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1、QBA 361Monte Carlo SimulationIf a manager wants to predict a discrete number (i.e., expected revenues, customer arrivals per hour), a Monte Carlo Simulation technique can be used.Example: A textbook publishing company is considering the release of three books next year. Because of a cash flow proble
2、m, the company is interested in predicting the expected revenue and its range from sales of these books. Using the information below and the Monte Carlo Simulation method, simulate 10 realizations of the first years sales experiences.Expected Sales in Year 1BookExpected number of book sales (year 1)
3、Selling Price (per book)A200$25B1,000$10C3,000$5Probability of Deviations from Expected SalesPercent Deviation in SalesProbability80%0.1900.21000.41100.21200.1Step 1: Prepare a cumulative distribution for sales deviations.Percent Deviation in SalesProbabilityCumulative Probability80%0.10.1900.20.310
4、00.40.71100.20.91200.11.0Step 2: Identify Random Number AssignmentsRandom Number Assignment TablePercent Deviation in SalesRandom Number Assignment8001 109011 3010031 7011071 9012091 100Step 3: Identify Random NumbersThis can be done by going to the Random Number table or by using a program such as
5、excel to generate random numbers.Step 4: Run the SimulationRealizationRandomNumberBook AExpectedRevenue$5,0001RandomNumberBook BExpectedRevenue$10,0002RandomNumberBook CExpectedRevenue$15,0003Total Sales Revenue1525,000468,00055015,000628,00072885,5005310,0003013,50029,0003104,0004710,0009918,00032,
6、0004375,0006610,0009118,00033,0005355,0003210,000112,00027,0006845,5005710,000712,00027,5007375,0006310,0002813,50028,500824,0007411,0003515,00030,0009244,50038,0002913,50026,00010605,0007411,0008516,50032,5001 We expect to sell 200 books $25 each for a total of $5,000 expected revenue 2 We expect t
7、o sell 1,000 books $10 each for a total of $10,000 expected revenue 3 We expect to sell 3,000 books $5 each for a total of $15,000 expected revenue 4 Random number 52 falls in the range of expected sales being 100% of projection (100% of $5,000 = $5,000)5 Random number 6 falls in the range of expect
8、ed sales being 80% of projection (.80 * $10,000 = $8,000)6 Random number 50 falls in the range of expected sales being 100% of projection (1.0 * $15,000 = $15,000)7 Total revenue = the addition of the expected revenues for Book A, Book B, and Book C ($5,000 + $8,000 + $15,000 = $28,000)Results of the SimulationRange of expected sales revenues = $26,000 - $33,000 with the average being $29,350
