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ISM 270 Service Engineering and Management Lecture 6: Forecasting

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Vijay Mehrotra Director and Associate Professor, San Francisco University Author of regular column ‘Analyze This!’ in Analytics Magazine Former CEO of Onward, Inc, which became part of Blue Pumpkin and Advertising.com Ph.D. Stanford, 1992

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Announcements Homework 3 due today Project proposal due next week Next week: Qing Wu, Google

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Forecasting Demand for Services

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

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Delphi Forecasting Question: In what future election will a woman become president of the united states for the first time? Year 1 st Round Positive Arguments 2 nd Round Negative Arguments 3 rd Round 2008 2012 2016 2020 2024 2028 2032 2036 2040 2044 2048 2052 Never Total

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N Period Moving Average Let : MA T = The N period moving average at the end of period T A T = Actual observation for period T Then: MA T = (A T + A T-1 + A T-2 + …..+ A T-N+1 )/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 8382 22 4 818382 29 5 98 8783 Sept. 5 6 1009387 12 793

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Exponential Smoothing Let : S T = Smoothed value at end of period T A T = Actual observation for period T F T+1 = Forecast for period T+1 Feedback control nature of exponential smoothing New value (S T ) = Old value (S T-1 ) + [ observed error ] or :

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Exponential Smoothing Hotel Example Saturday Hotel Occupancy ( =0.5) Actual Smoothed Forecast Period Occupancy Value Forecast Error Saturday t A t S t F t |A t - F t | Aug. 1 1 7979.00 8 2 8481.50 79 5 15 3 8382.25 82 1 22 4 8181.63 82 1 29 5 9889.81 8216 Sept. 5 6 10094.91 9010 Mean Absolute Deviation (MAD) = 6.6 Forecast Error (MAD) = ΣlA t – F t l/n

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Exponential Smoothing Implied 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

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What explains changes over time?

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Pull out the Influence of Seasonality and Trend

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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 A t S t T t F t | A t - F t | 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 IndexForecast Error Period t A t value S t I t F t | A t - F t| 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 0.7211236495 March 15 1733 2035.76 0.8291653 80

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More sophisticated forecasting techniques Nonlinear Regression Data mining Machine Learning Simulation-based

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Managing Service Projects

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The Nature of Project Management Characteristics of Projects: purpose, life cycle, interdependencies, uniqueness, and conflict. Project Management Process: planning (work breakdown structure), scheduling, and controlling. Selecting the Project Manager: credibility, sensitivity, ability to handle stress, and leadership. Building the Project Team: Forming, Storming, Norming, and Performing. Principles of Effective Project Management: direct people individually and as a team, reinforce excitement, keep everyone informed, manage healthy conflict, empower team, encourage risk taking and creativity. Project Metrics: Cost, Time, Performance

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Work Breakdown Structure 1.0 Move the hospital (Project) 1.1 Move patients (Task) 1.1.1 Arrange for ambulance (Subtask) 1.1.1.1 Prepare patients for move 1.1.1.2 Box patients personnel effects 1.2 Move furniture 1.2.1. Contract with moving company 1.1.1.1 Prepare patients for move 1.1.1.2 Box patients personnel effects 1.2 Move furniture 1.2.1. Contract with moving company

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Project Management Questions What activities are required to complete a project and in what sequence? When should each activity be scheduled to begin and end? Which activities are critical to completing the project on time? What is the probability of meeting the project completion due date? How should resources be allocated to activities?

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Example: Planning a Tennis Tournament What is the earliest / latest each activity can be begin / be completed? Given the plan, how likely is it that things will run behind schedule?

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Tennis Tournament Activities ID Activity Description Network Immediate Duration Node Predecessor (days) 1 Negotiate for Location A - 2 2 Contact Seeded Players B - 8 3 Plan Promotion C 1 3 4 Locate Officials D 3 2 5 Send RSVP Invitations E 3 10 6 Sign Player Contracts F 2,3 4 7 Purchase Balls and Trophies G 4 4 8 Negotiate Catering H 5,6 1 9 Prepare Location I 5,7 3 10 Tournament J 8,9 2

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Notation for Critical Path Analysis Item Symbol Definition Activity duration t The expected duration of an activity Early start ES The earliest time an activity can begin if all previous activities are begun at their earliest times Early finish EF The earliest time an activity can be completed if it is started at its early start time Late start LS The latest time an activity can begin without delaying the completion of the project Late finish LF The latest time an activity can be completed if it is started at its latest start time Total slack TS The amount of time an activity can be delayed without delaying the completion of the project

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Scheduling Formulas ES = EFpredecessor (max) (1) EF = ES + t (2) LF = LSsuccessor (min) (3) LS = LF - t (4) TS = LF - EF (5) TS = LS - ES (6) or

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Tennis Tournament Activity on Node Diagram J2J2 B8B8 START A2A2 C3C3 D2D2 G4G4 E 10 I3I3 F4F4 H1H1 TS ESEF LSLF

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Early Start Gantt Chart for Tennis Tournament ID Activity Days Day of Project Schedule 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 A Negotiate for 2 Location B Contact Seeded 8 Players C Plan Promotion 3 D Locate Officials 2 E Send RSVP 10 Invitations F Sign Player 4 Contracts G Purchase Balls 4 and Trophies H Negotiate 1 Catering I Prepare Location 3 J Tournament 2 Personnel Required 2 2 2 2 2 3 3 3 3 3 3 2 1 1 1 2 1 1 1 1 Critical Path Activities Activities with Slack

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Resource Leveled Schedule for Tennis Tournament ID Activity Days Day of Project Schedule 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 A Negotiate for 2 Location B Contact Seeded 8 Players C Plan Promotion 3 D Locate Officials 2 E Send RSVP 10 Invitations F Sign Player 4 Contracts G Purchase Balls 4 and Trophies H Negotiate 1 Catering I Prepare Location 3 J Tournament 2 Personnel Required 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 1 1 Critical Path Activities Activities with Slack

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Incorporating Uncertainty in Activity times A M D B F(D) P(DB) =.01 optimistic most pessimistic likely TIME

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Formulas for Beta Distribution of Activity Duration Expected Duration Variance Note: (B - A )= Range or

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Activity Means and Variances for Tennis Tournament Activity A M B D V A 1 2 3 11.111 B 5 8 11 C 2 3 4 D 1 2 3 E 6 9 18 F 2 4 6 G 1 3 11 H 1 1 1 I 2 2 8 J 2 2 2

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Uncertainly Analysis Assumptions 1. Use of Beta Distribution and Formulas For D and V 2. Activities Statistically Independent 3. Central Limit Theorem Applies ( Use “student t” if less than 30 activities on CP) 4. Use of Critical Path Activities Leading Into Event Node Result Project Completion Time Distribution is Normal With: For Critical Path Activities

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Completion Time Distribution for Tennis Tournament Critical Path Activities D V A 2 4/36 C 3 4/36 E 10 144/36 I 3 36/36 J 2 0 = 20 188/36 = 5.2 =

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Question What is the probability of an overrun if a 24 day completion time is promised? 24 P (Time > 24) =.5 -.4599 =.04 or 4% Days

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Costs for Hypothetical Project Cost (0,0) Schedule with Minimum Total Cost Duration of Project Total Cost Indirect Cost Opportunity Cost Direct Cost

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Activity Cost-time Tradeoff C C*C* D*D* D Activity Duration (Days) Normal Crash Slope is cost to expedite per day Cost Sometimes opportunity is presented to ‘crash’ a project - Spend lots of money to get ahead of (back on) schedule

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Cost-Time Estimates for Tennis Tournament Time Estimate Direct Cost Expedite Cost Activity Normal Crash Normal Crash Slope A 2 1 5 15 10 B 8 6 22 304 C 3 2 10 13 D 2 1 11 17 E 10 6 20 40 F 4 3 8 15 G 4 3 9 10 H 1 1 10 10 I 3 2 8 10 J 2 1 12 20 Total 115

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Progressive Crashing Project Activity Direct Indirect Opportunity Total Duration Crashed Cost Cost Cost Cost 20 Normal 115 45 8 168 19 I* 117 41 6164 18 37 4 17 33 2 16 29 0 15 25 -2 14 21 -4 13 17 -6 12 A*,B* 166 13 -8171 Normal Duration After Crashing Activity Project Paths Duration A-C-D-G-I-J 16 A-C-E-I-J 20 A-C-E-H-J 18 A-C-F-H-J 12 B-F-H-J 15

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Applying Theory of Constraints to Project Management Why does activity safety time exist and is subsequently lost? 1. The “student syndrome” procrastination phenomena. 2. Multi-tasking muddles priorities. 3. Dependencies between activities cause delays to accumulate. The “Critical Chain” is the longest sequence of dependent activities and common (contended) resources. Measure Project Progress as % of Critical Chain completed. Replacing safety time with buffers - Feeding buffer (FB) protects the critical chain from delays. - Project buffer (PB) is a safety time added to the end of the critical chain to protect the project completion date. - Resource buffer (RB) ensures that resources (e.g. rental equipment) are available to perform critical chain activities.

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Accounting for Resource Contention Using Feeding Buffer J2J2 B8B8 START A2A2 C3C3 D2D2 G4G4 E 10 I3I3 F4F4 H1H1 FB=7 FB=5 NOTE: E and G cannot be performed simultaneously (same person) Set feeding buffer (FB) to allow one day total slack Project duration based on Critical Chain = 24 days

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Incorporating Project Buffer J2J2 B4B4 START A2A2 C3C3 D2D2 G2G2 E5E5 I3I3 F2F2 H1H1 FB=2 FB=3 NOTE: Reduce by ½ all activity durations > 3 days to eliminate safety time Redefine Critical Chain = 17 days Reset feeding buffer (FB) values Project buffer (PB) = ½ (Original Critical Chain-Redefined Critical Chain) PB=4

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Sources of Unexpected Problems

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