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Process Analysis and Design Operations Strategy Process Analysis Manufacturing Service System Design Matrix Service Blueprinting Service Classifications Waiting Line Analysis Services 62

Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

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Page 1: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Process Analysis and Design

Operations Strategy Process Analysis Manufacturing

Service SystemDesign Matrix

Service Blueprinting

Service Classifications

Waiting Line Analysis

Services

62

Page 2: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

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

63

Page 3: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

Suggestions for Managing Queues1. Determine an acceptable waiting time

2. Divert customer’s attention while waiting

3. Inform your customers of what to expect

4. Keep other employees out of sight

5. Segment customers

6. Train employees to be friendly

7. Encourage customers during slack periods

8. Adopt a long-term perspective

63

Page 4: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

Suggestions for Managing QueuesFor 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.

63

Page 5: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

Components of the Queuing Phenomenon

CustomerArrivals

Server(s)

Waiting Line

Servicing System

Exit

PopulationSource?Infinite or

Finite

Service Rate?Constant or

Variable

Infinite Queue LengthFCFS

Balking or Reneging?

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Page 6: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

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)

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Page 7: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

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!

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Page 8: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

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.

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Page 9: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

Line Structures

Single Channel

Multichannel

SinglePhase

Multiphase

One-personbarber shop

Car wash

Hospitaladmissions

Bank tellers’windows

65

(Also, “Mixed”; See text pages 251-52)

Page 10: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

Properties of Waiting Line Models

Model LayoutSourcePopulation Service Pattern

1 Single channel Infinite Exponential

2 Single channel Infinite Constant

3 Multichannel Infinite Exponential

4 Single or Multi Finite Exponential

These four models share the following characteristics:· Single phase· Poisson arrival· FCFS· Unlimited queue length

66

(See formulas for each model in text on page 253)

Page 11: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

Waiting Line ModelsCharacteristics 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 system67

Page 12: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

 Characteris-

tics of Waiting

Lines

  

Definition

Model 1(single

channel,exp. service

rate)

Model 2(single

channel,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 system1/(-) orWq +(1/) 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)

Page 13: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

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

Page 14: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

.8333 = cust/hr 30

cust/hr 25 = =

cust/hr 30 = mins) (1hr/60 mins 2

customer 1 =

cust/hr 25 =

Example: Model 1 (worked problem)

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) =

) - ( L

22

q

WP2

Page 15: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

Example: Model 1 (worked problem)C) What is the average number of customers in the system?

5 = 25)- (30

25 =

- =

s

L

D) What is the average waiting time in line?

mins 10 = hrs .1667 = 25)-030(3

25 =

) - ( =

qW

WP3

Page 16: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

Example: Model 1 (worked problem)E) What is the average waiting time in the system?

mins 12 = hrs .2 = 25-30

1 =

-

1 =

s W

F) What is the probability that exactly two cars will bein the system (one being served and the other waiting in line)?

p = (1-n

n

)( ) p = (1- = 2

225

30

25

30)( ) .1157

WP4

Page 17: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

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

Page 18: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

Example: Model 2 (worked problem)

A) The average number of customers in line.

B) The average waiting time in the system.

= + = .06667 hrs +

1

15 / hr = .1333 hrs =

1 8 mins

= ( - )

= (10)

(2)(15)(15 - 10) =

2 2 2

.6667

Wq = ( - )

= )( - 10)

= .06667 hrs =

210

2 15 15(4 mins

WP6

Ws Wq

Lq

Page 19: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

Approximating Customer Waiting Time

70

A “quick and dirty” method has been developed to compute average waiting time for multiple servers (see text, pp. 261-2). 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.

Page 20: Process Analysis and Design Operations StrategyProcess AnalysisManufacturing Service System Design Matrix Service Blueprinting Service Classifications

Irwin/McGraw-Hill

Utilization and Time in System

0

30

60

90

120

150

50% 60% 70% 80% 90% 100%Utilization

Tim

e in

Sys

tem

70