1. ISM 270 Service Engineering and Management Lecture 7: Forecasting and Managing Service Capacity

2. Announcements  Brenda Deitrich (Mathematical Sciences, IBM) visited UCSC today Should be available to watch online at: Should be available to watch online at: http://ucsc.citris-uc.org/ 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 Forecasting and Capacity Planning Supply Chains in Services Supply Chains in Services Capacity Management Game Capacity Management Game Project Presentations Project Presentations

3. 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 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

7. 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

8. 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

9. 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 :

10. 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

11. Exponential Smoothing Implied Weights Given Past Demand Substitute for If continued:

12. 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

13. Saturday Hotel Occupancy Effect of Alpha ( =0.1 vs. =0.5) Actual Forecast

14. Recall from Charles Ng: Start with historical volume: What explains changes over time?

15. Pull out the Influence of Seasonality and Trend

16. Estimate the relationship of price and promotion changes to volume

17. Once estimated separately, all these effects can be combined to predict volume. This is the model.

18. 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

19. 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

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

21. Managing Waiting Lines – Queueing Models

22. Essential Features of Queuing Systems Departure Queue discipline Arrival process Queue configuration Service process Renege Balk Calling population No future need for service

23. Arrival Process StaticDynamic AppointmentsPrice Accept/Reject BalkingReneging Random arrivals with constant rate Random arrival rate varying with time Facility- controlled Customer- exercised control Arrival process

24. Distribution of Patient Interarrival Times

25. Temporal Variation in Arrival Rates

26. Poisson and Exponential Equivalence Poisson distribution for number of arrivals per hour (top view) Poisson distribution for number of arrivals per hour (top view) One-hour One-hour 1 2 0 1 interval 1 2 0 1 interval Arrival Arrivals Arrivals Arrival Arrival Arrivals Arrivals Arrival 62 min. 40 min. 123 min. Exponential distribution of time between arrivals in minutes (bottom view)

27. Queue Configurations Multiple Queue Single queue Take a Number Enter 34 8 2 610 12 11 5 7 9

28. 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 robinPriorityPreemptive Processing time of customers (SPT rule)

29. 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:

30. 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 (Little’s Law for ALL queues):

31. Congestion as 0 1.0 100 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

32. Single Server General Service Distribution Model : M/G/1 1. For Exponential Distribution: 2. For Constant Service Time: 3. Conclusion: Congestion measured by L q is accounted for equally by variability in arrivals and service times.

33. Queuing System Cost Tradeoff Let: C w = Cost of one customer waiting in queue for an hour C s = Hourly cost per server C = Number of servers Total Cost/hour = Hourly Service Cost + Hourly Customer Waiting Cost Total Cost/hour = C s C + C w L q Note: Only consider systems where Note: Only consider systems where

34. General Queuing Observations 1. Variability in arrivals and service times contribute equally to congestion as measured by L q. 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, W S. 6. Multiple-servers preferred to single large server (team) if minimizing mean time in queue, W Q.

35. Laws of Service  Maister’s First Law: Customers compare expectations with perceptions.  Maister’s Second Law: Is hard to play catch-up ball.  Skinner’s Law: The other line always moves faster.  Jenkin’s Corollary: However, when you switch to another other line, the line you left moves faster.

36. Managing Capacity and Demand

37. Segmenting Demand at a Health Clinic Smoothing Demand by Appointment Scheduling Day Appointments Monday 84 Tuesday 89 Wednesday 124 Thursday 129 Friday 114

38. Hotel Overbooking Loss Table Number of Reservations Overbooked 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

39. Daily Scheduling of Telephone Operator Workshifts Scheduler program assigns tours so that the number of operators present each half hour adds up to the number required Topline profile 12 2 4 6 8 10 12 2 4 6 8 10 12 Tour 12 2 4 6 8 10 12 2 4 6 8 10 12

40. 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

41. Seasonal Allocation of Rooms by Service Class for Resort Hotel First class Standard Budget Percentage of capacity allocated to different service classes 60% 50% 30% 20% 50% Peak Shoulder Off-peak Shoulder (30%) (20%) (40%) (10%) Summer Fall Winter Spring Percentage of capacity allocated to different seasons 30% 20% 10% 30% 50% 30%

42. Demand Control Chart for a Hotel Expected Reservation Accumulation 2 standard deviation control limits

43. 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 C u = 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. C o = 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, C o 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 C o = pD-(1-p)(F-D) = pF - (F-D)