B7801: Operations Management
27 March 1998 - Agenda
•Mass Customization
•National Cranberry Cooperative
•Capacity Management
•Queue and customer management
Why is capacity management important?
1) Driver of Financial Performance
ROA =
PROFIT
MARGIN
ASSET
x TURNOVER
•direct labor
•overhead costs
•productivity
•facility utilization
•equipment utilization
•inventory turnover
2) Driver of Operating Performance
delivery performance
• fill rate
• lead time
service levels
• wait times
• availability
increasing
Capacity Utilization
decreasing
Matching demand and capacity
# units/hr.
poor service / lost revenue
excess assets
and costs
capacity
demand
time
How do firms match capacity to demand?
Key steps in capacity planning
STEP 1: Forecast demand
– forecast quantities
– forecast methods
– understanding errors and uncertainties
What is demand for our
product/service like?
What are its main characteristics?
How accurately can we predict it?
STEP 2: Assess the options for meeting demand
–
–
–
–
capacity increases/decreases
capacity allocation
inventory
demand management
STEP 3: Construct and evaluate the plans
– planning methodology
– evaluation/robustness
• scenario analysis
• simulation
What options do we have available
to meet demand?
What constraints do we face?
What is the relationship between
capacity and service levels?
What is our cost structure?
How do we go about developing a
plan?
What is the effect of forecast
uncertainty on plan performance?
A hierarchy of time scales
Long Term
(1-10 yrs.)
Medium Term
(3 mon. - 1 yr.)
Short Term
(hourly, daily,wkly)
facility expansion
hiring/firing
technology investments
make/buy
capacity allocation
hiring/firing
overtime
inventory build-up
detailed prod. scheduling
staff scheduling
detailed allocation
An example: National Cranberry Cooperative
•
Forecasting demand
– peak season same as previous year
– no increase in total volume
– increase to 70% wet
•
Assessing options to meet demand
– do nothing
– overtime
– capacity expansion (bins, dryers)
•
Constructing and evaluating a plan
– methodology (trial and error, incremental analysis)
– process flow analysis to determine cost/performance
• overtime cost
• truck backup
– evaluation/robustness
• average cost/benefit estimates
• worst-case performance (peak day) (also remember McDonald’s,BK!!)
• simulation
•
Time scales (med: add dryer, short: overtime on demand)
Forecasting
•
What to forecast
– level of aggregation
• one location vs. region
• individual product vs. product family
• daily, weekly or monthly
Aggregate where possible, but
keep enough detail to make your
planning decisions.
– trade-off: detail vs. forecast accuracy
•
Forecast methodology
– subjective methods (Delphi method)
– time series (exponential smoothing)
– causal methods (regression)
•
Forecast errors
– point estimate = “best guess”
– magnitude of error
• MAD (mean absolute deviation)
• MSD (mean square deviation)
– distribution of errors
If data is available and product or
service is mature, use data
intensive methods; otherwise,
resort to subjective methods.
Try to quantify forecast errors as
well as point estimates. Factor
forecast uncertainty into your
plans.
Ex: Aggregate planning in an ice tea bottling plant
•
•
•
•
demand forecast next 9 months:
27, 20, 36, 45, 78, 97, 118, 121, 82 (x10,000 units (12-oz.))
20 workers required
capacity is 3,000 units/hour
wages:
– $15/hr regular time
– $16/hr second shift (8 hr shifts)
– $20/hr overtime
•
hiring/firing
– 16 hrs. of training @ $15/hr.
– 80 hrs. severance pay @ $16/hr.
•
•
•
500,000 unit warehouse. Extra storage is $1/month per 100 units.
unit revenue = $0.40, unit cost (material) = $0.20
$2M working capital line of credit (18% per year). Current balance is $1M.
Strategy 1: Chase demand
(production = demand)
Monthly Demand/Production
x10,000 units/month
140
120
100
80
60
40
20
Jan
Feb
Mar
April
May
Demand
June
Prod
July
Aug
Sept
Chase strategy financials
J an
Feb
Ma r
April
Ma y
J une
J uly
Aug
Sept
Uni ts
Dem and
Sale s
Rev . (Ca sh In)
Labor Hrs. Av a il
(x 10,000 uni ts)
(x 10,000 uni ts)
(x $10,000 )
Std (x 100 hrs)
2 nd Sh irt (x 100 hrs)
OT (x 100 hrs)
Produc tion Plan
Prod . Ou tp ut (x 10,000 uni ts)
New Hire s
No. Fi red
Reg . Ho urs (x 100 hrs)
2 nd Sh ift Hrs (x 100 hrs)
OT Ho urs (x 100 hrs)
Ext. WH (x 10,000 uni ts)
Inv e ntory
Start (x 10,000 uni ts)
End (x 10,000 uni ts)
Units in WH
(x 10,000 uni ts)
Co. (x 10,000 uni ts)
Extern (x 10,000 uni ts)
Cas h Out
Opera tions
Ma teri al s (x $10,000 )
Std La bo r (x $10,000 )
2 nd Sh ift La bo r (x $10,000 )
OT La bo r (x $10,000 )
Hi ri n g Cost (x $10,000 )
Firi ng Co st (x $10,000 )
Ext. WH (x $10,000 )
Plant Financing Cos ts
Fin . Co st (pre v. m on .) (x $10,000 )
Total Ca sh Out
(x $10,000 )
Cas h Bala nc e
(x $10,000 )
Total Pla n Rev .
Total Ope r. Cst
Total Fin. Cst.
Plant Earnings
(x $10,000 )
(x $10,000 )
(x $10,000 )
(x $10,000 )
2 7.00
2 7.00
1 0.80
2 0.00
2 0.00
8 .0 0
3 6.00
3 6.00
1 4.40
4 5.00
4 5.00
1 8.00
7 8.00
7 8.00
3 1.20
9 7.00
9 7.00
3 8.80
1 18 .0 0
1 18 .0 0
4 7.20
1 21 .0 0
1 21 .0 0
4 8.40
8 2.00
8 2.00
3 2.80
3 2.00
0 .0 0
1 6.00
3 2.00
0 .0 0
1 6.00
3 2.00
0 .0 0
1 6.00
3 2.00
0 .0 0
1 6.00
3 2.00
3 2.00
1 6.00
3 2.00
3 2.00
1 6.00
3 2.00
3 2.00
1 6.00
3 2.00
3 2.00
1 6.00
3 2.00
3 2.00
1 6.00
2 4.00
0
0
1 6.00
0 .0 0
0 .0 0
0 .0 0
2 4.00
0
0
1 6.00
0 .0 0
0 .0 0
0 .0 0
3 6.00
0
0
2 4.00
0 .0 0
0 .0 0
0 .0 0
4 8.00
20
0
3 2.00
0 .0 0
0 .0 0
0 .0 0
7 2.00
0
0
3 2.00
1 6.00
0 .0 0
0 .0 0
9 6.00
0
0
3 2.00
3 2.00
0 .0 0
0 .0 0
1 20 .0 0
0
0
3 2.00
3 2.00
1 6.00
0 .0 0
1 20 .0 0
0
0
3 2.00
3 2.00
1 6.00
0 .0 0
8 4.00
0
20
3 2.00
2 4.00
0 .0 0
0 .0 0
2 0.00
1 7.00
1 7.00
2 1.00
2 1.00
2 1.00
2 1.00
2 4.00
2 4.00
1 8.00
1 8.00
1 7.00
1 7.00
1 9.00
1 9.00
1 8.00
1 8.00
2 0.00
1 7.00
0 .0 0
2 1.00
0 .0 0
2 1.00
0 .0 0
2 4.00
0 .0 0
1 8.00
0 .0 0
1 7.00
0 .0 0
1 9.00
0 .0 0
1 8.00
0 .0 0
2 0.00
0 .0 0
4 .8 0
2 .4 0
0 .0 0
0 .0 0
0 .0 0
0 .0 0
0 .0 0
4 .8 0
2 .4 0
0 .0 0
0 .0 0
0 .0 0
0 .0 0
0 .0 0
7 .2 0
3 .6 0
0 .0 0
0 .0 0
0 .0 0
0 .0 0
0 .0 0
9 .6 0
4 .8 0
0 .0 0
0 .0 0
0 .4 8
0 .0 0
0 .0 0
1 4.40
4 .8 0
2 .5 6
0 .0 0
0 .0 0
0 .0 0
0 .0 0
1 9.20
4 .8 0
5 .1 2
0 .0 0
0 .0 0
0 .0 0
0 .0 0
2 4.00
4 .8 0
5 .1 2
3 .2 0
0 .0 0
0 .0 0
0 .0 0
2 4.00
4 .8 0
5 .1 2
3 .2 0
0 .0 0
0 .0 0
0 .0 0
1 6.80
4 .8 0
3 .8 4
0 .0 0
0 .0 0
2 .5 6
0 .0 0
1 .5 0
8 .7 0
-97 .90
1 .4 7
8 .6 7
-98 .57
1 .4 8
1 2.28
-96 .45
1 .4 5
1 6.33
-94 .77
1 .4 2
2 3.18
-86 .76
1 .3 0
3 0.42
-78 .38
1 .1 8
3 8.30
-69 .47
1 .0 4
3 8.16
-59 .23
0 .8 9
2 8.89
-55 .32
$ 24 9.60
$ 19 3.20
$ 11 .7 2
$ 44 .6 8
1 00 .0 0%
7 7.40 %
4 .7 0%
1 7.90 %
Strategy 2: Level production
Monthly Demand/Production
x10,000 units/month
140
120
100
80
60
40
20
Jan
Feb
Mar
April
May
Demand
June
Prod
July
Aug
Sept
Level strategy financials
J an
Feb
Ma r
April
Ma y
J une
J uly
Aug
Sept
Uni ts
Dem and
Sale s
Rev . (Ca sh In)
Labor Hrs. Av a il
(x 10,000 uni ts)
(x 10,000 uni ts)
(x $10,000 )
Std (x 100 hrs)
2 nd Sh irt (x 100 hrs)
OT (x 100 hrs)
Produc tion Plan
Prod . Ou tp ut (x 10,000 uni ts)
New Hire s
No. Fi red
Reg . Ho urs (x 100 hrs)
2 nd Sh ift Hrs (x 100 hrs)
OT Ho urs (x 100 hrs)
Ext. WH (x 10,000 uni ts)
Inv e ntory
Start (x 10,000 uni ts)
End (x 10,000 uni ts)
Units in WH
(x 10,000 uni ts)
Co. (x 10,000 uni ts)
Extern (x 10,000 uni ts)
Cas h Out
Opera tions
Ma teri al s (x $10,000 )
Std La bo r (x $10,000 )
2 nd Sh ift La bo r (x $10,000 )
OT La bo r (x $10,000 )
Hi ri n g Cost (x $10,000 )
Firi ng Co st (x $10,000 )
Ext. WH (x $10,000 )
Plant Financing Cos ts
Fin . Co st (pre v. m on .) (x $10,000 )
Total Ca sh Out
(x $10,000 )
Cas h Bala nc e
(x $10,000 )
Total Pla n Rev .
Total Ope r. Cst
Total Fin. Cst.
Plant Earnings
(x $10,000 )
(x $10,000 )
(x $10,000 )
(x $10,000 )
2 7.00
2 7.00
1 0.80
2 0.00
2 0.00
8 .0 0
3 6.00
3 6.00
1 4.40
4 5.00
4 5.00
1 8.00
7 8.00
7 8.00
3 1.20
9 7.00
9 7.00
3 8.80
1 18 .0 0
1 18 .0 0
4 7.20
1 21 .0 0
1 21 .0 0
4 8.40
8 2.00
8 2.00
3 2.80
3 2.00
0 .0 0
1 6.00
3 2.00
1 6.00
1 6.00
3 2.00
1 6.00
1 6.00
3 2.00
1 6.00
1 6.00
3 2.00
1 6.00
1 6.00
3 2.00
1 6.00
1 6.00
3 2.00
1 6.00
1 6.00
3 2.00
1 6.00
1 6.00
3 2.00
1 6.00
1 6.00
6 9.33
10
0
3 2.00
0 .0 0
1 4.22
1 2.33
6 9.33
0
0
3 2.00
1 4.22
0 .0 0
6 1.67
6 9.33
0
0
3 2.00
1 4.22
0 .0 0
9 5.00
6 9.33
0
0
3 2.00
1 4.22
0 .0 0
1 19 .3 3
6 9.33
0
0
3 2.00
1 4.22
0 .0 0
1 10 .6 7
6 9.33
0
0
3 2.00
1 4.22
0 .0 0
8 3.00
6 9.33
0
0
3 2.00
1 4.22
0 .0 0
3 4.33
6 9.33
0
0
3 2.00
1 4.22
0 .0 0
0 .0 0
6 9.33
0
0
3 2.00
1 4.22
0 .0 0
0 .0 0
2 0.00
6 2.33
6 2.33
1 11 .6 7
1 11 .6 7
1 45 .0 0
1 45 .0 0
1 69 .3 3
1 69 .3 3
1 60 .6 7
1 60 .6 7
1 33 .0 0
1 33 .0 0
8 4.33
8 4.33
3 2.66
3 2.66
2 0.00
5 0.00
1 2.33
5 0.00
6 1.67
5 0.00
9 5.00
5 0.00
1 19 .3 3
5 0.00
1 10 .6 7
5 0.00
8 3.00
5 0.00
3 4.33
3 2.66
0 .0 0
2 0.00
0 .0 0
1 3.87
4 .8 0
0 .0 0
2 .8 4
0 .2 4
0 .0 0
0 .1 2
1 3.87
4 .8 0
2 .2 8
0 .0 0
0 .0 0
0 .0 0
0 .6 2
1 3.87
4 .8 0
2 .2 8
0 .0 0
0 .0 0
0 .0 0
0 .9 5
1 3.87
4 .8 0
2 .2 8
0 .0 0
0 .0 0
0 .0 0
1 .1 9
1 3.87
4 .8 0
2 .2 8
0 .0 0
0 .0 0
0 .0 0
1 .1 1
1 3.87
4 .8 0
2 .2 8
0 .0 0
0 .0 0
0 .0 0
0 .8 3
1 3.87
4 .8 0
2 .2 8
0 .0 0
0 .0 0
0 .0 0
0 .3 4
1 3.87
4 .8 0
2 .2 8
0 .0 0
0 .0 0
0 .0 0
0 .0 0
1 3.87
4 .8 0
2 .2 8
0 .0 0
0 .0 0
0 .0 0
0 .0 0
1 .5 0
2 3.37
-11 2.5 7
1 .6 9
2 3.25
-12 7.8 2
1 .9 2
2 3.81
-13 7.2 3
2 .0 6
2 4.19
-14 3.4 3
2 .1 5
2 4.20
-13 6.4 3
2 .0 5
2 3.82
-12 1.4 4
1 .8 2
2 3.11
-97 .35
1 .4 6
2 2.40
-71 .35
1 .0 7
2 2.01
-60 .57
$ 24 9.60
$ 19 4.45
$ 15 .7 1
$ 39 .4 3
1 00 .0 0%
7 7.91 %
6 .3 0%
1 5.80 %
Strategy 3: Mixed
Monthly Demand/Production
x10,000 units/month
140
120
100
80
60
40
20
Jan
Feb
Mar
April
May
Demand
June
Prod
July
Aug
Sept
Mixed strategy financials
J an
Feb
Ma r
April
Ma y
J une
J uly
Aug
Sept
Uni ts
Dem and
Sale s
Rev . (Ca sh In)
Labor Hrs. Av a il
(x 10,000 uni ts)
(x 10,000 uni ts)
(x $10,000 )
Std (x 100 hrs)
2 nd Sh irt (x 100 hrs)
OT (x 100 hrs)
Produc tion Plan
Prod . Ou tp ut (x 10,000 uni ts)
New Hire s
No. Fi red
Reg . Ho urs (x 100 hrs)
2 nd Sh ift Hrs (x 100 hrs)
OT Ho urs (x 100 hrs)
Ext. WH (x 10,000 uni ts)
Inv e ntory
Start (x 10,000 uni ts)
End (x 10,000 uni ts)
Units in WH
(x 10,000 uni ts)
Co. (x 10,000 uni ts)
Extern (x 10,000 uni ts)
Cas h Out
Opera tions
Ma teri al s (x $10,000 )
Std La bo r (x $10,000 )
2 nd Sh ift La bo r (x $10,000 )
OT La bo r (x $10,000 )
Hi ri n g Cost (x $10,000 )
Firi ng Co st (x $10,000 )
Ext. WH (x $10,000 )
Plant Financing Cos ts
Fin . Co st (pre v. m on .) (x $10,000 )
Total Ca sh Out
(x $10,000 )
Cas h Bala nc e
(x $10,000 )
Total Pla n Rev .
Total Ope r. Cst
Total Fin. Cst.
Plant Earnings
(x $10,000 )
(x $10,000 )
(x $10,000 )
(x $10,000 )
2 7.00
2 7.00
1 0.80
2 0.00
2 0.00
8 .0 0
3 6.00
3 6.00
1 4.40
4 5.00
4 5.00
1 8.00
7 8.00
7 8.00
3 1.20
9 7.00
9 7.00
3 8.80
1 18 .0 0
1 18 .0 0
4 7.20
1 21 .0 0
1 21 .0 0
4 8.40
8 2.00
8 2.00
3 2.80
3 2.00
0 .0 0
1 6.00
3 2.00
0 .0 0
1 6.00
3 2.00
0 .0 0
1 6.00
3 2.00
0 .0 0
1 6.00
3 2.00
3 2.00
1 6.00
3 2.00
3 2.00
1 6.00
3 2.00
3 2.00
1 6.00
3 2.00
3 2.00
1 6.00
3 2.00
3 2.00
1 6.00
2 4.00
0
0
1 6.00
0 .0 0
0 .0 0
0 .0 0
2 4.00
0
0
1 6.00
0 .0 0
0 .0 0
0 .0 0
4 8.00
0
0
3 2.00
0 .0 0
0 .0 0
0 .0 0
4 8.00
20
0
3 2.00
0 .0 0
0 .0 0
0 .0 0
9 6.00
0
0
3 2.00
3 2.00
0 .0 0
4 .0 0
9 6.00
0
0
3 2.00
3 2.00
0 .0 0
3 .0 0
9 6.00
0
0
3 2.00
3 2.00
0 .0 0
0 .0 0
9 6.00
0
0
3 2.00
3 2.00
0 .0 0
0 .0 0
9 6.00
0
20
3 2.00
3 2.00
0 .0 0
0 .0 0
2 0.00
1 7.00
1 7.00
2 1.00
2 1.00
3 3.00
3 3.00
3 6.00
3 6.00
5 4.00
5 4.00
5 3.00
5 3.00
3 1.00
3 1.00
6 .0 0
6 .0 0
2 0.00
1 7.00
0 .0 0
2 1.00
0 .0 0
3 3.00
0 .0 0
3 6.00
0 .0 0
5 0.00
4 .0 0
5 0.00
3 .0 0
3 1.00
0 .0 0
6 .0 0
0 .0 0
2 0.00
0 .0 0
4 .8 0
2 .4 0
0 .0 0
0 .0 0
0 .0 0
0 .0 0
0 .0 0
4 .8 0
2 .4 0
0 .0 0
0 .0 0
0 .0 0
0 .0 0
0 .0 0
9 .6 0
4 .8 0
0 .0 0
0 .0 0
0 .0 0
0 .0 0
0 .0 0
9 .6 0
4 .8 0
0 .0 0
0 .0 0
0 .4 8
0 .0 0
0 .0 0
1 9.20
4 .8 0
5 .1 2
0 .0 0
0 .0 0
0 .0 0
0 .0 4
1 9.20
4 .8 0
5 .1 2
0 .0 0
0 .0 0
0 .0 0
0 .0 3
1 9.20
4 .8 0
5 .1 2
0 .0 0
0 .0 0
0 .0 0
0 .0 0
1 9.20
4 .8 0
5 .1 2
0 .0 0
0 .0 0
0 .0 0
0 .0 0
1 9.20
4 .8 0
5 .1 2
0 .0 0
0 .0 0
2 .5 6
0 .0 0
1 .5 0
8 .7 0
-97 .90
1 .4 7
8 .6 7
-98 .57
1 .4 8
1 5.88
-10 0.0 5
1 .5 0
1 6.38
-98 .43
1 .4 8
3 0.64
-97 .86
1 .4 7
3 0.62
-89 .68
1 .3 5
3 0.47
-72 .95
1 .0 9
3 0.21
-54 .76
0 .8 2
3 2.50
-54 .46
$ 24 9.60
$ 19 1.91
$ 12 .1 5
$ 45 .5 4
1 00 .0 0%
7 6.89 %
4 .8 7%
1 8.24 %
Components of the Queuing Phenomenon
Servicing System
Servers
Customer
Arrivals
Waiting Line
Exit
Some Service Generalizations
1. Everyone is an expert on services.
2. Services are idiosyncratic.
3. Quality of work is not quality of service.
4. High-contact services are experienced, whereas goods
are consumed.
5. We cannot inventory services (capacity becomes
dominant issue)
Capacity Management in Services
• You cannot store service
output
• If you cannot store output,
you store the demand
Strategic Service Vision
• Who is our customer?
• How do we differentiate our service in
the market?
• What is our service package and the
focus?
• What are the actual processes,
systems, people, technology and
leadership?
Service-System Design Matrix
Degree of customer/server contact
High
none
some
much
Low
Face-to-face
total
customization
Face-to-face
loose specs
Sales
Opportunity
Face-to-face
tight specs
On-site
technology
Production
Efficiency
Phone
Contact
Mail contact
Low
High
Three Contrasting Service Designs
• The production line approach
• The self-service approach
• The personal attention approach
Some Performance Measures
•
•
•
•
Average time spent waiting in queue
Average time in system
Average length of queue
Average number of customers in
system
• Probability that a customer waits
before service begins
• Server utilization
Strategies for effective capacity management
• Maximize process flexibility
– mix flexibility
– volume flexibility
• Standardize the product/service reduce variety
– risk pooling
– reduced forecast error
• Centralize operations
– risk pooling
– reduced forecast error
• Reduce lead time
– reduced forecast error
– minimize overshooting/undershooting demand
Some Service Generalizations
1. Everyone is an expert on services.
2. Services are idiosyncratic.
3. Quality of work is not quality of
service.
Some Service Generalizations
4. High-contact services are experienced, whereas
goods are consumed.
5. Effective management of services requires an
understanding of marketing and personnel, as
well as operations.
6. Services often take the form of cycles of
encounters involving face-to-face, phone,
electromechanical, and/or mail interactions
Characteristics of a WellDesigned Service System
1. Each element of the service system is consistent
with the operating focus of the firm.
2. It is user-friendly.
3. It is robust.
4. It is structured so that consistent performance by
its people and systems is easily maintained
Characteristics of a WellDesigned Service System
5. It provides effective links between the
back office and the front office so that
nothing falls between the cracks.
6. It manages the evidence of service quality
in such a way that customers see the value
of the service provided.
7. It is cost-effective
Components of the Queuing
Phenomenon
Servers
Customer
Arrivals
Waiting Line
Exit
Customers arrivals to a bank
• Average customers per minute = 10
• Average service time = 30 seconds
– HOW MANY TELLERS ARE NEEDED?
Case I:
Case II:
Case III:
No variability
Variability in arrival process
Variability in arrival & service processes
How many tellers?: Variability in both arrival
and service processes
# Tellers
Avg. Delay
Utilization
6
17.6
0.833
7
4.9
0.714
8
1.7
0.625
9
0.6
0.556
Methods for reducing impact of
variability
• Demand
– better forecasting
– pricing
– appointment systems
• Process
–
–
–
–
–
–
standardization
training
automation
self-service
variable staffing
use of inventory
Tools for capacity planning in
service systems
• Queueing models
– fast
– little data needed
• Simulation
– can handle complexity
• Linear programming
– to allocate capacity over multiple facilities or multiple
locations
– scheduling and other constraints can be readily
incorporated
Line Structures
Single
Phase
Multiphase
Single Channel
One-person
barber shop
Car wash
Multichannel
Bank tellers’
windows
Hospital
admissions
Degree of Patience
No Way!
BALK
No Way!
RENEG
Key facts needed for a model
• Average number of customer arrivals
per unit of time
• Average service time per customer
• The number of servers
Assumptions in our models
•
•
•
•
•
•
•
FCFS
Events occur one at a time
We are interested in long run avg performance
Unlimited storage
Utilization < 100%
No predictable variation
Unpredictable variation
– arrivals - Poisson processes
– service - exponential distributed processing times
Operating Focus
• Customer treatment
• Speed and convenience of service delivery
• Variety of services
• Quality of tangibles
• Unique skills
Service-System Design Matrix
Degree of customer/server contact
Buffered
core (none)
High
Permeable
system (some)
Reactive
system (much)
Low
Face-to-face
total
customization
Face-to-face
loose specs
Sales
Opportunity
Face-to-face
tight specs
On-site
technology
Production
Efficiency
Phone
Contact
Mail contact
Low
High
Three Contrasting Service
Designs
• The production line approach
• The self-service approach
• The personal attention approach
Example: Model 1
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)
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?
Example: CVS
Manager is considering two ways of using
cashiers: ( Assume customers arrive randomly
at a rate of 15 per hour)
• 1 fast clerk -- serves at an average of 2
minutes per customer
or
• 2 moderate clerks -- each serves at an
average of 4 minutes per customer
Some Performance Measures
•
•
•
•
•
Average time spent waiting in queue
Average time in system
Average length of queue
Average number of customers in system
Probability that a customer waits before
service begins
• Server utilization
Example: Model 1
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 1
B) What is the average number of customers in line?
2
(25) 2
Lq =
=
= 4.167
 (  -  ) 30(30 - 25)
C) What is the average number of customers in the system?

25
Ls =
=
=5
 -  (30 - 25)
13
Example: Model 1
D) What is the average waiting time in line?

25
Wq =
=
= .1667hrs = 10 mins
( - ) 30(30 - 25)
E) What is the average waiting time in the system?
1
1
Ws =
=
= .2 hrs = 12 mins
 -  30 - 25
14
m m s.xls
M/M/s Q ueueing Form ula Spreadsheet
In p u ts :
lam bda
mu
O u tp u ts :
s
1
D e fin itio n s o f te r m s :
25
30
Lq
4.1667
lam bda = arrival rate
m u = service rate
s
= num ber of servers
Lq
= average num ber in the queue
Ls
= average num ber in the system
Wq
= average wait in the queue
Ws
= average wait in the system
P(0) = probability of zero custom ers in the system
P(delay) = probability that an arriving custom er has to wait
Ls
Wq
5.0000
0.1667
Ws
0.2000
P (0 )
0.1667
P (d e la y )U tiliz a tio n
0.8333
0.8333
Example: CVS
Manager is considering two ways of using
cashiers: ( Assume customers arrive randomly
at a rate of 15 per hour)
• 1 fast clerk -- serves at an average of 2
minutes per customer
or
• 2 moderate clerks -- each serves at an
average of 4 minutes per customer
m m s .x ls
M /M /s Q u e u e in g F o r m u la S p r e a d s h e e t
In p u ts :
la m b d a
mu
O u tp u ts :
s
0
1
2
D e fin itio n s o f te r m s :
15
30
Lq
0 .5 0 0 0
0 .0 3 3 3
la m b d a = a r r iv a l r a te
mu
= s e r v ic e r a te
s
= n u m b e r o f s e rv e rs
Lq
= a v e r a g e n u m b e r in th e q u e u e
Ls
= a v e r a g e n u m b e r in th e s y s te m
W q
= a v e r a g e w a it in th e q u e u e
W s
= a v e r a g e w a it in th e s y s te m
P ( 0 ) = p r o b a b ility o f z e r o c u s to m e r s in th e s y s te m
P ( d e la y ) = p r o b a b ility th a t a n a r r iv in g c u s to m e r h a s to w a it
Ls
Wq
1 .0 0 0 0
0 .5 3 3 3
0 .0 3 3 3
0 .0 0 2 2
Ws
0 .0 6 6 7
0 .0 3 5 6
P (0 )
0 .5 0 0 0
0 .6 0 0 0
P ( d e l a y )U t i l i z a t i o n
0 .5 0 0 0
0 .1 0 0 0
0 .5 0 0 0
0 .2 5 0 0
m m s .x ls
M /M /s Q u e u e in g F o rm u la S p re a d s h e e t
In p u t s :
la m b d a
mu
D e f in it io n s o f t e r m s :
15
15
la m b d a = a rriv a l ra te
m u = s e rv ic e ra te
s
= n u m b e r o f s e rv e rs
Lq
= a v e ra g e n u m b e r in th e q u e u e
Ls
= a v e ra g e n u m b e r in th e s y s te m
Wq
= a v e ra g e w a it in th e q u e u e
Ws
= a v e ra g e w a it in th e s y s te m
P (0 ) = p ro b a b ility o f z e ro c u s to m e rs in th e s y s te
P (d e la y ) = p ro b a b ility th a t a n a rriv in g c u s to m e r h
O u tp u ts :
s
Lq
Ls
Wq
Ws
0
1 in f in ity in f in ity in f in ity in f in ity
2 0 .3 3 3 3 1 .3 3 3 3 0 .0 2 2 2 0 .0 8 8 9
3 0 .0 4 5 5 1 .0 4 5 5 0 .0 0 3 0 0 .0 6 9 7
P (0 )
0 .0 0 0 0
0 .3 3 3 3
0 .3 6 3 6
P ( d e la y )U t iliz a t io n
1 .0 0 0 0
0 .3 3 3 3
0 .0 9 0 9
1 .0 0 0 0
0 .5 0 0 0
0 .3 3 3 3
m m s .x ls
M /M /s Q u e u e in g F o rm u la S p re a d s h e e t
In p u t s :
la m b d a
mu
D e f in it io n s o f t e r m s :
7 .5
15
la m b d a = a rriv a l ra te
m u = s e rv ic e ra te
s
= n u m b e r o f s e rv e rs
Lq
= a v e ra g e n u m b e r in th e q u e u e
Ls
= a v e ra g e n u m b e r in th e s y s te m
Wq
= a v e ra g e w a it in th e q u e u e
Ws
= a v e ra g e w a it in th e s y s te m
P (0 ) = p ro b a b ility o f z e ro c u s to m e rs in th e s y s te m
P (d e la y ) = p ro b a b ility th a t a n a rriv in g c u s to m e r h a s to w
O u tp u ts :
s
0
1
2
3
Lq
0 .5 0 0 0
0 .0 3 3 3
0 .0 0 3 0
Ls
Wq
Ws
P (0 )
1 .0 0 0 0
0 .5 3 3 3
0 .5 0 3 0
0 .0 6 6 7
0 .0 0 4 4
0 .0 0 0 4
0 .1 3 3 3
0 .0 7 1 1
0 .0 6 7 1
0 .5 0 0 0
0 .6 0 0 0
0 .6 0 6 1
P ( d e la y )U t iliz a t io n
0 .5 0 0 0
0 .1 0 0 0
0 .0 1 5 2
0 .5 0 0 0
0 .2 5 0 0
0 .1 6 6 7
M/M/s Queue with Priority
s servers, one line, priority (high or low)
Poisson arrivals, high priority arrival rate = 1, low priority arrival rate = 2
Exponential service time, service rate at each server = 
Performance measures (high and low):
utilization,
probability of delay
average number of customers in system ===> On-line queueing spreadsheets
average throughput time
average queue length
average waiting time
M/M/s-Priority Queueing Spreadsheet
m m s _ p rio rit y . x ls
M / M / s P rio rit y Q u e u e in g F o rm u la S p re a d s h e e t
I n p u ts:
D e fi n i ti o n s o f te r m s:
la m b d a H IG H
0 .1 6 6 6 7
la m b d a H IG H = a rriva l ra t e o f h ig h p rio rit y c la s s
la m b d a L O W
0 .1 6 6 6 7
la m b d a L O W = a rriva l ra t e o f lo w p rio rit y c la s s
0 .2 5
mu
mu
= s e rvic e ra t e (a s s u m e d t h e s a m e fo r b o t h H IG H a n d L O W )
s
= n u m b e r o f s e rve rs
Lq
= a ve ra g e n u m b e r in t h e q u e u e
Ls
= a ve ra g e n u m b e r in t h e s y s t e m
Wq
= a ve ra g e w a it in t h e q u e u e
Ws
= a ve ra g e w a it in t h e s y s t e m
P (0 )
= p ro b a b ilit y o f z e ro c u s t o m e rs in t h e s y s t e m
H i g h P r i o r i ty
L o w P r i o r i ty
B o th C l a sse s
O u tp u ts:
s
Lq
Ls
Wq
Ws
U ti l i z a ti o n
Lq
Ls
Wq
Ws
U ti l i z a ti o n
P (0 )
P (d e l a y )
T o ta l U ti l .
0
1
0.6667
0.0000
1.0000
1.0000
2
in fin it y
0.2667
in fin it y
0.9333
in fin it y
1.6000
in fin it y
5.6000
0 . 6 6 6 7 in fin it y
0.3333
0.8000
in fin it y
1.4667
in fin it y
4.8000
in fin it y
8.8000
0.3333
0.2000
0.5333
0.6667
3
0.0517
0.7183
0.3099
4.3099
0.2222
0.0930
0.7596
0.5579
4.5579
0.2222
0.2542
0.1808
0.4444
4
0.0104
0.6770
0.0621
4.0621
0.1667
0.0155
0.6822
0.0932
4.0932
0.1667
0.2621
0.0518
0.3333
5
0.0019
0.6686
0.0116
4.0116
0.1333
0.0026
0.6693
0.0159
4.0159
0.1333
0.2634
0.0126
0.2667
6
0.0003
0.6670
0.0020
4.0020
0.1111
0.0004
0.6671
0.0025
4.0025
0.1111
0.2636
0.0026
0.2222
7
0.0001
0.6667
0.0003
4.0003
0.0952
0.0001
0.6667
0.0004
4.0004
0.0952
0.2636
0.0005
0.1905
8
0.0000
0.6667
0.0000
4.0000
0.0833
0.0000
0.6667
0.0001
4.0001
0.0833
0.2636
0.0001
0.1667
9
0.0000
0.6667
0.0000
4.0000
0.0741
0.0000
0.6667
0.0000
4.0000
0.0741
0.2636
0.0000
0.1481
10
0.0000
0.6667
0.0000
4.0000
0.0667
0.0000
0.6667
0.0000
4.0000
0.0667
0.2636
0.0000
0.1333
Suggestions for Managing
Queues
• Do not overlook the effects of perceptions
management.
• Determine the acceptable waiting time for
your customers.
• Install distractions that entertain and
physically involve the customer.
• Get customers out of line.
• Only make people conscious of time if they
grossly overestimate waiting times
Perceptions of waiting times
• Unoccupied delays feel longer than
occupied delays
• Pre-process delays feel longer than inprocess delays
• Anxious delays feel longer than relaxed
delays
• Unacknowledged delays feel longer than
acknowledged delays
• Waiting alone vs. waiting with others
Suggestions for Managing
Queues
• Modify customer arrival behavior.
• Keep resources not serving customers out
of sight.
• Segment customers by personality types.
• Adopt a long-term perspective.
• Never underestimate the power of a
friendly server
What did we learn?