Advance waiting line theory and simulation modeling
Download
1 / 17

Advance Waiting Line Theory and Simulation Modeling - PowerPoint PPT Presentation


  • 715 Views
  • Updated On :

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Advance Waiting Line Theory and Simulation Modeling' - ardith


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

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


Alternative waiting lines l.jpg
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


Alternative waiting lines4 l.jpg
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


Assumptions l.jpg
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


Poisson distribution l.jpg
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


Waiting line formulas l.jpg
Waiting Line Formulas

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


P 0 probability of 0 units in multiple channel system l.jpg
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


Single channel single phase manual car wash example l.jpg
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


Single channel single phase automated car wash example l.jpg
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


Comparisons l.jpg
Comparisons

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


Simulation modeling l.jpg

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


Monte carlo simulation l.jpg
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


Monte carlo simulation examples l.jpg
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


Building a simulation model l.jpg
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


Simulation example using single channel single phase waiting line l.jpg
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


Slide17 l.jpg

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


ad