Unisys

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

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

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

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. (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. (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. Part 3. A Method That Worked

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. 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. 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. 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. Example 2. Contingency Table

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. Example 3 . Conditional Expectations

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

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. Sample Results

28. Part 4. Conclusions

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. 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. 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. Q&A