEL - 386
A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 36 37 38 39 40 41BCDEFGHIJProblem 2: Financial PlanningInitial Funds Annual Return Min Max Withdrawal Scenarios Safe Assets Risky Assets $800,000 $450,000 Total
Rutgers - BEN-ISRAEL - 386
Q1Cost per lbFood 1 $7 Food 1 3 1 0 $12Food 2 $1 Food 2 Obtained 1 12 1 12 12 Required 12 6Vitamin A Vitamin C Purchased Total cost>= >=Q2 Profit per acre Wheat $200 Resource usage Wheat Labor 3 Fertilizer 2 Corn $300Corn 2 4Used 100
Rutgers - BEN-ISRAEL - 386
Rutgers - BEN-ISRAEL - 386
11666578.xls1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28A Dairy ProblemBCDEFLaborPasteurize Raw Milk 0Activities Separate Whole Milk 0.01 Activities Separate Whole Milk -1 0.8 0.2 0 $0.20 10000 6666.6
Rutgers - BEN-ISRAEL - 386
11666630.xls1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25A Molecular ProductsBCDEFGHLaborActivities Turn A into Turn C Into B and C B and D 3 1Limit 200B C D Direct Unit Cost Amount of ActivityActivitie
Rutgers - BEN-ISRAEL - 386
11666657.xls1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21A B C Multi-Period Production Problem Unit Production Cost $23.85 $24.25 $24.90 $25.15 $24.35 $23.75DEFGMonth 1 2 3 4 5 6Demand 1050 1200 1400 1175 850 1100Initial Inv
Rutgers - BEN-ISRAEL - 386
max 5A + 4B + 25x3 [6x1 + 3x2 + 5x3 ] ST A = 2x1 + x2 2x3 B = 3x1 + 2x2 3x3 8A + 7B + 6x3 7(A + B + x3 ) x 1 , x2 0 0 x3 20 0 A 30 0 B 20 For symmetry, we could also include C, dened to be the units of product C sold, but of course that wo
Rutgers - BEN-ISRAEL - 386
11666651.xls1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26A B Eli Daisy Problem Purchasing price/oz C1 $6 C2 $4 Selling price/oz D1 $6CDEFGD2 $5Blending plan (oz of each chemical used in each drug) D1 D2 Total
Rutgers - BEN-ISRAEL - 386
11666584.xls1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21A Bexter Labs ProblemBC D E Average Quality Requirement Activities Process Raw Material 1 1 2 0 $3.00 0 Unit Selling Price $5.00 $4.00 $25.00F 7GProduct A Product B Produc
Rutgers - BEN-ISRAEL - 386
11666647.xlsA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 SunCo OilBCDEFGHThe changing cells are the barrels of
Rutgers - BEN-ISRAEL - 386
into the cutlets in whatever proportion you want: let white meat be meat 1 and dark meat by meat 2. xi yjk = Number of type i = 1, 2 turkeys purchased = Pounds of meat j = 1, 2 put in cutlets of type k = 1, 2 max 4(y11 + y21 ) + 3(y12 + y22 ) [10x1
Rutgers - BEN-ISRAEL - 386
11666641.xls1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44A B C D E F Busville (Note: there are multiple optimal solutions, some with integer values, some not) Distances
Rutgers - BEN-ISRAEL - 386
11666668.xls1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25A Wild Turkey Company Turkeys Pounds White Meat Pounds Dark Meat CostBCDEFType 1 5 2 $10.00 Cutlet 1 70% 50 $4.00 Type 1 8.67 Pounds Obtained 53 27Type 2 3
Rutgers - BEN-ISRAEL - 386
11666629.xlsA B 1 Audit Scheduling 2 3 Activity 4 Code A Determine terms 5 B Appraise risk 6 C Identify transactions 7 D System description 8 E Verify description 9 F Evaluate controls 10 G Design audit 11 12CDEFGHIJDuration Start
Rutgers - BEN-ISRAEL - 386
11666568.xlsA B 1 Audit Scheduling 2 3 Activity 4 Code A Determine terms 5 B Appraise risk 6 C Identify transactions 7 D System description 8 E Verify description 9 F Evaluate controls 10 G Design audit 11 12 13 14 15CD End Time Cost/Day To Cra
Rutgers - BEN-ISRAEL - 386
basketweavers.XLS1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25A B Basketweavers UniversityCDEFGHRequirements (along side) that are met by taking available courses (along top) (1 if it fills reqt, 0 if not) Calcul
Rutgers - BEN-ISRAEL - 386
11666541.xls1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25A B Basketweavers UniversityCDEFGHRequirements (along side) that are met by taking available courses (along top) (1 if it fills reqt, 0 if not) Calculus OR