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Rutgers - BEN-ISRAEL - 711
Published: October 6, 1866 Copyright The New York Times
Rutgers - BEN-ISRAEL - 711
Sally ClarkPage 102/10/2007Using Statistical Evidence in Courts: A Case Study Or What Went Wrong in the Case of Sally Clark?1 IntroductionThe debate about the usage of statistical evidence in criminal courts has a long history.1 Whilst the ca
Rutgers - BEN-ISRAEL - 711
Airline Yield Management with Overbooking, Cancellations, and No-ShowsJANAKIRAM SUBRAMANIANIntegral Development Corporation, 301 University Avenue, Suite 200, Palo Alto, California 94301SHALER STIDHAM JR.Department of Operations Research, CB 318
Rutgers - BEN-ISRAEL - 711
Dynamic Pricing in Airline Seat Management for Flights with Multiple Flight LegsPENG-SHENG YOUDepartment of Business Administration, Chang Jung University, 396, Section 1, Chang Jung Road, Town of Kway Jen, Tainan 711, TaiwanConsider a multiple b
Rutgers - BEN-ISRAEL - 386
Operations Management (33:623:386:03 & 10), Spring 2008Schedule (tentative)Class # 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 Date Wed Mon Wed Mon Wed Mon Wed Mon Wed Mon Wed Mon Wed Mon Wed Mon Wed Mon Wed Mon Wed
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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 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 69BCDEFGHLOOKUP, VLOOKUP and HLOOKUP
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Example of errors in computingThe numbers in Cells Ci are called Ci Let: C2 := 2*C1 - 1*C1 C3 := 3*C2 - 2*C1 C4 := 4*C3 - 3*C1, etc. All these should be equal to C1 This happens if C1 is an integer See what happens if: Example 1: C1 = 0.001 Example
Rutgers - BEN-ISRAEL - 386
CONTRACTORS3 contractors can do a job. The job has to be done in The relevant data is as follows: Contractor Can do the job in Charges 1 20 100 2 10 200 3 18 days 90 $/day 12 daysDetermine a plan to do the job in minimal cost. Contractors can be h
Rutgers - BEN-ISRAEL - 386
The Bags Problem: The problem data Time Required Hours/Unit Regular Deluxe Cutting 0.70 1.00 Sewing 0.50 0.83 Finishing 1.00 0.67 Inspection 0.10 0.25 Profit 10.00 9.00 Hours Available 630 600 708 135The Bags Problem: Data and variables Time Requir
Rutgers - BEN-ISRAEL - 386
SHELLEquipment Bag Problem - First Example LP Regular 0.7 0.5 1 0.1 $10.00 Regular 500 Deluxe vailable A 1 630 0.833 600 0.667 708 0.25 135 $9.00 Deluxe 300Cut/Dye Sew Finish Inspect/Pack ProfitVariable x1 Objective FunctionVariable x2Make
Rutgers - BEN-ISRAEL - 386
1100 1050 1000 950 900 850 800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50 0 -50 -100 -150 -200 Row 11100 1050 1000 950 900 850 800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50 0 -50 -100 -150 -200 Row 11100 1050 1000
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11666531.xlsA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16BCDEFGDiet Problem Corn 10 50 30 900 $0.60 0.00 Provided 46.54 243.65 100.00 4500.00 Soy 9 45 90 1200 $0.30 0.71 Oats 11 58 10 1000 $0.35 3.65 Cost $1.49 Fish Min Max 8 40 50 120 5 2
Rutgers - BEN-ISRAEL - 386
The Bike Wheels Problem: The dataSpokes Rims Wheels Machine time 0.04 0.6 Labor time 0.01 0.5 1.2 Cost 0.05 4 11 Selling price 0.1 10 50 Available 378 267Spokes Rims Wheels1 1-72 -1 1The Bike Wheels Problem: VariablesSpokes Rims Wheels Mach
Rutgers - BEN-ISRAEL - 386
11666619.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 Bicycle Wheel Production Problem - "Grid" Version Activities Make Rims 0.6 0.5 0 1 0 $4.00 150EFMachine Time Labor Spokes Rims Wheels Direct Unit Cost Amount of Act
Rutgers - BEN-ISRAEL - 386
The Perfume Problem: The DataProcess Raw Material 1 1 3 0 4 0 $3.00 Activities Refine Brute 0 3 -1 1 0 0 $4.00 Refine Chanelle 0 2 0 0 -1 1 $4.00Raw Material Lab Time Regular Brute Luxury Brute Regular Chanelle Luxury Chanelle Direct Unit CostLi
Rutgers - BEN-ISRAEL - 386
11666542.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 Perfume Problem - "Grid" VersionCDEFRaw Material Lab Time Regular Brute Luxury Brute Regular Chanelle Luxury Chanelle Direct Unit Cost Amount of Activity
Rutgers - BEN-ISRAEL - 386
PIGSKIN.XLSA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20BCDEFMultiperiod Production Problem Start inventory 50 1 Demand Prod. cost/unit Holding cost/unit 100 $12.50 $0.625 2 150 $12.55 $0.628 Month 3 4 300 350 $12.70 $12.80 $0.63
Rutgers - BEN-ISRAEL - 386
11666599.xlsA 1 2 3 4 5 6 7 8BCDEFGHIndustrial Gases Transportation Problem Unit shipping costs to Customer Total 1 2 3 4 5 Available Plant 1 $8 $6 $7 $10 $9 45 FromPlant 2 $9 $12 $5 $13 $7 60 Plant 3 $14 $9 $12 $16 $5 55 Total requ
Rutgers - BEN-ISRAEL - 386
11666564.xlsA 1 2 3 4 5 6 7 8 9 10 11 12BCDGroovy Juice Mixers, Inc. Minimum % Tropical Breeze Guava Jive Maximum % Tropical Breeze Guava Jive Grape Guava Papaya 0% 20% 20% 0% 40% 0% Grape Guava Papaya 100% 25% 25% 100% 50% 5% Grape Guava P
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 Profit summary 28 29 30 31 Total profitBCDEFChandler Blending Problem Monetary inputsQuality level per barrel of crudesRequired quality level per barrel of prod
Rutgers - BEN-ISRAEL - 386
11666649.xlsA 1 2 3 4 5 6 7 8BCDPickles - Separate Advertising Min demand 5000 4000 30% 60% Adv Rate 3 5 Prod Cost $0.60 $0.85 Budget $16,000Sweet Dill Min Sweet Max SweetDATA11666649.xlsE 1 2 3 4 5 6 7 8FSelling $1.45 $1.75Co
Rutgers - BEN-ISRAEL - 386
INVEST.XLSA 1 2 3 4 5 6 7 8 9BCDEFGInvestment Problem Investment Min % Max% A 0% 30% B 25% 100% C 0% 40% Initial Cash Interest Rate Now $(1.00) $(1.00) Year 1 $0.20 $0.10 $(1.00) Year 2 $1.40 $1.60 Year 3 $1.25$1,000 8.00%DATAIN
Rutgers - BEN-ISRAEL - 386
INVEST.XLSA 1 2 3 4 5 6 7 8 9 10BCDInvestment Problem: Data Interest Rate Investment A B C Funds 8% Now $1.00 $1.00 $0.00 $1,000.00 8% Year 1 -$0.20 -$0.10 $1.00 $0.00 8% Year 2 $0.00 -$1.40 $0.00 $0.00DATAINVEST.XLSE 1 2 3 4 5 6 7 8
Rutgers - BEN-ISRAEL - 386
conmine1 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 B Consolidated MiningCDEFGFrom Mine Blue Mesa Dry PassShipping Cost To Boise West TX Capacity $4.50 $3.00 800 $3.50 $6.00 1000 Boise West TX $17.00 $
Rutgers - BEN-ISRAEL - 386
11666586.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 41A B C National Vehicular Seating, Inc. Production Data Assembly Hours Sewing Hours Weight Cost, Plant 1 Cost, Plant 2 Reg
Rutgers - BEN-ISRAEL - 386
11666663.xlsA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23BCDEFWidgetCo Project Scheduling (AON) Requires C -1 -C -26 -26Code 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 Insp
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
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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
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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
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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
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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