unisys “a forecasting method that worked” hossam zaki [email protected] agifors rymsg, ny...
TRANSCRIPT
2Unisys
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
4Unisys
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
5Unisys
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
6Unisys
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
7Unisys
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
8Unisys
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
9Unisys
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
10Unisys
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
11Unisys
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
13Unisys
(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
14Unisys
(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
15Unisys
(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
17Unisys
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
18Unisys
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
19Unisys
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
20Unisys
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
22Unisys
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
23Unisys
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
24Unisys
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
25Unisys
Step 6. Forecast
• For each District , Truck Size, DTR, WE/WD combination– Read current reservations (= R )– Compute
• Forecast = f1 + f2 * R
26Unisys
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
27Unisys
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%
29Unisys
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
30Unisys
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
31Unisys
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