Introduction to operations and supply chain management 3e bozarth chapter 06sup

Advanced Waiting Line Theory and
Simulation Modeling
Chapter 6 - Supplement


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.
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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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Single-Channel, Single-Phase

Figure 6S.1
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Multiple-Channel, Single-Phase

Figure 6S.2
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Single-Channel, Multiple-Phase

Figure 6S.3
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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, firstcome, first-served, urgency, speed, desirability of different
customer types
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P0 = Probability of 0 Units
in Multiple-Channel System

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Waiting Lines for
Different Environments

Table 6S.1
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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%

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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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Adding a Second Crew

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Adding a Second Crew

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Comparisons

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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

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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).

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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.
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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
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