Info3010, Week 12 notes
Info3010, Week 12 notes Info3010
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This 5 page Class Notes was uploaded by Rebecca Evans on Wednesday April 6, 2016. The Class Notes belongs to Info3010 at Tulane University taught by Srinivas Krishnamoorthy in Spring 2016. Since its upload, it has received 18 views. For similar materials see Business Modeling in Business at Tulane University.
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Date Created: 04/06/16
Week 12 notes th March 30 Notes Monte Carol Simulation Use when decisions are made with random events Decision Tree: only random events with discrete outcomes o Discrete outcome=countable or limited number of outcomes Monte Carlo Simulation: random events w/ discrete and continuous outcomes o Continuous outcome=every possible outcome in a range o Can use parametric and structural sensitivity easily =RAND(x) function o Generates random number between 0 and 0.99999… o Re-calculates by pressing F9 (on PC) o Every number is equally likely (uniform distribution) o If make a histogram of 1000 trials of RAND fxn, all bars should be equal height Uniform distribution outside 0-1 o Ex. Get random number between 10 and 25: 10+(25-10) x RAND() 10= lower limit (25-10)=range Why? at least 10 (lower limit) and rand can be anywhere between 0-1 so multiply by range to put outcome between 10-25 o Get random integer values between 60 and 75 RANDBETWEEN(60,75) =RANDBETWEEN gives integer values only Simulating 2 outcome discrete distributions o Ex. Simulate event that may happen with probability of 0.4 =IF(RAND()<0.4, 1, 0) Why? Rand will give number between 0-1 0-0.4 0.4-1 Hit flop 40% 60% Binary 1=hit and 0=flop Random Number from a Normal Distribution Normal Distribution 3 2 1 0 0 0.2 0.4 0.6 0.8 1 1.2 Ex. Mean=100, SD=20 NORM.INV(RAND, 100, 20)=will give number on x-axis normal distribution probability will create a norm distribution histogram use rand fxn to replace probability Baby Lee’s Doughnuts Baby Lee’s Doughnuts stocks exactly 33 super-duper doughnuts every day. Each super-duper doughnut sells for $2. Unsold doughnuts are eaten by Baby Lee at the end of the day. Daily demand for super-duper doughnuts is a random event and is given by the following probability distribution. Develop a simulation model to determine the mean and standard deviation of daily revenue obtained from the sale of the super-duper doughnuts. Decision tree 0.4 32 o 0.3 33 0.3 34 Make range from 0-1 with 3 possible outcomes3 sub-ranges Boundary of ranges correspond with probabilities of each value 32 33 34 0 0.4 0.7 0.4 0.7 1 40% 30% 30% In excel B C D E 2 Demand 32 33 34 3 Probability 0.4 0.3 0.3 Simulation Calculations Demand: =IF(B10<C3,C2,IF(B10<C3+D3,D2,E2)) Revenue: selling price*min(demand, in stock) Or revenue=C6*IF(C10<C5,C10,C5) = selling price*if(demand<in stock, demand, in stock) Simulation Trials Link upper right box to revenue (next to trial #) Select entire tabledatawhat if analysisdata tableleave row input blankcolumn input=any random cell outside of the table (to trick excel) Use to simulate number of days in business and revenue Output Mean revenue=average(all trial cells) =average(C18:C1017) Standard deviation =stdev(all trial cells) =stdev(C18:C1017) April 1 Notes Mt Morris Community Association The Mt. Morris Community Association makes annual door to door solicitations for funds. Residents of each solicited house are asked to donate either $15 or $25. An analysis from previous years’ solicitations indicates that a. An adult is home 80% of the time b. When someone is at home, there is only a 40% chance that he or she will make a donation. c. Of the people making donations, there is a 55% chance that they will contribute $15, and a 43% chance that they will contribute $25. Occasionally (2% chance), a person makes a donation in excess of $25. Such distributions follow a discrete uniform distribution between $30 and $50 (in increments of $1). The director of the association plans to visit 30 houses tomorrow. Set up a model to determine the probability that the director will receive more than $250 in donations from these 30 houses. Excel a) 80% chance someone is home at first house 80% chance that random number will fall into the at home or not at home range 0 .8 1 At home Not at home 1 0 Use binary code for 1=at home and not at home=0 =IF(RAND()<C2,1,0) =if(random number<.8, then 1, if not then 0) Recalculate random event=F9 b) 40% chance of someone at home making donations 0 .4 1 Donate Don’t donate 40% 60% =IF(RAND()<C3,1,0) gives probability Must multiply by previous cell (chance at home) because it’s is a 40% chance they donate IF at home o =IF(RAND()<C3,1,0)*C13 (C13==IF(RAND()<C2,1,0)) c) size of donation Random number =rand() 0 0.55 0.98 1 $15 $25 $30- 50 55% 443% 2% If(random number<0.55, donate $15, if not then If(random number<(0.55+0.43), then donate $25, if not then randbetween($30, 50)*if donate cell o Randbetween=integer between o Always better to link to data cells than put in numbers =IF(E13<C8,C4,IF(E13<(C8+C9),C5,RANDBETWEEN(30,50)))*D13 30 homescopy formulas all the way down o Lock formulas= F4 o Lock inputs from data box o Don’t lock things reference to other cells from table because they are references that need to change Use green box to copy and drag all the way down Simulate 1,00 days of business o Copy total cell into upper right hand o Data”what if” analysisleave row input blankcolumn input=random blank cellenter New Function*** =countif(range, criteria)/total number of instances o Count through range and count number of times a criteria is met o Condition goes in “” o =COUNTIF(C51:C1050,">250")/1000 o Give percent chance that of donations being over $250 Percentage changes every time but stays in a certain range Increase number of trialsnarrow range of answers
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