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## INTRO TO MANAGEMENT SCI

by: Mrs. Oleta Okuneva

93

0

2

# INTRO TO MANAGEMENT SCI COB 291

Mrs. Oleta Okuneva
JMU
GPA 3.74

Scott Stevens

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COURSE
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Scott Stevens
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This 2 page Class Notes was uploaded by Mrs. Oleta Okuneva on Saturday September 26, 2015. The Class Notes belongs to COB 291 at James Madison University taught by Scott Stevens in Fall. Since its upload, it has received 93 views. For similar materials see /class/214051/cob-291-james-madison-university in College of Business at James Madison University.

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Date Created: 09/26/15
Dr Stevens COB 291 Final Exam Practice Questions Additional Simulation Questions Questions 1 116 refer to the situation below Our queuing theory equations are useful for computing average time in system W but they aren t very useful in determining the actual distribution of time in system Here we use simulation to address this latter problem HVIPORTANT In this problem we will break with traditional queuing terminology the word line will be used to refer to the system in all of the discussion that follows Hence a customer who is 1 in line is being served We deal with a single channel system in which arrivals are Poisson 7t 04 customersminute service times are exponential u 05 customerminute service is FCFS and the maximum line length is three customers For these assumptions and rounding slightly we get P0 045 P1 036 P 015 and P3 004 In particular this means that when a new custom er arrives at this system he or she is 45 likely to find it empty 36 likely to find a single customer in line and so on If three customers are already in line when the new customer arrives he or she leaves without receiving service A new arrival that does join the line must obviously wait for his or her own service to be complete In addition he or she must wait for the service of all customers who precede him or her in line Since service times are exponential the amount of time that a new arrival will have to wait for any given customer s service to be completed is given by lu x In RN In this expression In is the natural logarithm function and RN is the value of a uniform ly distributed random variable on the interval 0l We ll use this information to determine the distribution of time in line for a new arrival ll Create the discrete process generator for the whether the new arrival joins the line as the 1 2nd or 3quoti customer or leaves without service Use the events in that order Call this process generator Process Generator A This process generator would result in the outcome 2 d in line for any random number between a 045 and 081 b 036 and 045 c 015 and 036 d 081 to 096 e 004 to 019 12 The random number 045 used in Process Generator A would mean that the new arrival a is lst in line b is 2nd in line c is 3quoti in line d leaves without service e is French 13 Call the continuous process generator for service times Process Generator B Recall that this generator is given by lu x In RN If the random number used in this process generator is 212 the resulting service time is closest to a 1 minute b 2 minutes c 3 minutes d 4 minutes e 10 minutes 14 In determining how long a single simulated customer spends in line we would have to use a Process Generator A one time Process Generator B one time b Process Generator A one time Process Generator B up to three times c Process Generator A up to three times Process Generator B one time d Process Generator A up to three times Process Generator B up to three times e Process Generator A one time Process Generator B exactly four times The simulation of a new arrival was conducted 100 times and the time the customer spent in line is summarized in the chart below For example in 20 of the runs the customer spent more than 1 minute but not more than two minutes in line Questions 5 and 6 use this chart 20 o Freq uency N 0 V LO LO l 00 07 2 2 2 2 2 2 2 2 2 O N 0 V LO LO l 00 9to10 10to11 11to12 12to13 H V 22232 i 0 22232 H gt1 We said that P3 04 meaning that the new arrival should leave without service 4 of the time The chart on the previous page shows this happening waiting time 0 only 3 of the time This apparent discrepancy means that the simulation does not properly use the process generators is probably due to rounding errors is surprising but doesn t necessarily mean that the simulation is flawed it unsurprising since the problem involves stochastic elements is an illusion since the chart shows 4 of the customers leave without waiting The queuing model says that W is 356 minutes yet the chart shows that the most common waiting time is between one and two minutes The difference between one to two minutes and 356 minutes is too large to attribute to statistical uncertainty This large apparent discrepancy is probably due to rounding errors makes sense since the chart does not say that the average waiting time is between 1 and two minutes is primarily due to too small a sample size Only 100 simulated arrivals is not important since 13 arrivals did experience waits between 3 and 4 minutes means that the simulation does not really model the situation described Simulation s main disadvantage as a management science technique is that tends to be expensive andor time consuming it can only be applied to a narrow range of well defined problems its results are often too complex to explain to nontechnical people it is not widely used by practicioners in comparison to other techniques like queuing etc none of the above ad are true 2232

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