Lecture Fundamentals of operations management (4/e): Chapter 16 - Davis, Aquilano, Chase

Chapter supplement 11 Waiting line theory. This chapter introduce the major characteristics that exist in waiting lines and describe how they can impact a customer’s waiting time, identify the various constraints and/or conditions that waiting line theory and its associated equations require for the results to be valid, present waiting line theory in the form of a set of equations that represent various types of waiting line configurations that can be encountered.

Waiting Line Theory

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supplement 11

DAVIS AQUILANO CHASE

PowerPoint Presentation by Charlie Cook

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Supplement Objectives

Supplement Objectives

• Introduce the major characteristics that exist in waiting lines and describe how they can impact a customer’s waiting time

• Identify the various constraints and/or conditions that waiting line theory and its associated equations

require for the results to be valid

• Present waiting line theory in the form of a set of

equations that represent various types of waiting line configurations that can be encountered

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Waiting Line Characteristics

Waiting Line Characteristics

• Major Components

–The source population

–The way customers arrive at the service facility –The physical line itself

–The way customers are selected from the line –The characteristics of the service facility itself –The condition of the customers when they exit

the system

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Framework for Viewing Waiting Line Structures

Framework for Viewing Waiting Line Structures

Exhibit S11.1

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Population Source

Population Source

• Finite Population

–Limited size of the customer pool

• Each customer leaving or returning to the pool

changes the probability of a customer requiring service.

• Infinite Population

–A customer pool so large that subtractions or

additions to the pool do not significantly affect system probabilities.

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Arrival Characteristics

Arrival Characteristics

• Pattern of Arrivals

–Controllable or uncontrollable

• Size of Arrival Units

–One at a time or in batches

• Distribution Pattern

–Constant or statistically distributed rates of

arrivals

• Degree of Patience

–Whether the arrival stays in line or leaves

• Balking or reneging

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Arrival Characteristics in Queues

Arrival Characteristics in Queues

Exhibit S11.2

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Physical Features of Lines

Physical Features of Lines

• Length

–Infinite potential length

–limited line capacity

• Number of Lines

–Single or multiple lines

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Customer Selection

Customer Selection

• Factors in a Queuing Discipline

Exhibit S11.3

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Service  Facility  Structure

Service  Facility  Structure

Exhibit S11.4

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Arrival Characteristics (cont’d)

Arrival Characteristics (cont’d)

• Service Rate

–The capacity of a service station, usually

expressed in terms of customers per hour.

–The reciprocal of the service rate is the average

time to serve a customer.

• Capacity Utilization

–The percentage of time a service station is busy

serving a customer.

• Exit

–Customer returns to the waiting population.

–Customer does not return to the population.

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Waiting Line Equations

Waiting Line Equations

Average total waiting time in the system is equal to the  average waiting time in the system plus the average 

service time:

Little’s Formula—the average total number of 

customers in the system is directly related to the total  time in the system:

1

l

t

s

n

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Properties of Specific Waiting Line Models

Properties of Specific Waiting Line Models

Exhibit S11 5

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Equations for  Solving Six  Model  Problems

Equations for  Solving Six  Model  Problems

Exhibit S11.6a

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Equations for  Solving Six  Model  Problems (cont’d)

Equations for  Solving Six  Model  Problems (cont’d)

Exhibit S11.6b

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Notations 

for  Equations  (Exhibit  S11.6)

Notations 

for  Equations  (Exhibit  S11.6)

Exhibit S11.7

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Calculating the Relationship between  Capacity Utilization and Waiting Time

Calculating the Relationship between  Capacity Utilization and Waiting Time

Exhibit S11.8

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The Relationship between Capacity Utilization 

and Waiting Time

The Relationship between Capacity Utilization 

and Waiting Time

Exhibit S11.9

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The Trade­off between Balking and Reneging

The Trade­off between Balking and Reneging

Exhibit S11.10