Transcript OPSM 451 Service Operations Management

Koç University
OPSM 301 Operations Management
Class 13:
Service Design
Waiting-Line Models
Zeynep Aksin
[email protected]
Announcements
 Lab activity will count as Quiz 2
 Exam on 15/11 @ 14:00 in SOS Z27
– Study hands-on by solving problems
– Study class notes
– Read from book to strengthen your background
 On 17/11 exam solutions in class
 I won’t have office hours on Monday, Canan Uckun will
hold additional office hours Monday 13:00-15:00
 Today
– Service Design (Ch 7 p. 265-270)
– Waiting-Line Models (Quantitative Module D)
– Quiz 3
Services ..
 .. lead to some desired transformation or improvement in
the condition of the consuming unit
 …are provided to customers and cannot be produced
independently of them
 …are produced, distributed and consumed
simultaneously
Service Product – Service Process
 In most cases the product is your process (eg.
concert, amusement park)
 Product design involves process design like we
have seen before
 However customer contact and participation is
distinguishing feature
– Customer controlled arrivals
– Service unique to customer: different service times
– Customer experiences process flows
Where is the customer?
Marketing
Service Design
Co-production
Production
Measurement
Quality Assurance
Customer Interaction and Process Strategy
Low
High
Mass Service
Personal
banking
Commercial
Banking
Full-service
stockbroker
General purpose
law firms
Boutiques
Retailing
Service Factory
Law clinics
Fast food
restaurants
Warehouse and
catalog stores
Service Shop
For-profit
hospitals
Fine dining
restaurants
Airlines
Degree of Interaction and Customization
Hospitals
Low
Limited service
stockbroker
No frills
airlines
High
Degree of Labor Intensity
Professional Service
Service Design Tools: Service Blueprinting
 A blueprint is a flowchart of the service process.
Answers questions: ‘who does what, to whom?’,
‘how often?’, ‘under what conditions?’
 Shows actions of employee and customer, front
office and back office tasks, line of visibility and line
of interaction
 Instrumental in understanding the process and to
improve the design. Are there redundancies, or
unnecesssarily long paths? Fail points? Possible
poka-yokes that might prevent failures?
Service Blueprint for Service at Ten Minute
Lube, Inc.
Techniques for Improving Service Productivity
Strategy
 Separation
 Self-service
Technique
 Structure service so
customers must go where
service is offered
 Self-service so customers
examine, compare and
evaluate at their own pace
 Postponement
 Customizing at delivery
 Focus
 Restricting the offerings
Techniques for Improving Service Productivity Continued
 Modules
 Modular selection of service.
Modular production
 Automation
 Separating services that lend
themselves to automation
 Scheduling
 Training




Precise personnel scheduling
Clarifying the service options
Explaining problems
Improving employee flexibility
If you can’t reduce it, fix it: Contact
enhancement




consistent work hours
well trained service personnel
good queue discipline
reduce waiting
This motivates our analysis of queueing systems
A Basic Queue
Server
A Basic Queue
Customer
Arrivals
Server
A Basic Queue
Server
A Basic Queue
Customer
Departures
Server
A Basic Queue
Customer
Arrivals
Queue
(waiting line)
Server
Customer
Departures
A Basic Queue
Customer
Arrivals
Queue
(waiting line)
Server
Line too long?
Customer balks
(never enters queue)
Customer
Departures
Line too long?
Customer reneges
(abandons queue)
Three Parts of a Queuing System at Dave’s
Car-Wash
A common assumption: Poisson distribution
 The probability that a customer arrives at any time does
not depend on when other customers arrived
 The probability that a customer arrives at any time does
not depend on the time
 Customers arrive one at a time
 Interarrival times distributed as a negative exponential
distribution
Picture of negative exponential distribution:
interarrival times at an outpatient clinic
Independence from other customer’s arrival: interarrival
times at an ATM
Time independent arrivals:
cumulative arrivals at an ATM
Single-Channel, Single-Phase System
Service system
Arrivals
Ships at
sea
Queue
Service
facility
Ship unloading system
Served
units
Empty
ships
Waiting ship line
Dock
Single-Channel, Multi-Phase System
Service system
Arrivals
Cars
in area
Queue
Service
facility
Service
facility
McDonald’s drive-through
Cars
& food
Waiting cars
Pay
Served
units
Pick-up
Multi-Channel, Single Phase System
Service system
Arrivals
Queue
Service
facility
Served
units
Service
facility
Example: Bank customers wait in single line for one of
several tellers.
Multi-Channel, Multi-Phase System
Service system
Arrivals
Queue
Service
facility
Service
facility
Service
facility
Service
facility
Served
units
Example: At a laundromat, customers use one of several
washers, then one of several dryers.
Queueing Analysis-Performance measures
Avg Wait
in Queue (Wq)
Arrival
Rate (
Service
Rate (
Avg Number
in Queue (Lq )
Queueing Analysis
Service
Rate (
Arrival
Avg Time in System (Ws)
Rate (
Avg Number in System (Ls)
Elements of Queuing System
Arrivals
Processing
order
Waiting
line
Service
System
Exit
Waiting Line Models
Source
Layout
Population
Single channel Infinite
Service Pattern
Exponential
B
Multichannel
Exponential
C
Single channel Infinite
Model
A
Infinite
Constant
These three models share the following characteristics:
Single phase, Poisson Arrivals, FCFS, and
Unlimited Queue Length
Notation
 = Arrivalrat e
 = Service rat e
1
 Averageservice t ime
1
 Averaget imebet ween arrivals



 = = Rat io of t ot alarrivalrat e t o sevice rat e

for a single server
Lq  Averagenumber wait ingin line
Notation
Ls = Averagenumber in system
(including thosebeing served)
Wq = Averagetime waitingin line
Ws  Averagetotaltimein system
(including time to be served)
n  Number of units in thesystem
S = Number of identicalservicechannels
Pn  P robability of exactlyn units in system
Pw  P robability of waitingin line
Operating Characteristics –Model A
Utilization (fraction of time server is busy)



Average waiting times
W
1

Wq 

 W

Average numbers

L
 
Little’s Law
L=  W

Lq 
 L
 
Lq  Wq
Example: Model A
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)
B)
C)
D)
E)
F)
What is the average utilization of the employee?
What is the average number of customers in line?
What is the average number of customers in the system?
What is the average waiting time in line?
What is the average waiting time in the system?
What is the probability that exactly two cars will be in
the system?
Example: Model A
A) What is the average utilization of the employee?
 = 25 cust/hr
1 customer
=
= 30 cust/hr
2 mins (1hr/60 mins)
 25 cust/hr
= =
= .8333
 30 cust/hr
Example: Model A
B) What is the average number of customers in line?

(25)
Lq =
=
= 4.167
 (  -  ) 30(30 - 25)
2
2
C) What is the average number of customers in the
system?

25
LS =
=
=5
 -  (30 - 25)
Example: Model A
D) What is the average waiting time in line?

25
Wq =
=
= .1667 hrs = 10 mins
 (  -  ) 30(30 - 25)
E) What is the average waiting time in the system?
1
1
Ws =
=
= .2 hrs = 12 mins
 -  30 - 25
Example: Model A
F) What is the probability that exactly two cars will be
in the system?
 
p = (1 - )( )
 
n
n
2
25 25
p 2 = (1 - )( ) = .1157
30 30
Example: Model B
Recall Model A:
If an identical window (and an identically
trained server) were added, what would the
effects be on the average number of cars in
the system and the total time customers
wait before being served?
Example: Model B
Average number of cars in the system

Ls = Lq +

Lq = 0.1733
(by interpolation)

25
Ls = Lq + = .1733 + = 1.006

30
Example: Model B
Total time customers wait before being served
Lq
.1733 customers
Wq =
=
= .006 mins
 25 customers/ min
Example: Model C
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 total waiting time in the system.
Example: Model C
A) The average number of customers in line.
2
(10) 2
Lq =
=
= .6667
2 (  -  ) (2)(15)(15 - 10)
B) The average total waiting time in the system.

10
Wq =
=
= .06667 hrs = 4 mins
2 (  -  ) 2(15)(15 - 10)
1
1
Ws = Wq + = .06667 hrs +
= .1333 hrs = 8 mins

15/hr
Example: Secretarial Pool
 4 Departments and 4 Departmental secretaries
 Request rate for Operations, Accounting, and
Finance is 2 requests/hour
 Request rate for Marketing is 3 requests/hour
 Secretaries can handle 4 requests per hour
 Marketing department is complaining about the
response time of the secretaries. They demand
30 min. response time
 College is considering two options:
– Hire a new secretary
– Reorganize the secretarial support
Current Situation
Accounting
Finance
Marketing
Operations
2 requests/hour
4 requests/hour
2 requests/hour
4 requests/hour
3 requests/hour
4 requests/hour
2 requests/hour
4 requests/hour
Current Situation: waiting times
Accounting, Operations, Finance:
W = service time + Wq
W = 0.25 hrs. + 0.25 hrs
= 30 minutes
Marketing:
W = service time + Wq
W = 0.25 hrs. + 0.75 hrs
= 60 minutes
Proposal: Secretarial Pool
Accounting
2
Finance
Marketing
2
3
2
Operations
9 requests/hour
Proposal: Secretarial Pool
Wq = 0.0411 hrs.
W= 0.0411 hrs. + 0.25 hrs.= 17 minutes
In the proposed system, faculty members in all departments
get their requests back in 17 minutes on the average. (Around 50%
improvement for Acc, Fin, and Ops and 75% improvement for
Marketing)
Deciding on the
Optimum Level of Service
Cost
Total expected cost
Minimum
total cost
Cost of providing
service
Cost of waiting time
Low level
of service
Optimal
service level
High level
of service