OPSM 301 Operations Management Class 13: Service Design Waiting-Line Models Koç University Zeynep Aksin [email protected].

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


ServerCustomerArrivals


Server


Server

CustomerDepartures


Server

Queue(waiting line)Customer

Arrivals

CustomerDepartures


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?


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


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


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?


Average number of cars in the system

17330= . Lq

0061 = 30

25 +.1733 = + = .LL qs

+ =

qs LL

(by interpolation)


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

OPSM 301 Operations Management Class 13: Service Design Waiting-Line Models Koç University Zeynep Aksin [email protected].

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