Unisys

“A Forecasting Method that Worked”

Hossam Zakihossam.zaki@unisys.com

AGIFORS RYMSG, NYMarch 2000

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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

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

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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

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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

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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

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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

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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

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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

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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

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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

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Part 2. Methods That Did Not Work

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(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

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(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

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(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

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Part 3. A Method That Worked

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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

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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

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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

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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

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Example 2. Contingency Table

R/A 0 1 2 … m

0 4 4 2

1 0 8 2

2

…

n

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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

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Example 3 . Conditional Expectations

R/A 0 1 2 … m TR E(A|R)

0 4 4 2 10 0.8

1 8 2 10 1.2

2

…

n

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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

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Step 6. Forecast

• For each District , Truck Size, DTR, WE/WD combination– Read current reservations (= R )– Compute

• Forecast = f1 + f2 * R

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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

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Sample Results

Error -4 -1 0 1 4

District 0 2 18 7 1

0% 7% 64% 25% 4%

Zone 8 46 157 187 22

2% 11% 37% 45% 5%

Area 42 111 344 499 96

3% 10% 32% 45% 8%

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Part 4. Conclusions

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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

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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

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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

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Q&A