opsm 301 operations management class 13: service design waiting-line models koç university zeynep...
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OPSM 301 Operations Management
Class 13:
Service Design
Waiting-Line Models
Koç University
Zeynep [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?
Service Design
Production
Quality Assurance
Marketing
Co-production
Measurement
Customer Interaction and Process Strategy
Mass Service Professional Service
Service Factory Service Shop
Commercial Banking
General purpose law firms
Fine dining restaurants
Hospitals
Airlines
Full-service stockbroker
Retailing
Personal banking
Boutiques
Law clinics
Fast food restaurants
Warehouse and catalog stores
No frills airlines
Limited service stockbroker
For-profit hospitals
Degree of Interaction and Customization
Deg
ree
of L
abor
Inte
nsity
Low High
High Low
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
Separation
Self-service
Postponement
Focus
Structure service so customers must go where service is offered
Self-service so customers examine, compare and evaluate at their own pace
Customizing at delivery
Restricting the offerings
Strategy Technique
Techniques for Improving Service Productivity - Continued
Modules
Automation
Scheduling Training
Modular selection of service.
Modular production Separating services that lend
themselves to automation
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 QueueA Basic Queue
Server
A Basic QueueA Basic Queue
ServerCustomerArrivals
A Basic QueueA Basic Queue
Server
A Basic QueueA Basic Queue
Server
CustomerDepartures
A Basic QueueA Basic Queue
Server
Queue(waiting line)Customer
Arrivals
CustomerDepartures
A Basic QueueA Basic Queue
Server
Queue(waiting line)Customer
Arrivals
CustomerDepartures
Line too long?Customer balks
(never enters queue)
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
ArrivalsServed units
Service facility
Queue
Service system
Dock
Waiting ship lineShips at sea
Ship unloading system Empty ships
Single-Channel, Single-Phase System
Cars& food
Single-Channel, Multi-Phase System
ArrivalsServed units
Service facility
Queue
Service system
Pick-up
Waiting carsCars in area
McDonald’s drive-through
Pay
Service facility
Arrivals
Served units
Service facilityQueue
Service system
Service facility
Example: Bank customers wait in single line for one of several tellers.
Multi-Channel, Single Phase System
Service facility
Arrivals
Served units
Service facilityQueue
Service system
Service facility
Example: At a laundromat, customers use one of several washers, then one of several dryers.
Service facility
Multi-Channel, Multi-Phase System
Queueing AnalysisQueueing Analysis-Performance measures-Performance measures
Arrival
Rate ( Avg Number
in Queue (Lq )
Service
Rate (
Avg Waitin Queue
(Wq)
Queueing AnalysisQueueing Analysis
Arrival
Rate (
Service
Rate (Avg Time in System (Ws)
Avg Number in System (Ls)
Elements of Queuing System
Arrivals ServiceWaitingline
Exit
Processingorder
System
Waiting Line ModelsWaiting Line Models
Model LayoutSourcePopulation Service Pattern
A Single channel Infinite Exponential
B Multichannel Infinite Exponential
Single channel Infinite Constant
These three models share the following characteristics:
Single phase, Poisson Arrivals, FCFS, andUnlimited Queue Length
C
Notation
linein tingnumber wai Average
server single afor
rate sevice torate arrival totalof Ratio = =
arrivalsbetween timeAverage
timeservice Average
rate Service =
rate Arrival =
1
1
qL
linein tingnumber wai Average
server single afor
rate sevice torate arrival totalof Ratio = =
arrivalsbetween timeAverage
timeservice Average
rate Service =
rate Arrival =
1
1
qL
Notation
linein waitingofy Probabilit
systemin units exactly ofy Probabilit
channels service identical ofNumber =
system in the units ofNumber
served) be to time(including
systemin time totalAverage
linein waiting timeAverage = q
served) being those(including
systemin number Average = s
Pw
nPn
S
n
Ws
W
L
linein waitingofy Probabilit
systemin units exactly ofy Probabilit
channels service identical ofNumber =
system in the units ofNumber
served) be to time(including
systemin time totalAverage
linein waiting timeAverage = q
served) being those(including
systemin number Average = s
Pw
nPn
S
n
Ws
W
L
Operating Characteristics –Model A
Utilization (fraction of time server is busy)
Average waiting times
Average numbers
W 1
W Wq
L LLq
L= W
Little’s Law
qq WL
Example: Model AExample: Model ADrive-up window at a fast food restaurant: Customersarrive at the rate of 25 per hour. The employee can serve one customer every two minutes. AssumePoisson 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?
.8333 = cust/hr 30cust/hr 25
= =
cust/hr 30 = mins) (1hr/60 mins 2
customer 1 =
cust/hr 25 =
Example: Model AExample: Model A
A) What is the average utilization of the employee?
Example: Model AExample: Model A
B) What is the average number of customers in line?
4.167 = 25)-30(30
(25) =
) - ( =
22
qL
C) What is the average number of customers in the system?
5 = 25)-(30
25 =
- =
SL
Example: Model AExample: Model A
D) What is the average waiting time in line?
mins10= hrs .1667 = 25)-030(3
25 =
) - ( = Wq
E) What is the average waiting time in the system?
mins 12 = hrs .2 = 25-30
1 =
-
1 =
Ws
Example: Model AExample: Model A
F) What is the probability that exactly two cars will be in the system?
n
np ))(-(1 =
.1157 = )30
25)(
30
25-(1 =
2
2p
Example: Model BExample: 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 BExample: Model B
Average number of cars in the system
17330= . Lq
0061 = 30
25 +.1733 = + = .LL qs
+ =
qs LL
(by interpolation)
Example: Model BExample: Model B
Total time customers wait before being served
mins006= mincustomers/ 25
customers .1733 = = .
LW q
q
Example: Model CExample: 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 CExample: Model C
A) The average number of customers in line.
6667= 10)-(2)(15)(15
(10) =
) - (2 =
22
.Lq
B) The average total waiting time in the system.
mins4 = hrs .06667 = 10)-51)(15(2
10 =
) - (2 = Wq
mins 8 = hrs .1333 = 15/hr
1 + hrs .06667 =
1 + = qs WW
Example: Secretarial PoolExample: 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 SituationCurrent Situation
Accounting
Finance
Marketing
Operations
2 requests/hour
2 requests/hour
3 requests/hour
2 requests/hour
4 requests/hour
4 requests/hour
4 requests/hour
4 requests/hour
Current Situation: waiting times
W = service time + Wq
W = 0.25 hrs. + 0.25 hrs = 30 minutes
Accounting, Operations, Finance:
Marketing:
W = service time + Wq
W = 0.25 hrs. + 0.75 hrs = 60 minutes
Proposal: Secretarial PoolProposal: Secretarial Pool
Accounting
Finance
Marketing
Operations
9 requests/hour
2
2
3
2
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
Total expected cost
Cost of waiting time
Cost
Low level of service
Optimal service level
High level of service
Minimum total cost
Cost of providing service