ISM 270

1
ISM 270

• Service Engineering and Management
• Lecture 7 Forecasting and Managing Service
  Capacity

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Announcements

• Brenda Deitrich (Mathematical Sciences, IBM)
  visited UCSC today
• Should be available to watch online at
• http//ucsc.citris-uc.org/
• Project Proposal Due today
• Homework 4 due next week
• 15 check for Responsive Learning Technologies
• Final four weeks
• Forecasting and Capacity Planning
• Supply Chains in Services
• Capacity Management Game
• Project Presentations

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Today

• Forecasting
• Queueing Models

4
Forecasting Demand for Services
5
Forecasting Models

• Subjective Models Delphi Methods
• Causal Models Regression Models
• Time Series Models Moving Averages Exponential
  Smoothing

6
Delphi ForecastingQuestion In what future
election will a woman become president of the
united states for the first time?
Year 1st Round Positive Arguments 2nd Round Negative Arguments 3rd Round
2008
2012
2016
2020
2024
2028
2032
2036
2040
2044
2048
2052
Never
Total
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N Period Moving Average
Let MAT The N period moving average at the
end of period T AT Actual
observation for period T Then MAT (AT AT-1
AT-2 .. AT-N1)/N Characteristics
Need N observations to make a forecast
Very inexpensive and easy to understand
Gives equal weight to all observations
Does not consider observations older than N
periods
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Moving Average Example
Saturday Occupancy at a 100-room Hotel

Three-period Saturday
Period Occupancy Moving Average
Forecast Aug. 1 1
79 8
2 84 15
3 83 82
22 4
81 83 82 29 5
98 87 83 Sept. 5
6 100 93 87
12 7 93


9
Exponential Smoothing
Let ST Smoothed value at end of period T
AT Actual observation for period T FT1
Forecast for period T1 Feedback control
nature of exponential smoothing New value
(ST ) Old value (ST-1 ) observed error

or
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Exponential SmoothingHotel Example
Saturday Hotel Occupancy ( 0.5)
Actual
Smoothed Forecast
Period Occupancy
Value Forecast
Error Saturday t
At St
Ft At -
Ft Aug. 1 1
79 79.00 8 2
84 81.50 79 5 15
3 83 82.25
82 1 22 4
81 81.63 82 1 29
5 98 89.81
82 16 Sept. 5 6
100 94.91 90 10
Mean
Absolute Deviation (MAD) 6.6



Forecast Error (MAD) SlAt Ftl/n

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Exponential SmoothingImplied Weights Given Past
Demand
Substitute for
If continued
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Exponential Smoothing Weight Distribution
Relationship Between and N
(exponential smoothing constant) 0.05 0.1
0.2 0.3 0.4 0.5 0.67 N (periods
in moving average) 39 19 9
5.7 4 3 2
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Saturday Hotel Occupancy
Effect of Alpha ( 0.1 vs. 0.5)
Actual
Forecast
Forecast
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Recall from Charles NgStart with historical
volume What explains changes over time?
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Pull out the Influence of Seasonality and Trend
16
Estimate the relationship of price and promotion
changes to volume
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Once estimated separately, all these effects can
be combined to predict volume. This is the
model.
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Exponential Smoothing With Trend Adjustment
Commuter Airline Load Factor Week Actual
load factor Smoothed value Smoothed
trend Forecast Forecast error t
At St
Tt
Ft At - Ft 1
31 31.00
0.00 2 40
35.50 1.35
31 9 3
43 39.93 2.27 37 6 4
52
47.10 3.74 42
10 5 49
49.92 3.47
51 2 6
64 58.69
5.06 53
11 7 58
60.88 4.20
64 6 8
68 66.54
4.63 65
3

MAD
6.7
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Exponential Smoothing with Seasonal Adjustment
Ferry Passengers taken to a Resort Island
Actual
Smoothed Index Forecast
Error Period t At
value St It
Ft At - Ft

2003 January 1 1651
.. 0.837
.. February 2
1305 ..
0.662 .. March
3 1617 ..
0.820 .. April
4 1721 ..
0.873 .. May
5 2015 ..
1.022 .. June
6 2297 ..
1.165 .. July
7 2606 ..
1.322 .. August
8 2687 ..
1.363 .. September
9 2292 ..
1.162 .. October 10
1981 ..
1.005 .. November 11
1696 ..
0.860 .. December 12 1794
1794.00 0.910
..
2004 January 13
1806 1866.74 0.876 -
-
February 14 1731
2016.35 0.721 1236 495 March
15 1733 2035.76
0.829 1653 80
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More sophisticated forecasting techniques

• Nonlinear Regression
• Data mining
• Machine Learning
• Simulation-based

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Managing Waiting Lines Queueing Models
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Essential Features of Queuing Systems
Renege
Arrival process
Departure
Queue discipline
Calling population
Service process
Queue configuration
No future need for service
Balk
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Arrival Process
Arrival process
Static
Dynamic
Random arrivals with constant rate
Random arrival rate varying with time
Facility- controlled
Customer- exercised control
Appointments
Price
Accept/Reject
Balking
Reneging
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Distribution of Patient Interarrival Times

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Temporal Variation in Arrival Rates

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Poisson and Exponential Equivalence

• Poisson distribution for number of arrivals per
  hour (top view)
• 
  
• 
  One-hour
• 1 2 0
  1 interval
• Arrival Arrivals Arrivals
  Arrival

62 min.
40 min.
123 min.
Exponential distribution of time between arrivals
in minutes (bottom view)
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Queue Configurations

Multiple Queue
Single queue
Take a Number

Enter
3
4
2
8
6
10
12
7
11
9
5
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Queue Discipline

Queue discipline
Static (FCFS rule)
Dynamic
selection based on status of queue
Selection based on individual customer attributes
Number of customers waiting
Round robin
Priority
Preemptive
Processing time of customers (SPT rule)
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Queuing Formulas
Single Server Model with Poisson Arrival and
Service Rates M/M/1 1. Mean arrival rate 2.
Mean service rate 3. Mean number in service 4.
Probability of exactly n customers in the
system 5. Probability of k or more customers
in the system 6. Mean number of customers in the
system 7. Mean number of customers in
queue 8. Mean time in system 9. Mean time in
queue
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Queuing Formulas (cont.)
Single Server General Service Distribution
Model M/G/1 Mean number of customers in queue
for two servers M/M/2 Relationships among
system characteristics (Littles Law for ALL
queues)
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Congestion as
100 10 8 6 4 2 0
With
Then
0 0 0.2 0.25 0.5 1 0.8
4 0.9 9 0.99 99
0
1.0
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Single Server General Service Distribution Model
M/G/1
1. For Exponential Distribution
2. For Constant Service Time
3. Conclusion Congestion measured by Lq is
accounted for equally by variability in
arrivals and service times.
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Queuing System Cost Tradeoff

• Let Cw Cost of one customer waiting in
  queue for an hour
• Cs Hourly cost per server
• C Number of servers
• Total Cost/hour Hourly Service Cost Hourly
  Customer Waiting Cost
• Total Cost/hour Cs C Cw Lq
• Note Only consider systems where

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General Queuing Observations
1. Variability in arrivals and service times
contribute equally to congestion as measured
by Lq. 2. Service capacity must exceed
demand. 3. Servers must be idle some of the
time. 4. Single queue preferred to multiple
queue unless jockeying is permitted. 5.
Large single server (team) preferred to
multiple-servers if minimizing mean time in
system, WS. 6. Multiple-servers preferred to
single large server (team) if minimizing mean
time in queue, WQ.
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Laws of Service

• Maisters First LawCustomers compare
  expectations with perceptions.
• Maisters Second LawIs hard to play catch-up
  ball.
• Skinners LawThe other line always moves
  faster.
• Jenkins CorollaryHowever, when you switch to
  another other line, the line you left moves
  faster.

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Managing Capacity and Demand
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Segmenting Demand at a Health Clinic

Smoothing Demand by Appointment Scheduling Day
Appointments Monday
84 Tuesday
89 Wednesday
124 Thursday
129 Friday
114
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Hotel Overbooking Loss Table

• 
  Number of Reservations Overbooked
• No- Prob-
• shows ability 0 1
  2 3 4 5
  6 7 8 9
• 0 .07 0
  100 200 300 400 500
  600 700 800 900
• 1 .19 40 0
  100 200 300 400
  500 600 700 800
• 2 .22 80
  40 0 100 200 300
  400 500 600 700
• 3 .16 120 80
  40 0 100 200
  300 400 500 600
• 4 .12 160 120
  80 40 0 100
  200 300 400 500
• 5 .10 200 160
  120 80 40 0
  100 200 300 400
• 6 .07 240 200
  160 120 80 40
  0 100 200 300
• 7 .04 280 240
  200 160 120 80
  40 0 100 200
• 8 .02 320 280
  240 200 160 120
  80 40 0 100
• 9 .01 360 320
  280 240 200 160
  120 80 40 0
• Expected loss, 121.60 91.40 87.80
  115.00 164.60 231.00 311.40 401.60
  497.40 560.00

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Daily Scheduling of Telephone Operator Workshifts

Topline profile
Scheduler program assigns tours so that the
number of operators present each half hour
adds up to the number required
Tour
12 2 4 6 8 10
12 2 4 6 8 10
12
12 2 4 6 8 10
12 2 4 6 8 10
12
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LP Model for Weekly Workshift Schedule with Two
Days-off Constraint

Schedule matrix, x day off Operator
Su M Tu W
Th F Sa 1
x x
...
2 x
x
3
... x x
4
... x x
5

x x
6
x x
7
x
x 8
x
x Total
6 6 5
6 5 5
7 Required 3 6
5 6 5 5
5 Excess 3
0 0 0 0
0 2
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Seasonal Allocation of Rooms by Service Class for
Resort Hotel

First class Standard Budget
20
20
20
30
50
30
50
60
Percentage of capacity allocated to different
service classes
50
30
30
10
Peak Shoulder
Off-peak Shoulder (30)
(20) (40)
(10) Summer Fall
Winter
Spring Percentage of capacity allocated to
different seasons
42
Demand Control Chart for a Hotel

Expected Reservation Accumulation
2 standard deviation control limits
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Yield Management Using the Critical Fractile
Model

Where x seats reserved for full-fare
passengers d demand for full-fare
tickets p proportion of economizing
(discount) passengers Cu lost revenue
associated with reserving one too few seats at
full fare (underestimating demand). The lost
opportunity is the difference between the fares
(F-D) assuming a passenger, willing to pay
full-fare (F), purchased a seat at the discount
(D) price. Co cost of reserving one to
many seats for sale at full-fare (overestimating
demand). Assume the empty full-fare seat
would have been sold at the discount price.
However, Co takes on two values, depending on
the buying behavior of the passenger who would
have purchased the seat if not reserved for
full-fare.
if an economizing passenger
if a full fare
passenger (marginal gain) Expected value of Co
pD-(1-p)(F-D) pF - (F-D)