Sophia Miles - Operation management
abnj619
OPMT310Chapter10WaitingLines.pptx
Economics of the Waiting Line Problem
A central problem in many service settings is the management of waiting time.
Reducing waiting time costs money.
When people waiting are employees, it is easy to value their time.
When people waiting are customers, it is more difficult to value their time.
Lost sales is one (low) value.
10-3
The Practical View of Waiting Lines
10-4
More on Waiting Lines
One important variable is the number of arrivals over the hours that the service system is open.
Customers demand varying amounts of service, often exceeding normal capacity.
We can control arrivals.
Short lines
Specific hours for specific customers
Specials
We can affect service time by using faster or slower servers.
10-5
The Queuing System
Source population and the way customers arrive at the system
The servicing system
The condition of the customers exiting the system
Do they go back to source population or not?
10-6
Components of the Queuing System Visually
10-7
Customers come in
Customers are served
Customers leave
Customer Arrivals
Finite population: limited-size customer pool that will use the service and, at times, form a line
When a customer leaves his/her position as a member of the population, the size of the user group is reduced by one.
Infinite population: population large enough so that the population size caused by subtractions or additions to the population does not significantly affect the system probabilities
10-8
Distribution of Arrivals
Arrival rate: the number of units arriving per period
Constant arrival distribution: periodic, with exactly the same time between successive arrivals
Variable (random) arrival distributions: arrival probabilities described statistically
Exponential distribution
Poisson distribution
10-9
Customer Arrivals in Queues
10-10
Other Arrival Characteristics
Arrival patterns
Size of arrival units
Degree of patience
Balking
Reneging
10-11
The Queuing System
Length
Infinite potential length
Limited line capacity
Number of lines
Queue discipline: a priority rule or set of rules for determining the order of service to customers in a waiting line
10-12
Service Time Distribution
Constant
Service provided by automation
Variable
Service provided by humans
Described using exponential distribution
10-13
Line Structure
10-14
Exiting the Queuing System
10-15
Properties of Some Specific Waiting Line Models
10-16
Notation for Equations
10-17
Equations for Solving Three Model Problems
10-18
Example 10.1: Customers in Line
Western National Bank is considering opening a drive-through window for customer service. Management estimates that customers will arrive at the rate of 15 per hour. The teller who will staff the window can service customers at the rate of one every three minutes.
Part 1 Assuming Poisson arrivals and exponential service, find
Utilization of the teller
Average number in line
Average number in system
Average waiting time in line
Average waiting time in system, including service
10-19
Example 10.1: Solution
10-20
Computer Simulation of Waiting Lines
Some waiting line problems are very complex.
Assumed waiting lines are independent.
When a services is becomes the input to the next, we can no longer use the simple formulas.
This is also true for any problem where conditions do not meet the requirements of the equations.
Here, computer simulation must be used.
10-21
Simulating Waiting Lines
Waiting lines that occur in series and parallel cannot be solved mathematically.
Assembly lines
Work centers
These waiting lines are easily simulated on a computer.
10-22
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