1. Unisys “A Forecasting Method that Worked” Hossam Zaki hossam.zaki@unisys.com AGIFORS RYMSG, NY March 2000

2. Unisys 2 Presentation Outline Part 1. RM for One-Way Truck Rental Part 2. Methods That Did Not Work Part 3. A Method That Worked Part 4. Conclusions Q&A

3. Unisys 3 Part 1. Revenue Management for One- Way Truck Rental (1WTR)

4. Unisys 4 1WTR Business Overview Objective – Ground transportation of people from point A to point B Process – Rent to customers trucks of the size they choose – Customers pick up truck at Point A, drive it to point B and return it to company on an agreed upon date. – Local rental (A = B) is not part of the project RM Problems – Problem # 1: Repositioning – Problem # 2: Rate Making

5. Unisys 5 RM Problem # 1: Repositioning Definition – Company (not customers) moves trucks from point A to point B – A move paid for by company is called a “hike” RM Problem – Find the minimum cost hiking scheme that will reposition the fleet to capture maximum revenue over the planning horizon Planning Horizon – 1 to 2 weeks

6. Unisys 6 RM Problem # 2: Rate Making (Pricing) Definition – Set prices for every truck size and rental day RM Problem – Determine prices over the planning horizon that will Maximize revenue Encourage rentals to deficit districts Account for competitor fleet, prices and brand Planning Horizon – 8 to 12 weeks

7. Unisys 7 Business Practices Reservation system – Exists with no controls – Multiple years of data – No revenue data in booking file – Local stations may create fake bookings to solicit trucks Cancellation, No-show and Walk-in do occur No overbooking No penalty for no show

8. Unisys 8 Business Attributes Seasonality – High: Memorial Day (end of May) to Labor Day (Early September) – Low: Otherwise Points of Sale – Two channels: 800 Number or local agents Customers – All ad-hoc individuals – No frequent customers, No upgrades, – No groups, No whole sale

9. Unisys 9 What to Forecast? Capacity – Definition Number of trucks of each size available for rent at each district on every day in the planning horizon – Main Characteristic Capacity moves according to customer demand not according to a published schedule Demand

10. Unisys 10 What to Forecast? Demand – Definition Number of trucks of each size required for rent at each district on every day in the planning horizon – Main Characteristic Demand Volume (Very Low per lane) – Average 3 / month/ lane (OD) – Maximum 40 / month / lane – Many zeros in the time series

11. Unisys 11 Product Attributes Truck size – Four sizes - two groups – Exchange rules & accessories Markets (OD) – 200 Districts (Cities) – 4000 lanes Rental Type: – Local or 1 Way Rental day – Week day or Week end

12. Unisys 12 Part 2. Methods That Did Not Work

13. Unisys 13 (1) Exponential Smoothing Methods Tested – Simple, Holts, Winter, ARIMA Observation – All did not provide acceptable results Analysis – All methods rely on historical actual rental data only and do not use reservations data Conclusion – Try to use reservations data to improve forecast

14. Unisys 14 (2) Booking Profile Tested – Forecast = r * R, where r is historical average ratio of actual to reservations r depends on booking lead time R is current reservations Observation – Did not provide acceptable results Analysis – Too many days have zero reservations Conclusion – Need a method that can handle zero reservations

15. Unisys 15 (3) Three Factors Tested – Forecast = R - cancellation - no-show + walk-ins – Forecast = R * cancellation factor * no show factor * walk-in factor Observation – Did not provide acceptable results Analysis – Insufficient data to compute each factor individually Conclusion – Need a method that handles all factors at once and can handle small demand

16. Unisys 16 Part 3. A Method That Worked

17. Unisys 17 Step 1. Collect Historical Data Construct Reservations (R) and Actual (A) files – Include last month + same month last x (e.g. 3) years – Account for shoulders (see next slide) Clean out data – Remove illogical observations, e.g. revenue < 0, rental date is outside planning horizon – Remove outliers Usually representing fake reservations

18. Unisys 18 Example 1. Accounting for Shoulders Match July reservations with July rentals Reservation File – Booking date for July rentals can be in June (early reservation), July, or August ( data input after rental) Actual Rental File – Rental date for July reservations can be in June (data input after rental), July, or August (data input after rental) Read in July data with 2 shoulders in June and August

19. Unisys 19 Step 2. Identify Significant Factors For 1WTR, the significant factors used are – District – Truck size – Month – Wk day (WD) or Wk end (WE) – Days to rental (DTR) = no. of days between booking date and rental date = booking lead time Re group data accordingly

20. Unisys 20 Step 3. Construct Contingency Table Table Structure – Rows are realizations of Reservations (R) – Columns are realizations of Actuals (A) Cell Data – Merge R and A files to compute F(R,A) = frequency of occurrence for each (R,A) combination in the historical data

21. Unisys 21 Example 2. Contingency Table

22. Unisys 22 Step 4. Compute Conditional Expectations For each value of R – Compute total row values TR = Sum F( R,A), over all A’s For each combination of A and R – Compute Probability of an A given R P (A|R) = F(R,A) / TR For each value of R – Compute Conditional Expectations of A given R E(A|R) = SUM [ P(A|R) * A], over all A’s

23. Unisys 23 Example 3. Conditional Expectations

24. Unisys 24 Step 5. Solve Least Squares Solve Least Squares – Find f1 and f2 that will minimize || E(A|R) - [ f1 + f2 * R] || 2 – If f1 <0, set f1 = 0 Note: – f1 is the expected number of rentals given no reservations – f1 = walk in if R = 0 on rental day

25. Unisys 25 Step 6. Forecast For each District, Truck Size, DTR, WE/WD combination – Read current reservations (= R ) – Compute Forecast = f1 + f2 * R

26. Unisys 26 Results 80 % to 87% of Forecasts are within +/- 1 of Actual A sample of results is presented on the next slide – Table shows number of times the forecasting error was -4, -1, 0, 1 and 4 trucks for a sample district, zone and area over a 2 week planning horizon – Note A District is equivalent roughly to a city This Zone includes 15 Districts This Area includes 3 Zones with 39 Districts

27. Unisys 27 Sample Results

28. Unisys 28 Part 4. Conclusions

29. Unisys 29 Conclusions Method worked well with small demand volume – No division by zero – Effectively uses all data points with zero R or A Method combines – Conditional Expectations (CE) and – Linear Least Squares (LLS), For lack of a better name, call it CELLS

30. Unisys 30 Conclusions The method relates reservations to actual \ Unlike exponential smoothing methods, this method does not relate future actual to past actual What repeats from history? – Relationship between reservations and actual repeats better than relationship between actual and time

31. Unisys 31 Extensions Method can be used to forecast demand in any reservations-based industry – Airline Passengers, Air Cargo, Hotels, Car Rentals, etc Method has many variations, and can be easily adapted for – Large demand volume – Computing variances – Forecast f1 (>=0) independently – Minimize | E(A|R) - [ f1 + f2 * R] | instead of || E(A|R) - [ f1 + f2 * R] || 2

32. Unisys 32 Q&A