### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Class Note for EMSE 388 at GW (5)

### View Full Document

## 18

## 0

## Popular in Course

## Popular in Department

This 49 page Class Notes was uploaded by an elite notetaker on Saturday February 7, 2015. The Class Notes belongs to a course at George Washington University taught by a professor in Fall. Since its upload, it has received 18 views.

## Popular in Subject

## Reviews for Class Note for EMSE 388 at GW (5)

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 02/07/15

EMSE 388 Quantitative Methods in Cost Engineering Sensitivity Analysis with Data Tables Time Value of Money A Special kind of TradeOff 100 10 annual interest now 110 one year later 110 10 annual interest now 121 one year later 100 10 annual interest now 121 two years later General Formulation PVX Present Value of dollar amount X R interest rate per period eg R 10 010 FVnX Future Value of X after n periods FVX F X1RquotPX PVXn mgtltgt Vltgtcgt gt Ry Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Note difference between 10 Annual Interest Rate and 10 Annual Interest Rate compounded monthly 1 100 10 Annual Interest 110 dollars after one year 2 100 10 Annual Interest compounded monthly over 12 periods 10 12 1 gtXlt10023811047 12100 Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 2 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Stream of Cash Flow Interest Rate 1000 At the End of Year Future Value Factor Present Value 0 5000 1 00 5000 1 1000 091 909 2 2000 083 1653 3 3000 075 2254 4 4000 068 2732 5 5000 062 3105 6 6000 056 3387 7 7000 051 3592 8 8000 047 3732 9 9000 042 3817 1000 10000 039 3855 NPV 24036 Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 3 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Constant Interest Rate Formulation Xk costrevenue at the end of period k R interest rate per period X NPVltX0X1Xn Z k k0 1 R Varying Interest Rate Formulation Xk costrevenue at the end of period k Rk interest rate during period k X NPVX0X1Xn k k H H1 R1 j1 Lecture Notes by Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 1 Page 4 EMSE 388 Quantitative Methods in Cost Engineering 0 Note cost gt Xk negative revenue gt Xk positive Comparison of Two Streams of Cash Flows Cash Flow for Two Projects 15000 10000 5000 000 a 5000 4 6 8 1 10000 I 15000 Pr0j t1 I Project2 Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 5 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Cash Flow Characteristics Project 1 Small StartUp Cost and Increasing Profits Cash Flow Characteristics Project 2 Large StartUp Costs and Decreasing Profits WHICH ONE WOULD YOU PREFER ANSWER DEPENDS ON THE INTEREST RATE Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 6 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Interest 1000 Rate Time Project 1 Project 2 0 5000 10000 1 1000 9000 2 2000 8000 3 3000 7000 4 4000 6000 5 5000 5000 6 6000 4000 7 7000 3000 8 8000 2000 9 9000 1000 10 10000 500 NPV 24036 22603 Is there an Interest Rate at which Project 2 would be preferred Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 7 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering R NPV1 NPV 2 NPV1 NPV 2 PREFERRED 24036 22603 1433 100 46315 33851 12464 NPV1 200 42938 32298 10639 NPV1 300 39839 30835 9004 NPV1 400 36992 29454 7538 NPV1 500 34374 28151 6223 NPV1 600 31962 26918 5045 NPV1 700 29739 25751 3988 NPV1 800 27687 24645 3041 NPV1 900 25790 23597 2193 NPV1 1000 24036 22603 1433 NPV1 1100 22411 21657 753 NPV1 1200 20904 20759 145 NPV1 1300 19506 19904 398 NPV2 1400 18207 19089 883 NPV 2 1500 16998 18313 1315 NPV2 1600 15873 17572 1699 NPV2 1700 14825 16865 2041 NPV2 1800 13847 16190 2343 NPV2 1900 12933 15544 2611 NPV2 2000 12080 14926 2846 NPV 2 Lecture Notes by Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 1 Page 8 EMSE 388 Quantitative Methods in Cost Engineering Difference between NPV1 and NPV2 as a function of Interest Rate Project1 15000 preferred 10000 39 39 gt PrOJeth 5000 preferred i i i i i i i i i i i i i i i i i i Jo o o o o o o o 0 5000 8 8 8 S 8 8 8 8 8 8 F m L0 0 CD 2 a l 2 Interest Rate NPV1 NPV 2 It appears that NPV 1 and NPV 2 break even between 12 and 13 Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 9 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering The Break Even Point for the interest rate can be calculated exactly using the GOALSEEKfunction in Excel GOALSEEK allows to search for root of the equation FQFQ where Fx is a continuous function GOALSEEK Method is similar to Bisection Method or NewtonRaphson Method Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 10 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering BISECTION METHOD 0 Starting at interval a1b1 established such that Fa1Fb1ltO EXAMPLE BISECTION METHOD V 0 Stop when lt5 or bk ak lt a F akbk 2 Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 11 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering NEWTONRAPHSON METHOD 0 Requires BestGuess and being able to calculate first order derivative EXAMPLE NEWTON RAPHSON METHOD Falj x a1 Fal Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 12 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering 0 Stop when lt 5 F ak bk 2 QUESTION DOES NEWTONRAPHSON ALWAYS WORK ANSWER NO EXAMPLE NEWTON RAPHSON METHOD 1Fltalgtltx algtFltalgt dx Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 13 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering o NewtonRaphson may not converge at all or may converge to another solution of the equation FxO GOALSEEK FUNCTION of EXCEL is similar to the NewtonRaphson method If a solution is not found does not necessarily mean that none exists Try different starting values Be careful when using this method Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 14 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Interest 1226 Rate Time Project 1 Project 2 NPV1 NPV 2 0 5000 10000 000 1 1000 9000 2 2000 8000 3 3000 7000 4 4000 6000 5 5000 5000 6 6000 4000 7 7000 3000 8 8000 2000 9 9000 1000 10 10000 500 NPV 20535 20535 Lecture Notes by Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 1 Page 15 EMSE 388 Quantitative Methods in Cost Engineering HOME WORK 1 1 Consider the cash flows of Project 1 and Project 2 Assume that at the beginning of the project the interest rate equals 10 and that over the duration of the project 10 years the interest rate increases each year by 05 Which Project is preferred based on Net Present Value 2 Determine the rate of increase in interest at which you would be indifferent between Project 1 and Project 2 based on Net Present Value Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 16 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Two Way Data Tables Description Case Study A product costs 300 per unit to make Demand for the product is determined by two factors 0 The price of the product ie the lower the price the higher the demand 0 The advertising budget ie the more you advertise the higher the demand It is estimated eg using market research that Demand D in thousands of units is D7002A 7PAP where A advertising budget in OOO s and P Price per Unit Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 17 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Profit can be calculated as a function ofA and P as well 1 ProfitTotal Revenue Total Cost 2 Total Revenue 1000DP 3 Total Cost Production Cost Advertising Cost 4 Production Cost 1000D3 5 Advertising Cost 1000A Advertising Budget A 12000 Price per Unit P 1000 Cost per Unit C 300 Demand in 100039s 3563 Revenue 35627501 Production Cost 10688250 Advertising Cost 12000000 Total Cost 22688250 Profit 12939251 Lecture Notes by Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 1 Page 18 EMSE 388 Quantitative Methods in Cost Engineering Using Data Tables in Excel we can produce a graph of the DEMAND as a function of A and P Demand Advertising Budget 3666 2000 4000 6000 8000 10000 12000 14000 16000 18000 100 6802 7001 7153 7281 7393 7494 7587 7673 7755 200 6287 6563 6774 6951 7107 7248 7377 7497 7610 300 5729 6064 6320 6535 6725 6896 7053 7199 7337 400 5149 5533 5827 6075 6293 6490 6670 6838 6996 500 4554 4983 5310 5586 5829 6048 6250 6437 6613 600 3950 4418 4776 5077 5342 5582 5802 6007 6199 700 3338 3842 4228 4553 4839 5097 5334 5555 5763 800 2719 3257 3669 4016 4321 4597 4850 5086 5308 900 2096 2666 3102 3469 3793 4085 4353 4603 4838 1000 1469 2068 2528 2915 3255 3563 3846 4109 4356 P ce Lecture Notes by Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 1 Page 19 EMSE 388 Quantitative Methods in Cost Engineering Demand O U V l r a 8 O H I I I o O 8 o o o Advertism I L0 l CD 9 Pnce Note that 0 Demand decreases when Price Increases 0 Demand increases when you spend more money on advertising Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 20 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Using Data Tables we can produce a graph of the Profit as a function of A and P Pfofit 2000 4000 6000 8000 10000 12000 14000 16000 18000 100 156030039 180017091 203057880 225612092 247856636 269881872 291741317 313469755 335091302 200 82867439 105628262 127737425 149510885 171070453 192478418 213771699 234974311 256102909 300 20000000 40000000 60000000 80000000 100000000 120000000 140000000 160000000 180000000 400 31487155 15333101 1725093 19249682 37071682 55104613 73297182 91616012 110037941 500 71 085767 59652252 46206963 31723548 16577995 962765 15007976 31259923 47741514 600 98492004 92527771 83269918 72312029 60269646 47457902 34063757 20208901 5977790 700 113500172 113668764 109107500 102104372 93543324 8387695 73373802 62208672 50502888 800 115959971 122862671 123459379 120799976 116062945 109851758 102524499 94314273 85382876 900 105755748 119945938 126125242 128167538 127569907 125099030 121209865 116198594 110270801 1000 82795134 10478793 116945097 124022316 127857661 129185509 127600369 124889551 1100 47002244 77281339 95787509 108212543 116756525 12254631 126250660 128304968 129011473 1200 1686648 37336034 62542103 80610766 94124005 104404351 112236717 118132145 122445391 1300 63326010 15125011 17114536 41108049 59838305 74 33 01 86999568 96927841 105027897 Max Profit 115959971 122862671 126125242 128167538 127857661 7 129185509 128304968 129011473 Note that o For a fixed advertising budget there is a price at which profit is optimal o For a fixed price there is an advertising budget at which profit is optimal less clear from the figure Lecture Notes by Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 1 Page 21 EMSE 388 Quantitative Methods in Cost Engineering Is there a combination of Advertising Budget and Price at which profit is maximized 7150000 7100000 750000 0 50000 r100000 150000 200000 l250000 l300000 350000 P rofit 100 cDo L0 990 o 99 3 Price 2 e 18000 Advertising Budget 6000 10000 14000 Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 22 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Using Solver to Maximize Profit General Formulation of Optimization Problems Max or Min Fx1 xn Subject to G1x1 X 2 O G2X1 Xn Z O Gmx1 xn20 Lecture Notes by Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 1 Page 23 EMSE 388 Quantitative Methods in Cost Engineering Function Fx1 X is called the objective function with variables x1 xn Functions Gjx1 xn j1 m are called the constrained functions or constraints The set Sx1xnG1x1xn20Gmx1xn20 is called the feasible set informally the set of allowable solutions IMPORTANT The feasible set is bounded l Optimization problem has a solution Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 24 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering ie there is a feasible solution that globally maximizes the objective function Objective Function Local Maxima 5 Global Maximum 0 b XZO X 3 l l l I I l conStra39nt FunCt39on Constraint Function l l l Feasible Set is Bounded Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 25 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Linear Optimization Problems Both the objective function and the constrained functions are of the form 611 x1 612 x 2 l an x n NonLinear Optimization Problems Objective function or constrained functions are nonlinear An optimization method solving a NonLinear Optimization problem may get trapped in a local maximum QUESTION Under what conditions on the objective function and the constraint functions is a typical maximization method guaranteed to find a global maximum Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 26 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering ANSWER When the objective function is CONCAVE and constraint functions are CONVEX A function is concave on ab when Vxy eab f1x1 1y2lfx1 1fyaV1 071 f1x11y Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 27 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering A function is convex on xy when Vx y 6 ab f1x11y Sifx11fyV1 01 fx11fy x i x f1x11y lt 39y Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 28 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering QUESTION Under what conditions on the objective function and the constraint functions is a typical minimization method guaranteed to find a global minimum ANSWER When the objective function is CONVEX and constraint functions are CONVEX An optimization problem is convex if 1 The constraint functions Gjx1 X are convex functions 2 If the optimization problem is a minimization problem the objective function Fx1 X is convex Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 29 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering 3 If the optimization problem is a maximization problem the objective function Fx1 X is concave Practical Implications o If you can show that the optimization problem is convex and your optimization algorithm finds an optimal solution your solution is a global optimum o If you cannot show that the optimization problem is convex and your optimization algorithm finds an optimal solution your solution is a local optimum and you can never guarantee global optimality Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 30 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Graph 3DConvex Maximization Problem P Constraint 1 Feasible Set Constraint 2 Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 31 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Basic approach to solving nonlinear maximization problem 1 Start at a feasible solution choose a feasible search direction of ascent and follow that direction until you go downhill 2 Choose a new search direction of ascent and follow that until you go downhill 3 Stop when you cannot find a feasible search direction of ascent Eg Steepest Ascent Method Conjugate Gradient Method Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 32 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Graph 3D Linear Maximization Problem I I i Global J Optimum Constraint 4 Constraint 2 C n5traint 3 FeaSIble Set Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 33 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Note that 0 Global Optimum of a Linear Optimization Problem is attained at a corner point of the feasible set 0 Corner points of a feasible set in a Linear Optimization Problem are called Extreme Points or Vertices 0 Each Linear Optimization problem has a finite number of extreme points Basic approach to solving linear optimization problem Enumerate extreme points evaluate the objective function at extreme points and stop when you cannot improve Eg Simplex Method Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 34 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering QUESTION WHY CAN YOU NOT USE A LINEAR OPTIMIZATION METHOD TO SOLVE A NONLINEAR OPTIMIZATION PROBLEM ANSWER LINEAROPTIMIZATION METHODS ARE TYPICALLY LIMITED TO ENUMERATING EXTREME POINTS AND A GLOBAL OPTIMUM OF A NON LINEAR OPTIMIZATION PROBLEM DOES NOT HAVE TO BE ATTAINED IN AN EXTREME POINT Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 35 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering QUESTION CAN YOU USE A NONLINEAR OPTIMIZATION METHOD TO SOLVE A LINEAR OPTIMIZATION PROBLEM ANSWER YES BUT THIS MAY OR MAY NOT BE COMPUTATIONALLY EFFICIENT EXAMPLE INTERIOR POINT METHOD OF KARMAKAR HAS BETTER THEORETICAL COMPUTATIONAL COMLEXITY THAN SIMPLEX METHOD Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 36 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Going back to the optimization problem of our case study Maximize Profit 1 OOOP 3000D 1000A Subject to P 313 Where D7002A 7P AP IS THIS OPTIMIZATION PROBLEM LINEAR IS THIS OPTIMIZATION PROBLEM CONVEX Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 37 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Using SOLVER in EXCEL and the GRG Optimization method1 we find the following optimal solution Advertising Budget A 13132 Price per Unit P 1009 Cost per Unit C 300 Demand in 100039s 3681 Revenue 37126246 Production Cost 11043777 Advertising Cost 13132200 Total Cost 24175977 Profit 12950269 1 GRG Optimization method is the Generalized Reduced Gradient optimization method a nonlinear optimization approach Details of this approach are beyond the scope of this course Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 38 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering HOMEWORK 2 PROVE OR PROVIDE COUNTER EXAMPLE IS THE SUM OF TWO CONCAVE FUNCTIONS CONCAVE IS THE PRODUCT OF TWO CONCAVE FUNCTIONS CONCAVE Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 39 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Twoway Data Tables and Decision Making Uncertainty Description Case Study Eli Daisy must decide on monthly storage capacity for a new drug The drug will sell for a period of 10 years at a price of 7 per unit The production cost per drug unit is 4 One additional unit of storage capacity will cost 75 to build per drug unit Storage capacity cost 1 annually per drug unit for maintenance Production can only occur at the beginning of the month Setup Cost for production are exorbitant You always produce the full storage capacity as FDA has a monthly expiration date on the drug Clearly the most ideal profitable scenario would be to produce the same amount as the monthly demand for the drug The monthly demand for the drug will be constant over this 10 year period but is uncertain Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 40 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Probability Monthly Demand 01 02 03 02 01 Note that 0391 100000 200000 300000 400000 500000 600000 0 You would prefer not to produce more on a monthly basis than your monthly demand as demand is constant 0 You do not want excess storage capacity as even unused storage space cost 1 annually in maintenance cost Lecture Notes by Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 1 Page 41 EMSE 388 Quantitative Methods in Cost Engineering Profit Calculation given fixed Storage Capacity and a known Monthly Demand for 10 years Profit Total Revenue Total Cost Total Revenue 10Units Sold per YearPrice Unit Sold Per Year 12 MinStorage Capacity Monthly Demand Total Cost Building Cost 10 Annual Maintenance Cost 10 Annual Production Cost Building Cost Storage Capacity15 Annual Maintenance Cost Storage Capacity1 Annual Production Cost 12Storage Capacity4 Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 42 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Capacity Planning 10 Year Period Variable Value Unit Production Cost 4 Sales price 7 Building cost per Unit Storage Capacity 75 Annual maintenance cost per unit of Storage Capacity 1 Storage Capacity Level 300000 Monthly demand 100000 Planning Horizon 10 Revenue over Planning Horizon Unit Monthly sales 100000 Total Revenue 84000000 Total Costs over Planning Horizon Building Cost Fixed 22500000 Maintenance Cost Variable 3000000 Production Costs Variable 144000000 Total costs 169500000 Profit 85500000 Lecture Notes by Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 1 Page 43 EMSE 388 Quantitative Methods in Cost Engineering Possible Capacity Levels are 100000 600000 What amount of storage capacity should Eli build for this 10 year period Solve Decision Problem using Expected Monetary Value EMV Expected Value of discrete random variable Y EYY Zyz39 PrY yi Zyi pi i1 i1 Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 44 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Max Profit Win 020 EMV 24 Trade Ticket EMV 45 1 0 Win 045 Ext 10 Keep Ticket 0 0 Interpretation y PrYy yPrYy 2400 02 480 100 08 080 400 EMV y PrYy yPrYy 1000 045 450 000 055 000 450 EMV Playing the lottery a lot of times will result in an average payoff equal to the EMV Lecture Notes by Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 1 Page 45 EMSE 388 Quantitative Methods in Cost Engineering Returning to our Case Study probabilities 01 02 03 02 01 01 pro t Monthtly Demand 33 3550000000 100000 200000 300000 400000 500000 600000 Mean pro t 100000 2750000000 2750000000 2750000000 2750000000 2750000000 2750000000 27500000 200000 2900000000 355500000000 355500000000 5500000000 65500000000 65500000000 46600000 Annuai 300000 8550000000 150000000 8250000000 8250000000 8250000000 8250000000 48900000 Capacity 400000 14200000000 5800000000 2600000000 3511000000000 3511000000000 3511000000000 5 26000000 500000 19850000000 11450000000 3050000000 5350000000 13750000000 13750000000 13700000 600000 25500000000 17100000000 8700000000 300000000 8100000000 16500000000 61800000 Monthly Monthly Probability Demand Probability Demand EMV 01 100 000 EMV 01 100 000 27500K 300000 51800K 300000 FIRST ROW 400000 600000 400000 600000 LAST ROW Lecture Notes by Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 1 Page 46 EMSE 388 Quantitative Methods in Cost Engineering 10 Year Capacity 100000 EMV 27500000 200000 EMV 46600000 300000 EMV 48900000 400000 EMV 26000000 500000 EMV 13700000 600000 EMV 61800000 CONCLUSION SET STORAGE CAPACITY AT 300000 Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 47 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering VARIANCE AND STANDARD DEVIATION OF Y Variance VarY 0 EYEY2 p yi ElYlY 2 Standard Deviation V 0y O Y Informal Interpretation 0 Standard deviation is the best guess distance from the mean for an arbritrary outcome Lecture Notes by Dr J Rene van Dorp Chapter 1 Page 48 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering SquaredIdevi39ation 100000 200000 300000 400000 500000 600000 Variance Std dev 100000 00000E00 00000E00 00000E00 00000E00 00000E00 00000 E00 00000E00 000 200000 57154E15 70560E13 70560E13 70560E13 70560E13 70560E13 63504E14 2520000000 300000 1 8063E16 25402E15 11290E15 1 1290E15 1 1290E15 11290E15 31046E15 5571929648 400000 28224E16 70560E15 00000EOO 70560E15 70560E15 70560E15 70560E15 8400000000 500000 34151E16 10161E16 28224E14 45158E15 22861E16 22861E16 11007E16 10491596637 600000 37326E16 11925E16 63504E14 34574E15 20392E16 51438E16 14183E16 11909055378 CONCLUSION A Storage Capacity of 300000 yields the highest expected profit of 48900000 over 10 years with a standard deviation of 55719296 IS THIS A GOOD INVESTMENT OPPORTUNITY ANSWER DEPENDS ON DECISION MAKER S RISK AVERNESS Pr EMV lt 0Storage Capacity1000000 Pr EMV lt 0Storage Capacity20000010 PrEMV lt 0Storage Capacity30000030 Lecture Notes by Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 1 Page 49

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "When you're taking detailed notes and trying to help everyone else out in the class, it really helps you learn and understand the material...plus I made $280 on my first study guide!"

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.