Reservations, Forecasting, Yield Management and ...

Reservations, Forecasting, Yield Management and Railroads Michael F. Gorman University of Dayton INFORMS November, 2005

Presentation Outline • • • • •

Introductory thoughts and comments – yield management and railroads Demand Forecast Project overview and considerations Statistical Forecast Methodologies and Assumptions Forecast results: Summary and Detailed Conclusions and Recommendations

2

Yield Management and Railroads •

What is yield management? – The process of allocating the right type of capacity to the right customer at the right price in order to maximize revenue or 'yield' (Kimes 1989)

• •

Do railroads “do” yield management? Examples of yield management-related activities in rail: – Market segmentation: • Differential pricing by commodity, customer, and service level • Train type and block space allocation, track allocation, locomotive allocation…

– Car allocation priorities (and BNSF’s car allocation pricing: COTs, LOGs) – Price bundling and unbundling – But, in general… no.

3

When does YM work? •

Yield Management suits industries where: – Demand is unstable or highly time-varied – The service/product is perishable – Market can be segmented – Capacity is fixed and well-known – Inventory of capacity is homogenous

Railroads have these

Railroads don’t have these

Do Railroads have these?

– Selling of service to their customers occurs well in advance of consumption • In effect, price is determined well in advance of consumption, but volume is not determined until the point of consumption • (no reservations)

– Low marginal costs of service • Railroads have the blessing, and the curse, of flexible capacity, which creates significant marginal costs of service (extra sections, extra locomotives, etc.) • And makes pricing to maximize yield a challenge (due to a created cost focus) 4

Yield Management Ingredients •

Demand forecast – – What is coming, at a detailed level, that is to be priced

•

Capacity identification – – What capacity is available, at a detailed level, that is to be sold

•

Demand management – – What component of demand that can be shifted to better match capacity; how can customers be differentiated

•

Pricing – – What price may drive the desired customer behavior (demand shifting); – What price roughly equates known revenue with an order now against expected foregone revenue of future reservations

•

Overbooking/Order acceptance – – When do you accept a customer car order (reservation), not knowing what orders are yet to come, or even which train capacities the customer may use?

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Railroads Fall Short on many of these critical ingredients: •

Demand forecast – Very little advanced knowledge of customer behavior – Generally, no reservations to speak of (BNSF has tried with “RSVP”, COTS, LOGS; CN may be an exception) – Many different products (origin, destination, train types, service levels, equipment types, time of day, day of week) to predict statistically

•

Capacity identification – Rail capacity is complex, not well-known, and not fixed – 5 different physical capacity constraints (car, yard, line, crew, loco); – Train is the sixth capacity type that uses all of these physical capacities and ties them all together – But, the train capacity changes daily with second sections, annulments and consolidations --- effectively negating the fixed capacity assumptions that are bedrock in most yield management applications. – Contrary to airlines, hotels, etc., rail capacity is much more flexible than pricing, so supply adjusts to demand. Despite a growing "run the plan" philosophy, we still reroute 10% or so (or more?) of all traffic... well beyond airlines or hotels. 6

Railroads fall short on these ingredients – cont. •

Demand Management – Shipping patterns are not easily swayed by price –

–

•

Pricing – Systems and commercial relationships limit ability of railroads to use price – –

•

Not much of demand is easily ported between days of week or equipment type. Production and delivery schedules aren't flexible enough to be swayed by production costs. Demand management principally takes the form of pushing off accepted loads to nonpeak days, which often results in service failures.

Rail pricing isn't nimble enough to take advantage of perceived mismatch of demand and supply conditions. Rail pricing systems are not made for quickly changing prices, and the majority of historical customer relationships and longer-term contracts are not geared towards fluctuating prices.

Load Acceptance – The load acceptance function is not executed in rail – –

Typically, railroads accept all orders, then fail to provide a car or on time service Akin to overbooking; But the “cost” of failure is not as well-known as in airlines, where an explicit cost is paid to “volunteers” 7

MFG Consulting – BNSF Network Predictability Project •

Objective: To evaluate predictability of network at various levels of aggregation to support operational decision-making. (Conversely, the “unpredictability” the limits operational decision-making.) – – –

•

Predictability: the “signal” or explainable portion of shipper behavior relative to the “noise” or unexplained fluctuations Levels of Aggregation: level of detail of forecast; hub complex, hub, equipment type, equipment length, shipper, time interval, etc. Operational decision-making: asset deployment to better match shipper demand patterns

Opportunity: Better visibility into “what is coming” will allow better asset deployment, improving both asset utilization and availability

•

Project Scope: – – – –

Three major intermodal ramps Historical Data: Jan 1, 2003 - March 31, 2005 In-gate data (821 days) Trailer and Container Loads only (not empties) Forecast at a level which may be used to improve flat car and double stack car positioning, lift forecasting, train planning (not aggregate financial forecasting)

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Operational Forecast Requirements •

We evaluate the feasibility of forecasting shipper patterns as an alternative to shipper reservations for each shipment –

“Reservation” level of detail: •

•

However, the desired level of detail for a forecast depends on its intended operational use –

•

Very different from financial forecasting

We can examine in gates at various levels of detail: – – –

•

Shipper, Date, Origin, Destination, Equipment, Length (and Service Level) (not time of day, but, would be nice)

Ramp Management Train Planning Car management

-– –

Total in-gates Total vans and containers by destination Total vans and containers (and lengths)

If we can forecast accurately at these levels of detail, the value derived from customer reservations is reduced to some degree –

If shipper-level forecast helps improve forecast accuracy, then forecasts can be made a more detailed level, then aggregated up

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Pictorial of Forecasting Aggregation How far down the “pyramid” can we go and maintain accuracy?

Hub Complex: Hubs A,B,C (Combined) Individual Hubs: A,B,C (Individual) Equipment Types (V, K) Equipment Length (20-28,40-48, 53)

Shipper (e.g. UPS, Hub, Schneider, Roadway)

Time Interval: Daily, Time of Day

Destination: Any (top) locations

We evaluate forecast accuracy at various levels of operational detail.

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Forecasting Parameters, Measures, Methods and Assumptions Summary •

Forecasting Parameters: – One day ahead forecast horizon – Static forecast – In-sample forecast evaluation

•

Measure of forecast quality: – Mean Absolute Error (MAE) – Mean Absolute Percent Error (MAPE)

•

Methods Explored: – Exponential Smoothing – Holt-Winters (with daily/monthly smoothing) – Stepwise autoregressive (by Day of Week)

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Forecast Evaluation Overview •

Summary Forecast: – –

• •

Dive Down detailed forecast: One day ahead forecasts – Holt-Winters Method Used –

•

Holt/Winters, Stepwise Autoregressive and Exponential Smoothing are evaluated At the Hub level of aggregation

Holt/Winters – Seasonal Multiplicative adjustment

Various forecast levels of detail (Dive Downs) –

Shipper Focused • • • •

–

Dive Down 1: Hub/Shipper Dive Down 2: Hub/Shipper/Equipment Type Dive Down 3: Hub/Shipper/Equipment Type/Equipment Length Dive Down 4: Hub/Shipper/Equipment Type/Equipment Length Destination (reservation level of detail, excluding service level)

Operations Focus (Exclude shipper disaggregation) • • •

Dive Down 1: Hub/Equipment Type Dive Down 2: Hub/Destination Dive Down 3: Hub/Destination/Equipment type

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Pictorial of Forecasting Aggregation Summary Forecast: Hub Level, Day of Week

Hub Complex: A,B,C Individual Hubs: A,B,C Equipment Types (V, K) Equipment Length (20-28,40-48, 53)

Shipper (UPS, Hub, Hunt, Roadway, etc.) Perhaps top 10 shippers out of 75.

Time Interval: Daily

Destination: Any of 10 top locations Out of 50, and “Other” 13

Stepwise Autoregressive vs. Holt-Winters

Winters with Weekly and Monthly Seas MAE Winters-Seas Winters Stepar ACHICAGO 69.76 86.69 62.15 BCICERO 46.20 53.06 40.24 CWILSPRING 77.30 91.26 67.63 Stepwise Autoregressive has lowest MAE, Holt-Winters with (daily) Seasonality performs comparably. •Holt-Winters will be used for “dive-down” forecasts – •Single equation with daily adjustment versus seven different day-of-week equations •More economical for automation •Leverages Uses “same time last year” information – more intuitive •Leverages More recent information - One day ahead forecast (uses last three days’ information to better adjust to within-month variations)

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Holt-Winters with Monthly/Daily Seasonality Chicago Dec Pred and Actual

Chicago Jan Pred and Actual

1,200 1,400

1,000 1,200

800

1,000

800

600

600

400 400

200

200

12 /1 /2 00 4 12 /3 /2 00 4 12 /5 /2 00 4 12 /7 /2 00 4 12 /9 /2 00 12 4 /1 1/ 20 0 12 4 /1 3/ 20 04 12 /1 5/ 20 04 12 /1 7/ 20 04 12 /1 9/ 20 04 12 /2 1/ 20 04 12 /2 3/ 20 04 12 /2 5/ 20 04 12 /2 7/ 20 04 12 /2 9/ 20 04 12 /3 1/ 20 04

1/ 1/ 20 05 1/ 3/ 20 05 1/ 5/ 20 05 1/ 7/ 20 05 1/ 9/ 20 05 1/ 11 /2 00 5 1/ 13 /2 00 5 1/ 15 /2 00 5 1/ 17 /2 00 5 1/ 19 /2 00 5 1/ 21 /2 00 5 1/ 23 /2 00 5 1/ 25 /2 00 5 1/ 27 /2 00 5 1/ 29 /2 00 5 1/ 31 /2 00 5

-

-

Chicago March Pred and Actual 1,200

1,000

800

600

400

200

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Holt-Winters generally tracks well when seasonal adjustments are included.

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Confidence Interval on Forecast: Hub Level

Hub-Level Forecast Method: Additive Holt/Winters Lower 95% Confidence Interval Origin Ramp Boundary 704 ACHICAGO 588 BCICERO WILSPRING 1,107

C

Upper 95% Confidence Interval Boundary 1,177 890 1,607

Even at the highest (Hub) level of aggregation, the 95% confidence interval around the forecasted value is 300-500 units.

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Shipper Dive Down 4: (Reservation Level of Detail) Hub, Shipper, Equipment Type, Length and Destination

Hub Complex: CH, WS, CI Individual Hubs: CH, WS, CI Equipment Types (V, K) Equipment Length (20-28,40-48, 53)

Shipper (UPS, Hub, Hunt, Roadway, etc.) Perhaps top 10 shippers out of 75.

Time Interval: Daily

Destination: Any of 10 top locations Out of 50, and “Other” 17

Date

UPS - Willowsprings JBHUNT - Chicago - All Equipment

300

250

500 200

Actual 150 Fcst

200 100

50

-

Date Date

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2/26/2005

Date

2/19/2005

3/29/2005

3/22/2005

-

3/15/2005

60

2/12/2005

40 Fcst

3/8/2005

Actual

Fcst

3/1/2005

Actual

2/22/2005

250

2/15/2005

100

2/8/2005

70

2/5/2005

0 300

1/29/2005

100 80

1/22/2005

Date

2/1/2005

JBHUNT - Chicago - All Equipment Types

1/15/2005

600 350

1/8/2005

0

1/1/2005

700

Units

50

1/26/2005

20

1/19/2005

100

1/12/2005

40

1/5/2005

120

12/29/2004

Hub Group - Chicago - All Equip

12/22/2004

140

12/15/2004

300 3/ 1/ 20 05 3/ 3/ 20 05 3/ 5/ 20 05 3/ 7/ 20 05 3/ 9/ 20 05 3/ 11 /2 00 3/ 5 13 /2 00 3/ 5 15 /2 00 3/ 5 17 /2 00 3/ 5 19 /2 00 3/ 5 21 /2 00 3/ 5 23 /2 00 3/ 5 25 /2 00 3/ 5 27 /2 00 3/ 5 29 /2 00 3/ 5 31 /2 00 5

Units

160

12/8/2004

400 Units

1/ 20 05 3/ 20 3/ 0 5 5/ 20 3/ 0 5 7/ 20 3/ 0 5 9/ 2 3/ 00 5 11 /2 3/ 0 05 13 /2 3/ 0 05 15 /2 3/ 0 05 17 /2 3/ 0 05 19 /2 3/ 0 05 21 /2 3/ 0 05 23 /2 3/ 0 05 25 /2 3/ 0 05 27 /2 3/ 0 05 29 /2 3/ 0 05 31 /2 00 5

3/

3/

Units

80

12/1/2004

11/26/2004

11/19/2004

11/12/2004

11/5/2004

10/29/2004

10/22/2004

10/15/2004

10/8/2004

10/1/2004

Units

Illustrative Graphs Shipper-Hub Level Forecast Accuracy (all Equipment) Roadway Express - Cicero - All Equipment Types

60

200

50

150

Actual

30

Fcst

20

10

-

Schneider National - Willow Springs

200

180

160

140

Actual

120

100 Forecast

Actual

80

Fcst

60

40

20

-

Date

CICERO - YELLOW - V - 48 Date

30

1.2

25

1

20

0.8

15 Fcst

10

5

0

0.6

0.4

3/29/2005

0 3/22/2005

20

3/15/2005

60

3/8/2005

Fcst

3/1/2005

120

2/22/2005

WILSPRING - SCHNEINATL - K - 53

2/15/2005

Actual Units

160

2/8/2005

80

2/1/2005

100

Units

3/29/2005

3/22/2005

3/15/2005

3/8/2005

3/1/2005

2/22/2005

2/15/2005

2/8/2005

2/1/2005

Units

180

12 /1 /2 00 3 12 /8 /2 00 12 3 /1 5/ 20 03 12 /2 2/ 20 03 12 /2 9/ 20 03 1/ 5/ 20 04 1/ 12 /2 00 4 1/ 19 /2 00 4 1/ 26 /2 00 4 2/ 2/ 20 04

3/29/2005

3/22/2005

3/15/2005

3/8/2005

3/1/2005

2/22/2005

2/15/2005

2/8/2005

2/1/2005

Units

Illustrative Graphs Shipper-Hub-Equipment-Length Level of Detail WILSPRING - UPS - V - 48

140

140 120

100 80 Actual

60 Fcst

40 40

20 0

Chicago - Hyundai - K - 48

Date

Actual

Actual

Predicted

0.2

0

-0.2

Date

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Comparison of Forecast Accuracy: Shipper-Specific Illustration Dive Down Levels 1-4 Schneider Forecast Dive Down: Customer Level 1 Ramp CONSTANT MAE MAPE N CHICAGO 4.59 2.15 16.83 CICERO 29.99 6.30 34.14 820.00 WILSPRING 85.17 13.46 28.42 821.00 Level 2 Ramp Equipment CONSTANT MAE MAPE N CHICAGO K 3.60 5.27 26.99 800.00 CICERO K 2.31 2.40 25.96 373.00 V 26.62 6.23 34.24 820.00 WILSPRING V 85.11 13.45 28.42 821.00 Level 3 Ramp Equipment Length CONSTANT MAE MAPE N CHICAGO K 53 3.51 3.26 10.52 CICERO K 53 2.50 1.89 52.02 176 V 48 0.86 0.96 2.77 778 53 26.44 6.21 34.27 820 WILSPRING V 48 (0.20) 1.62 10.91 818 53 84.55 13.41 28.42 821 Level 4 Ramp Dest Equip Length CONSTANT MAE MAPE N 53 3.33 13.78 19.58 CHICAGO SANBERNARK CICERO PORTLAND V 53 10.76 3.66 45.62 SPOKANE V 53 2.39 1.02 22.64 SSEATTLE K 53 2.54 1.76 49.79 V 53 15.30 4.14 44.65 STPAUL V 53 1.01 1.85 56.92 WILSPRING V 53 0.76 1.09 3.44 WILSPRING ALLIANCE V 53 10.23 2.99 51.69 DENVER V 53 3.21 1.68 66.84 FRESNO V 53 5.10 2.39 64.07 53 24.61 4.20 40.81 LOSANGELEV PHOENIX V 53 5.61 2.10 73.32 53 34.29 8.21 28.01 SANBERNARV STOCKTON V 53 7.30 3.97 54.14

All units forecast.

Four Groups not forecast

Seven by groups only one observation; 15 groups Not forecast (22 total)

820 817 176 820 396 733 821 819 820 820 820 821 820

60 groups one obs; 127 not forecast (187 total)

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Operational Dive Down 1: Hub and Equipment Type

Hub Complex: A, B, C Individual Hubs: A, B, C Equipment Types (V, K) Equipment Length (20-28,40-48, 53)

Shipper (UPS, Hub, Hunt, Roadway, etc.) Perhaps top 10 shippers out of 75.

Time Interval: Daily

Destination: Any of 10 top locations Out of 50, and “Other” 21

Operational Dive Down 1: Hub and Equipment Type Forecast Accuracy Summary

Sum of Value Ramp Equip CHICAGO K V CICERO K V WILSPRING K V

Sum of Value Ramp Equip CHICAGO K V CICERO K V WILSPRIN K V

Stat CONSTANT MAE MAPE 710.73 69.30 42.07 0.23 0.50 13.93 259.86 28.47 32.69 293.77 24.40 20.09 63.79 11.42 28.71 914.05 72.43 21.33

Date 1-Apr-05 23-Feb-05 1-Apr-05 1-Apr-05 1-Apr-05 1-Apr-05

N 821 761 821 821 821 821

Stat L95 U95 Fcst 95% Error Band 703.90 1,177.01 940.45 25% (2.31) 2.46 0.07 3217% 251.91 425.21 338.56 26% 322.60 478.37 400.49 19% 50.92 111.36 81.14 37% 1,036.75 1,515.57 1,276.16 19%

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Operational Dive Down 1: Hub and Equipment Type Illustrative Examples Willow Springs Trailers

Chicago Containers

1,600.00

1,200.00

1,400.00 1,000.00

1,200.00 800.00

Actual

800.00

Fcst

Units

Units

1,000.00

600.00

Actual

600.00

Fcst

400.00

400.00 200.00

MAPE=32%

200.00

Date

8/ 26 /2 00 3

8/ 19 /2 00 3

8/ 12 /2 00 3

8/ 5/ 20 03

7/ 29 /2 00 3

7/ 22 /2 00 3

7/ 15 /2 00 3

7/ 8/ 20 03

7/ 1/ 20 03

-

3/ 29 /0 5

3/ 22 /0 5

3/ 8/ 05

3/ 1/ 05

2/ 22 /0 5

2/ 15 /0 5

2/ 8/ 05

2/ 1/ 05

3/ 15 /0 5

MAPE=5%

-

Date

Cicero Trailers

Willow Springs Trailers 1,600.00

450.00

1,400.00

400.00 350.00

1,200.00

300.00

Fcst

Units

Actual

800.00

250.00

Actual Fcst

200.00

600.00

150.00 400.00

100.00

10 /2 7/ 04

10 /2 0/ 04

10 /1 3/ 04

10 /6 /0 4

9/ 29 /0 4

MAPE=26% 9/ 22 /0 4

-

9/ 15 /0 4

50.00

9/ 8/ 04

12 /2 7/ 04

12 /2 0/ 04

11 /2 9/ 04

11 /2 2/ 04

11 /1 5/ 04

11 /8 /0 4

12 /6 /0 4 Date

12 /1 3/ 04

MAPE=55%

-

9/ 1/ 04

200.00

11 /1 /0 4

Units

1,000.00

Date

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Operational Dive Down Forecast Accuracy Comparison Hub, Destination, Equipment Type Sum of Value Ramp Equip CHICAGO K V CICERO K V WILSPRING K V

Stat CONSTANT MAE MAPE 710.73 69.30 42.07 0.23 0.50 13.93 259.86 28.47 32.69 293.77 24.40 20.09 63.79 11.42 28.71 914.05 72.43 21.33

Ramp Stat WILSPRING Dest CONSTANT MAE LOSANGELE 209.35 18.77 SANBERNAR 202.39 21.54 STOCKTON 89.92 11.30 DENVER 89.17 8.73 ALLIANCE 64.79 9.17 PHOENIX 58.70 6.74 NBAY 58.45 5.97 KANCITY 32.39 4.04 RICHMOND 27.26 4.42 DALLAS 26.77 4.07 NBERGEN 26.55 4.56 WORCESTER 26.52 4.24 WILSPRING 25.35 3.77 ALBUQUERQ 17.89 2.96 OKLCITY 13.65 2.20 FRESNO 10.23 3.19 OMAHA 5.78 1.13

As operational forecast detail increases, forecast accuracy decreases at a slower rate than customer-specific forecasts. further, more “full” data sets are available for forecasting.

N 821 761 821 821 821 821

Sum of N

MAPE N 19.02 18.49 18.49 22.56 37.51 16.67 15.33 27.79 23.99 23.42 23.77 23.29 43.81 27.99 36.07 55.36 19.12

Sum of Value

821 821 821 821 821 821 820 820 821 820 820 820 817 820 820 820 488

Dest LOSANGELE SANBERNAR STOCKTON ALLIANCE RICHMOND PHOENIX DENVER OAKINTGAT FRESNO

Equip V K V K V K V K V K V K V K V V K

Ramp Stat WILSPRING CONSTANT MAE MAPE N 190.98 17.11 20.82 18.37 5.75 43.94 186.25 19.54 18.43 16.15 6.04 70.09 82.88 10.96 20.82 7.05 2.40 67.69 63.42 8.91 36.58 1.42 1.50 39.33 11.47 3.83 27.43 15.80 1.85 41.08 55.72 6.51 16.83 2.98 1.56 49.43 88.79 8.62 22.23 0.61 0.94 28.08 0.33 0.23 10.76 8.69 2.82 56.07 1.54 1.17 39.86

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821.00 821.00 821.00 820.00 821.00 820.00 821.00 805.00 821.00 821.00 821.00 815.00 821.00 806.00 239.00 820.00 818.00

General Statements Forecasting Accuracy and Feasibility •

Generally, the “finer” or more detailed the shipper-specific forecast, the less accurate it becomes – – – –

Noise begins to dominate trend Small deviations and fluctuations in shipper behavior have larger impact on error level Many forecast groups have miniscule expected values; making forecasting in any meaningful way a challenge However, forecasting at a disaggregate level, and then aggregating, is often more accurate at the aggregate level than an aggregate forecast • •

•

There seem to be strong shipper-specific patterns that are somewhat more easily forecast than the more aggregate level These patterns are lost when aggregated before forecasting

As we dive down the pyramid, fewer and fewer observations per forecast group, which hampers forecasting –

Many dates with zero units for small forecast groups • • •

–

Fewer days over which to build forecast Missing (zero) observations are “gapped” MAPE is only calculated for non-zero observations

In many cases, not enough observations exist to generate any forecast equation • •

Hardest groups to forecast, but aren’t included in our forecast error estimates Many of the forecast groups (even for large customers) are too small to forecast at all – would require “All Other Groups” aggregation to forecast them

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Observations •

We might not need to forecast at a “Reservation” level of detail (Customer, origin, destination, equipment type, equipment length) in order to have more proactive operations –

We just aggregate the reservation-level forecast into an operational level, for examples: • • • •

–

•

Origin – In gate planning, hub management Origin-Destination – train planning Origin-Equipment Type – lift planning (etc.)

Forecasting at this level generally has lower forecast error, and more detail does not significantly decrease forecast accuracy or ability

Forecast is a second best to actual reservations – –

Accuracy is reasonable, but nothing close to a reservation Anecdotal evidence of “regular, predictable” traffic is seemingly confirmed by graphical representation, but clearly contradicted by numerical summaries •

–

Aggregate volumes are predictable; marginal loads are nearly impossible to forecast with any level of detail

Knowing what is coming (via forecast) has different management implications than a reservation • •

Operations makes adjustments due to forecasted volume “Load Acceptance” (no such current function) can make a determination on whether a reservation should be accepted, or at what price and with what service level promise, as opposed to preparing for a forecasted volume

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