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Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 6S - 2
6S Chapter Objectives
Be able to: Describe different types of waiting line systems. Use statistics-based formulas to estimate waiting line
lengths and waiting times for three different types of waiting line systems.
Explain the purpose, advantages and disadvantages, and steps of simulation modeling.
Develop a simple Monte Carlo simulation using Microsoft Excel.
Develop and analyze a system using SimQuick.
Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 6S - 3
6S Alternative Waiting Lines
Single-Channel, Single-Phase Ticket window at theater
Multiple-Channel, Single-Phase Tellers at the bank, windows at post office
Single-Channel, Multiple-Phase Line at the Laundromat, DMV
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6S Single-Channel, Single-Phase
Figure 6S.1
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6S Multiple-Channel, Single-Phase
Figure 6S.2
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6S Single-Channel, Multiple-Phase
Figure 6S.3
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6S Common Assumptions
Arrivals At random (Poisson distribution)
Service times Variable (exponential, normal distributions) Fixed (constant service time)
Other Size of arrival population, order, balking, reneging, first-
come, first-served, urgency, speed, desirability of different customer types
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6S P0 = Probability of 0 Units in Multiple-Channel System
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6S Waiting Lines for Different Environments
Table 6S.1
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6S Single-Channel, Single-Phase Manual Car Wash Example
• Arrival rate = 7.5 cars per hour• Service rate = an average of 10 cars per hour• Utilization = / = 75%
Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 6S - 11
6S Single-Channel, Single-Phase Automated Car Wash Example
• Arrival rate = 7.5 cars per hour• Service rate = a constant rate of 10 cars per hour• Utilization = / = 75%
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6S Adding a Second Crew
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6S Adding a Second Crew
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6S Simulation Modeling
Advantages Off-line evaluation of new
processes or process changes
Time compression “What-if” analyses
Disadvantages They are not realistic. The more realistic a
simulation model, the more costly it will be to develop and the more difficult it will be to interpret.
Simulation models do not provide an “optimal” solution
Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 6S - 16
6S Monte Carlo Simulation
Maps random numbers to cumulative probability distributions of variables.
Probability distributions can be either discrete (coin flip, roll of a die) or continuous (exponential service time or time between arrivals).
Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 6S - 17
6S Building a Simulation Model with SimQuick
Four basic steps Develop a picture of system to be modeled (process
mapping). Identify objects, elements, and probability
distributions that define the system. Objects – People or products moving through system Elements - Pieces of the system
Determine experimental conditions (constraints) and required output information
Build and test model, capture and evaluate the data.
Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 6S - 18
6S Building a Simulation Model with SimQuick
An Excel-based application for simulating processes that allows use of constraints (see text example 6S.4)
Figure 6S.6
Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 6S - 19
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otherwise, without the prior written permission of the publisher. Printed in the United States of America.