Management Chapter 6S Method Two Multiple Server System With Arrival Rate Customers Per Hour And

Method two is a multiple server system with an arrival rate of 8 customers per hour and a service rate of

12 customers per hour. This analysis requires calculating the probability of zero customers in the system.

16

To summarize:

Method 1

Method 2

Number of Customers

1.81 customers

0.75 customers

Time in System

0.2262 hours

0.0938 hours

Method 1

Diff: 3

Reference: 6S.1 Alternative Waiting Lines

Keywords: multiple channel, system time, number in system, single phase, multiple phase, probability of 0 units,

number waiting

AACSB: Analytical Thinking

LO: 6S.1: Use statistics-based formulas to estimate waiting line lengths and waiting times for three different types of

waiting line systems.

41) Barber College is the best deal in town! For only $5, you can get a shampoo and cut by any one of four

untrained stylists completed in 7.5 minutes on average. Perhaps this is why customers show up on

average two minutes apart (both arrival times and service times are exponentially distributed).Develop a

full description of the system performance. How much does performance improve if another barber is

added to the customer service staff?

42) Frenzied cruise vacationers besiege Tatiana, their excursion coordinator, at the Port of Cozumel when

they realize that all water excursions have been cancelled for no reason in particular. It takes her 2.5

minutes to find the customers an alternative excursion activity and customers cluster around her at the

rate of 20 per hour. Calculate system performance characteristics if service times are exponentially

distributed and the arrivals follow a Poisson distribution.

43) Anxious cruise vacationers besiege Tatiana, their excursion coordinator, and her fourteen assistants at

the Port of Cozumel when they realize that all water excursions have been cancelled for no reason in

particular. It takes them 4 minutes to find the customers an alternative excursion activity and customers

cluster around them at the rate of 200 per hour. Calculate system performance characteristics if service

times are exponentially distributed and the arrivals follow a Poisson distribution.

18

44) It’s a beautiful sunny day after a week of rainy weather and both of the local car washes are busy. One

car wash is fully automated, touchless, and can wash a vehicle of any size to a dazzling luster in 5

minutes flat. The other car wash is a fund raiser staffed by eager amateurs that work on one car at a time

and can finish it in about 4 minutes (their time is governed by the Poisson distribution). Customer

arrivals at both car washes are Poisson distributed with a mean of 10 per hour. How long does it take the

average customer to work his way through either system? How many customers are in the systems on

average?

6S.2 Simulation Modeling

1) One advantage of simulation modeling is:

A) it allows the user to conduct a “what if” analysis.

B) the many simplifying assumptions that are often made when using it.

C) the fact that an optimal solution is reached.

D) the time and cost required to make a perfectly realistic simulation.

2) Which of the following statements about simulation is BEST?

A) Tools like optimization and regression analysis work best when they are simulated.

B) Simulation permits managers to test the effects of new policies and procedures without disrupting

customer service.

C) As computers have increased in processing power, simulation results have become less accurate.

D) Computer-based simulation is the only “true” simulation.

3) Which of the following is characteristic of Monte Carlo simulation?

A) Results are usually not valid, but provide managers with an approximation.

B) Time compression is not possible using this technique.

C) Statistical sampling is used to create outcomes for many trials.

D) Computer packages such as SimQuick and Arena can show on-screen graphics of customers moving

through the system or inventory accumulation.

4) Each outcome of flipping a fair coin is completely independent of the previous flip. This outcome is

known as:

A) simulation.

B) Monte Carlo.

C) 50/50.

D) memoryless.

5) The effect of the Excel formula =20*RAND()

A) is that twenty entries of a random variable with a mean of zero will be created.

B) is that twenty entries of a random variable with a mean of one will be created.

C) is that one entry of a random variable with a mean of twenty will be created.

D) is that one entry of a random variable with a mean of ten will be created.

The stream of random number for a Monte Carlo simulation of the system appear in this table>

Interarrival

Service

.114

.979

.899

.297

.925

.162

.085

.574

.824

.235

.151

.593

.223

.956

.477

.845

6) Use the data from Figure 6S–1. What time does the last customer exit the haberdashery if it opens at

8:00 a.m.?

A) 9:19

B) 9:10

C) 9:16

D) 9:26

7) Use the data from Figure 6S-1. How many customers are in the haberdashery at 8:38?

A) 0

B) 1

C) 2

D) 3

8) Use the data from Figure 6S-1. How many customers are in the haberdashery at 8:02?

A) 0

B) 1

C) 2

D) 3

9) Use the data from Figure 6S-1. How many customers are in the haberdashery at 9:08?

A) 0

B) 1

C) 2

D) 3

10) Use the data from Figure 6S-1. What is the total time the owner/operator is idle (has no customers)

from 8:00 am to 9:15 am?

A) 3 minutes

B) 8 minutes

C) 16 minutes

D) 20 minutes

11) Use the data from Figure 6S-1. What is the total time that customers must wait from 8:00 am to 9:15

am?

A) 17 minutes

B) 18 minutes

C) 19 minutes

D) 20 minutes

12) The term “time compression” refers to the phenomenon that a server tends to speed up the service

process if the waiting line exceeds some critical number of customers.

13) It is more costly to create a more realistic simulation than one that is less realistic.

14) Monte Carlo simulation uses statistical sampling to create outcomes for a large number of trials.

15) In most cases, simulation models provide optimal solutions to problems just like most of the

equations presented in your textbook.

16) Customers enter the stadium and purchase refreshments before they are shown to their seats by

experienced ushers. The customers are considered objects in the simulation model.

17) Customers enter the stadium and purchase refreshments before they are shown to their seats by

experienced ushers. The concession stand lines are considered elements in the simulation model.

18) Just before he retired for the evening, Saba started his simulation program to simulate five years of

hospital operations as he slept. His ability to generate five years of data overnight is a textbook example

of ________.

19) Simulation permits the modeler to discover what might happen should certain events occur, for

example, extreme levels of customer demand, equipment malfunction, etc. This type of analysis is known

as ________ analysis.

20) One approach to mathematical simulation where statistical sampling is used to generate outcomes for

a large number of trials is ________.

21) A process is ________ if the outcome of one trial does not have any impact on the next trial.

22) ________ is an Excel function that generates a uniformly distributed random number between 0 and 1.

23) Why would someone choose to use simulation to analyze a waiting line problem rather than use a

formula? What are the advantages and disadvantages of a simulation approach?

24) What is Monte Carlo simulation and how is it conducted?

25) Use the data from Figure 6S-1. What are the exit times of the system for the first eight customers of the

day?

26) Use the data from Figure 6S-1. Which customers wait and how long does each one wait? How many

minutes of idle time does the owner/operator enjoy from opening time at 8:00 am until his eighth

customer departs?