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Advance Waiting Line Theory and Simulation Modeling. Supplement 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.

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Advance Waiting Line Theory and Simulation Modeling

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Advance waiting line theory and simulation modeling l.jpg

Advance Waiting Line Theory and Simulation Modeling


Supplement objectives l.jpg

Supplement 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.

© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036


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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

© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036


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Alternative Waiting Lines

Multiple-Channel, Single-Phase

Single-Channel, Single-Phase

Single-Channel, Multiple-Phase

© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036


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Assumptions

  • Arrivals

    • At random (Poisson, exponential distributions)

    • Fixed (appointments, service intervals)

  • Service times

    • Variable (exponential, normal distributions)

    • Fixed (constant service time)

  • Other

    • Size of arrival population, priority rules, balking, reneging

© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036


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Poisson Distribution

Probability of n arrivals in T time periods

where  = arrival rate

© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036


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Waiting Line Formulas

© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036


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P0 = Probability of 0 Units in Multiple-Channel System

© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036


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Single-Channel, Single-PhaseManual Car Wash Example

  • Arrival rate  = 7.5 cars per hour

  • Service rate  = an average of10 cars per hour

  • Utilization  = / = 75%

© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036


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Single-Channel, Single-PhaseAutomated Car Wash Example

  • Arrival rate  = 7.5 cars per hour

  • Service rate  = a constant rate of10 cars per hour

  • Utilization  = / = 75%

© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036


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Comparisons

© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036


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Advantages

Off-line evaluation of new processes or process changes

Time compression

“What-if” analysis

Provides variance estimates in addition to averages

Disadvantages

Does not provide optimal solution

More realistic  the more costly and more difficult to interpret

Still just a simulation

Simulation Modeling

© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036


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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)

  • Random numbers 0 to 99 supplied by computer functions such as = INT(100*RAND()) in Excel.

© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036


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Monte Carlo Simulation Examples

  • Coin toss: Random numbers 0 to 49 for ‘heads’, 50 to 99 for ‘tails’

  • Dice throw: Use Excel function= RANDBETWEEN(1,6) for throws

  • Service time: Use Excel function= –(avg service time)*ln(RAND()) for exponential service time

© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036


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Building a Simulation Model

Four basic steps

  • Develop a picture of system to be modeled (process mapping)

  • Identify objects, elements, and probability distributions that define the system

    • Objects = items moving through system

    • Elements = pieces of the system

  • Determine experiment conditions (constraints) and desired outputs

  • Build and test model, capture the output data

© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036


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Simulation Example(Using single-channel, single-phase waiting line)

  • Process map

  • Time between arrivals (exponential distribution), service time (exponential distribution), objects = cars, elements = line and wash station

  • Maximum length for line, time spent in the system

  • Run model for a total of 100 cars entering the car wash, average the results for waiting time, cars in line, etc.

© 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036


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‘SimQuick’ SimulationAn Excel-based application for simulating processes that allows use of constraints (see text example 8S.5)


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