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Advance Waiting Line Theory and Simulation Modeling

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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

- 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

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

- 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

Probability of n arrivals in T time periods

where = arrival rate

- Arrival rate = 7.5 cars per hour
- Service rate = an average of10 cars per hour
- Utilization = / = 75%

- Arrival rate = 7.5 cars per hour
- Service rate = a constant rate of10 cars per hour
- Utilization = / = 75%

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

- 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.

- 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

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

- 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.

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