1. Process Analysis and Design
Operations Strategy
Process Analysis
Manufacturing
Services
Service System
Design Matrix
Service Blueprinting
Service Classifications
Waiting Line Analysis 62
Process Analysis & Design - Manufacturing, Facility Layout, Services 62

2. Queues (Waiting Lines)
People waiting to be served/machines waiting to be overhauled
Can’t have inventory in services!
The issue is the trade-off between cost of service and the cost of waiting
Perceptions Management
- What is an acceptable waiting time?
- Install distractions and involve customers.
- Get customer out of line.
- Make conscious of time only if necessary
- Keep unused resources out of sight
Modify arrivals
-Appointment Books, discounts
Personality types
- Express 63
Process Analysis & Design - Manufacturing, Facility Layout, Services 63

3. Suggestions for Managing Queues
Determine an acceptable waiting time
Divert customer’s attention while waiting
Inform your customers of what to expect
Keep other employees out of sight
Segment customers
Train employees to be friendly
Encourage customers during slack periods
Adopt a long-term perspective
Perceptions Management
- What is an acceptable waiting time?
- Install distractions and involve customers.
- Get customer out of line.
- Make conscious of time only if necessary
- Keep unused resources out of sight
Modify arrivals
-Appointment Books, discounts
Personality types
- Express 63
Process Analysis & Design - Manufacturing, Facility Layout, Services 63

4. Suggestions for Managing Queues
For example, can control arrivals by:
Restricting the line (short line) - e.g., Wendy’s drive-thru
Post business hours
Establishing specific hours for specific customers or price - e.g., run specials; increase price for adult haircuts
Can also provide faster (or slower) servers, machines, layouts, set-up times, etc.
Perceptions Management
- What is an acceptable waiting time?
- Install distractions and involve customers.
- Get customer out of line.
- Make conscious of time only if necessary
- Keep unused resources out of sight
Modify arrivals
-Appointment Books, discounts
Personality types
- Express 63
Process Analysis & Design - Manufacturing, Facility Layout, Services 63

5. Components of the Queuing Phenomenon
Server(s)
Waiting Line
Servicing System
Population
Source?
Infinite or
Finite
Service Rate?
Constant or
Variable
Customer
Arrivals
Exit
Finite: Number of machines needing repair when a company only has three machines.
Infinite: The number of people who could wait in a line for gasoline.
Constant: Items coming down an automated assembly line.
Variable: People spending time shopping.
Lamda = Arrival Rate
Poisson Distribution - # arrivals in T
If machine paced arrivals are constant
Mu = service rate
Follows Exponential Distribution
Infinite Queue Length
FCFS
Balking or Reneging? 64
Process Analysis & Design - Manufacturing, Facility Layout, Services 64

6. Queuing Components
Arrivals from a finite population - Limited size customer pool (important distinction, as probabilities change after each customer)
FCFS (First come, first served) - most common priority rule, but not only one - can have emergencies first, best customers first, triage, etc.
Balking (look and then leave) vs. Reneging (wait for awhile and then decide to leave)
Perceptions Management
- What is an acceptable waiting time?
- Install distractions and involve customers.
- Get customer out of line.
- Make conscious of time only if necessary
- Keep unused resources out of sight
Modify arrivals
-Appointment Books, discounts
Personality types
- Express 63
Process Analysis & Design - Manufacturing, Facility Layout, Services 63

7. Queuing Components (cont’d)
Poisson Distribution:
- The Poisson is the most common distribution used in queuing theory for arrivals
- The Poisson distribution is discrete, as the number of arrivals must be an integer
- The probability of n arrivals within a T minute period = PT(n)=(λT)n(e-λT)/n!
Perceptions Management
- What is an acceptable waiting time?
- Install distractions and involve customers.
- Get customer out of line.
- Make conscious of time only if necessary
- Keep unused resources out of sight
Modify arrivals
-Appointment Books, discounts
Personality types
- Express 63
Process Analysis & Design - Manufacturing, Facility Layout, Services 63

8. Queuing Components (cont’d)
Service Rates:
- The capacity of the server (in units per time pd) (e.g., a service rate of 12 completions per hour)
- Use the Exponential distribution when service times are random (as opposed to constant), where μ = avg # of customers served per time pd, and the probability the service time will be less than or equal to a time of length t: P = 1 – e-µt.
Perceptions Management
- What is an acceptable waiting time?
- Install distractions and involve customers.
- Get customer out of line.
- Make conscious of time only if necessary
- Keep unused resources out of sight
Modify arrivals
-Appointment Books, discounts
Personality types
- Express 63
Process Analysis & Design - Manufacturing, Facility Layout, Services 63

9. Line Structures Single Phase Multiphase One-person barber shop
Car wash
Hospital
admissions
Bank tellers’
windows
Single Channel
channel is number of servers
phase is number of stops
Multichannel
(Also, “Mixed”; See text pages ) 65
Process Analysis & Design - Manufacturing, Facility Layout, Services 65

10. Properties of Waiting Line Models
Source
Model
Layout
Population
Service Pattern 1
Single channel
Infinite
Exponential 2
Single channel
Infinite
Constant 3
Multichannel
Infinite
Exponential 4
Single or Multi
Finite
Exponential
(See formulas for each model in text on page 253)
These four models share the following characteristics:
Single phase
Poisson arrival
FCFS
Unlimited queue length 66
Process Analysis & Design - Manufacturing, Facility Layout, Services 66

11. Waiting Line Models Characteristics of a waiting line model:
Lq = Average number in line
Ls = Average number in system
Wq = Average time in line
Ws = Average time in system
ρ = Utilization of Server
Pn = Probability of exactly n in system nl ns tl ts
Rho -  Pn 67
Process Analysis & Design - Manufacturing, Facility Layout, Services 67

12. Characteris-tics of Waiting Lines Definition Model 1 (single channel,
Characteris-tics of Waiting Lines
Definition
Model 1
(single channel,
exp. service rate)
Model 2
constant service rate) Lq
Average number in line
2/[(-)]
2/[2(-)] Ls
Avg. number in system
/(-)
Lq + (/) Wq
Average time in line
/[(-)]
or Lq/
/[2(-)] Ws
Average time in system
1/(-) or
Wq +(1/)
 (“rho”)
Utilization of server
/ - Pn
Prob.of exactly n in system
[1-(/)](/)n Po
Prob. of exactly zero in system
1 - (/)
Where  = Arrival rate (e.g.,  = 2 would represent a mean arrival rate of 2 per minute),
and  = Service rate or avg number of customers served per time period (e.g., 1 per 3 mins =20 per hour).
 and  must be in the same units. (corrected 5/3/05)

13. Example: Model 1 (worked problem)
Drive-up window at a fast food restaurant.
Customers arrive at the rate of 25 per hour.
The employee can serve one customer every two minutes.
Assume Poisson arrival and Exponential service rates.
A) What is the average utilization of the employee?
B) What is the average number of customers in line?
C) What is the average number of customers in the system?
D) What is the average waiting time in line?
E) What is the average waiting time in the system?
F) What is the probability that exactly two cars will be
in the system?
WP1
Process Analysis & Design - Manufacturing, Facility Layout, Services
WP1

14. Example: Model 1 (worked problem)
A) What is the average utilization of the employee?
B) What is the average number of customers in line?
WP2
Process Analysis & Design - Manufacturing, Facility Layout, Services
WP2

15. Example: Model 1 (worked problem)
C) What is the average number of customers in the system?
D) What is the average waiting time in line?
WP3
Process Analysis & Design - Manufacturing, Facility Layout, Services
WP3

16. Example: Model 1 (worked problem)
E) What is the average waiting time in the system?
F) What is the probability that exactly two cars will be
in the system (one being served and the other waiting in line)?
WP4
Process Analysis & Design - Manufacturing, Facility Layout, Services
WP4

17. Example: Model 2 (worked problem)
An automated pizza vending machine heats and
dispenses a slice of pizza in 4 minutes.
Customers arrive at a rate of one every 6 minutes with the
arrival rate exhibiting a Poisson distribution.
Determine:
A) The average number of customers in line.
B) The average waiting time in the system.
WP5
Process Analysis & Design - Manufacturing, Facility Layout, Services
WP5

18. Example: Model 2 (worked problem)
A) The average number of customers in line. Lq l 2
(10) 2 = = =
.6667 2 m ( m - l )
(2)(15)(15 -
10)
B) The average waiting time in the system. l 10
Wq = = = hr s =
4 mins 2 m ( m - l ) 2 ( 15 )( 15 -
10) 1 1 Ws Wq = + = hr s + =
.1333 hrs =
8 mins m 15 / hr
WP6
Process Analysis & Design - Manufacturing, Facility Layout, Services
WP6

19. Approximating Customer Waiting Time
A “quick and dirty” method has been developed to compute average waiting time for multiple servers (see text, pp ). No assumptions about the underlying distributions are required! All that is needed are 4 numbers – the average and standard deviation of the inter-arrival time and service time. 70
Process Analysis & Design - Manufacturing, Facility Layout, Services 70

20. Utilization and Time in System70
Process Analysis & Design - Manufacturing, Facility Layout, Services 70