Leveraging Transaction Data for Online Pricing and Sourcing of Carrier Capacity in the Truckload Spot Market: Models and Application Hani S. Mahmassani
Rotterdam School of Management Erasmus University June 3, 2016
OUTLINE 1. Mo.va.on: Value of informa.on in vola.le environments– The Transporta.on Spot Market Based on PhD Dissertation 2. 3PL Broker Model of Christopher Lindsey 3. Online Pricing Engine
4. 5. 6. 7.
•
Model Framework
•
Behavioral Model Components
Part I conducted in collaboration with Diego Klabjan, and ECHO Global Logistics
Applica.on to Actual 3PL Data Improving Sourcing Process through Bundling Data: State Choice Experiment Model Es.ma.on and Results •
Reserva.on Price Calcula.ons
8. Takeaways and Q&A
The Broader Context § The so-called “Data Revolution” - Analytics, big data, and data mining (among other associated terms) have become pervasive in the practices of a number of businesses.
§ Though common in many industries, logistics has been slow to catch up. This is now changing. § Logistics companies have access to substantial databases of transactional and behavioral data. Happening at a company near you?
The Transporta2on Spot Market
§ The spot market exists to facilitate unfulfilled demand due to the uncertainty in shipper-‐carrier rela.onships for dedicated services. - Supply chain uncertainty - Shipper-‐Carrier contract structure 1
Kirkeby, K. 2007. Transportation: Commercial, Industry Surveys. Standard & Poor’s, New York. Tsai, M.-T. et al. 2011. Valuation of freight transportation contracts under uncertainty. Transportation Research Part E 47 (6). Caplice, C., Sheffi, Y. 2006. Combinatorial auctions for truckload transportation. In: Cramton, P., Shoham, Y., Steinberg, R. (Eds.), Combinatorial Auctions, Cambridge: MIT Press (Chapter 21). 2 3
Supply Chains and Shipper-‐Carrier Contracts • Supply chain uncertainty is the difference between perception (forecast demand) and reality (actual demand) 1 • The freight hauled by a carrier may differ significantly from what was awarded in the contract, because it was based on a forecast 2 Contract Structure • Contracts are op#ons that give shippers the right but not the obliga#on to a carrier’s services 2 – Volume commitments are frac.ons of traffic flow
• Carriers may refuse a frac.on of a shipper’s requests – Typically 70-‐80% 1 2
Chopra, S., Meindl, P. 2001. Supply Chain Management: Strategy, Planning, and Operation. Upper Saddle River, NJ: Prentice-Hall. Caplice, C., Sheffi,Y. 2006. Combinatorial auctions for truckload transportation. In: Cramton, P., Shoham,Y., Steinberg, R. (Eds.), Combinatorial Auctions, Cambridge: MIT Press (Chapter 21).
Characteristics of the Spot Market Characteristic
Description
Purpose
A mechanism by which fluctuations in the trucking market are facilitated. It exists to serve urgent or unfulfilled demand. 1
Physical form
Electronic marketplaces (i.e., load boards, shipper-carrier matching sites)
Typical transactions
Spot market contracts are on a load-by-load basis, as opposed to the lane-by-lane contracts common to transportation auctions for dedicated services.
Supply and Demand Characterized by capacity uncertainty and price volatility Size
1 Tsai, M.-T. et
• In 2010, 15% to 20% of total truck tons was moved on the spot market 2 • In 2012, it accounted for $141.8 billion of the 3PL sector; of that, non-asset based providers (i.e., brokers) accounted for $45.1 billion. 3
al. 2011.Valuation of freight transportation contracts under uncertainty. Transportation Research Part E 47 (6). TransCore Freight Solutions. The Spot Market: A Primer, for Shippers. http://www.dat.com/~/media/81E66B9B31424E4888BD48067619DFA5.ashx. Accessed 10/25/2013. 6 3 Armstrong & Associates. U.S. 3PL Market Size Estimates. http://http://www.3plogistics.com/3PLmarket.htm. Accessed 10/2/2013. 2
Role of Non Asset-‐Based 3PLs in the Spot Market § Non asset-‐based 3PLs own no physical assets related to the physical distribu.on of freight - i.e., rolling stock, warehouses, etc. § Match supply (carriers’ capacity) with demand (shippers’ shipments) for a price § Brokers exist in order to facilitate the spot market and provide a degree of trust and accountability § Increasingly rely on technology and informa.on to remain compe..ve § Example companies - Coyote Logis.cs - Echo Global Logis.cs - CH Robinson
3PL Broker Business Model § Quote prices to shippers before securing capacity from carriers § Consider the following example: The broker ends the search and selects the carrier expected to generate the highest profit - $20.
Carrier #1 - $105
Shipper
Broker quotes the shipper $100
Carrier #2 - $80
Broker
Carrier #3 – $85 Time
Research Mo2va2on & Objec2ves Mo2va2on § Pricing shipments and sourcing capacity in the spot market are difficult tasks; 3PLs some.mes make unprofitable deals. - Spot market is highly vola.le - Rela.vely short opera.ng .me frames
- Uncertainty on both sides of the market
§ However, the 3PL has informa.on to use to its advantage - Firsthand knowledge of both sides of the market - Tendencies of shippers and carriers through transac.onal data
§ How can that informa.on be used? Objec2ve § Develop methodological frameworks that improve the outcomes of 3PL pricing and sourcing decisions for truckload shipments using transac.onal data and relevant transporta2on and logis2cs theories.
Online Pricing Engine: Shipper Acceptance and Carrier Ranking
Online Pricing Engine: Shipper Acceptance and Carrier Ranking
• Shipper acceptance decreases with increasing cost while carrier acceptance increases with increasing price. • Probabilities are estimated using the variables created in the data mining process.
Objec2ves Predic.ve analy.cs for real-‐.me 3PL broker decisions of: - Pricing – recommend to 3PL brokers shipper quotes that are reasonable and poten.ally profitable - Sourcing – determine the poten.al carriers that give the best opportunity for a profitable spot market transac.on in real .me
Background § Sparse literature on 3PL spot market pricing and sourcing - Pricing • Cheng and Qi (2011) – Op.mal 3PL pricing decision in a single supply chain
- Sourcing • Caplice & Sheffi (2003) and Sheffi (2004) – benefits of economies of scope and non-‐price variables in auc.ons • Song & Regan (2003) – Combinatorial auc.on for simultaneous bidding over several shipping lanes • Figliozzi (2004) – Sequen.al auc.ons to model an ongoing transporta.on spot market
Background (cont.) § Non-‐asset 3PL spot market procurement process is fundamentally different - Search process rather than a tradi.onal auc.on
§ Proposed framework func.ons in real .me § Non-‐asset 3PLs are an important industry segment that is largely unexplored
Conceptual Framework: Behavioral Models
• Shipper acceptance decreases with increasing cost while carrier acceptance increases with increasing price. • Probabilities are estimated using the variables created in the data mining process.
Data § Data is from a U.S.-‐based 3PL provider § Historical shipments with informa.on on: - Origin and des.na.on - Price - Equipment type - Number of stops - Hazardous material status - Etc.
§ The data is processed and enters the Pricing/Sourcing framework
Conceptual Framework: Model Development: Behavioral Models Yi = {0,1}
Rejection or acceptance
Y = f ( Shipper / Carrier, Lane, Market, etc )
Choice attributes
N
1−Yi
L(b ) = ∏ PiYi [1 − Pi ] i =1
N
LL ( b) = log !" L ( b)#$ = ∑Yi log Pi + (1− Yi ) log (1− Pi ) i=1
exp( X i , β ) Pi = Pr (Yi = 1) = 1 + exp( X i , β )
Likelihood function Log-‐likelihood function
Logit model
… with further specifications to account for the choice-restricted nature of the data.
Conceptual Framework: Model Development: Profit Maximiza2on
Conceptual Framework: Model Development: Profit Maximiza2on z = max pS ≥0 E [ Profit | pS ]
• Based on the behavioral curves we calculate the expected profit. • Expected profit takes into account the shipper price and a distribution of simulated minimum carrier prices.
Variables included in shipper and carrier acceptance choice models
Valida2on Results § The pricing tool is validated for both shippers and carriers - Shipper prices are validated using historical revenue data - Carrier prices are validated using average market-‐to-‐market rates from a third party
Valida2on Results: Carrier Prices
The simulated carrier prices produced by the tool are comparable to both the third-party and historical prices, especially for shipment-types with many observations.
Valida2on Results: Carrier Prices Histogram of the difference between the model and third party carrier rates
Price Difference = Third party carrier rate – Model-estimated rate
Valida2on Results: Shipper Prices
The shipper prices produced by the tool are comparable to historical prices, though more tightly distributed about the mean.
Profit Analysis § We compare the profits the Pricing Tool could have generated to historical profits § Each metric – pricing tool profits and historical profits – is weighted by the likelihood of the deal occurring
Profit Analysis: Difference Between Pricing Tool and Historical Profits
In general, the tool produces profits that are slightly higher than historical profits.
Weighted Profit Difference = Weighted Ideal Profit – Weighted Historical Profit
(
)(
WeightedIdeal Pr ofit = Pr Shipper Pr iceOptimal ⋅ Shipper Pr iceOptimal − Carrier Pr ice Historical
(
)(
)
WeightedHistorical Pr ofit = Pr Shipper Pr ice Historical ⋅ Shipper Pr ice Historical − Carrier Pr ice Historical
)
Valida2on Results: Profit Analysis 25th75thStd. Percentile Percentile Deviation
Profit Measure Mean Profit per Mile of Profitable Shipments 8.76% Loss per Mile of Unprofitable Shipments 74.76% Total Change Profit Measure Profitable Shipments -5.41% Unprofitable Shipments 5.41% Total Profit 4.90%
56.49%
15.39%
-41.99%
88.97%
-70.79%
79.45%
Results based on a sample of 54,805 shipments. Model calibrated to produce prices and acceptance rates comparable to what was historically observed.
Valida2on Results: Profit Analysis
Profit Measure Profit per Mile of Profitable Shipments Loss per Mile of Unprofitable Shipments
Profit Measure Total Profit
Mean
25th75thStd. Percentile Percentile Deviation
$0.51
$0.31
$0.66
$0.30
-$0.52 Total Change +$581, 876
-$0.67
-$0.10
$0.70
3PL Broker Business Model § Quote prices to shippers before securing capacity from carriers § Consider the following example: The broker ends the search and selects the carrier Carrier #1 - $105 expected to generate the highest profit - $20.
Shipper
Broker quotes the shipper $100
Carrier #2 - $80
Broker
Carrier #3 – $85 Time
29
Opportunities for Improvement § The search for capacity could be improved if: - Brokers have a good guess of the minimum price each potential carrier would demand before the search for capacity begins - Brokers could source multiple shipments simultaneously, taking advantage of the economies of scope present in the spot market 1 Load #1 CHI
Load #2
Load #1
CHI
CHI
ATL BHM Chicago à Atlanta, Birmingham à Chicago 30
Load #2
CHI
ATL Chicago à Atlanta + Birmingham à Chicago
BHM
Caplice, C., Sheffi, Y. 2006. Combinatorial auctions for truckload transportation. In: Cramton, P., Shoham, Y., Steinberg, R. (Eds.), Combinatorial Auctions, Cambridge: MIT Press (Chapter 21). 1
Framework for Sourcing Capacity on the Spot Market Reservation Price Function
Set of Shipments to be Sourced
Shipment / Bundle attributes Shipment Assignment
Set of Available Carriers
• Optimal Shipment Assignments • Expected Reservation Prices / Profits
Carrier attributes
Time
§ The framework is as powerful as a user’s ability to segment carriers according to the likely levels of their reservation prices § The rest of the discussion will focus on demonstrating how a meaningful reservation price function may be developed
31
Spot Market Stated Choice Experiment Because real-world data was not known to exist, a hypothetical field experiment was performed You have two trucks that are each available to make a move. Currently, Truck #1 is located in Rockford, IL and Truck #2 is in Dayton, OH. A shipper has just contacted you to inquire about transporting the following loads: Shipment 1 2
Origin
Des2na2on
Pick-‐up Date Empty Miles (Travel Time) Loaded Miles (Travel Time) to Origin to Des2na2on Chicago, IL Cincinna., OH Today 90 mi (2hrs.) for Truck #1 295 mi (5 hrs.) for Truck #1 Columbus, OH Atlanta, GA Tomorrow 70 mi (1 hr.) for Truck #2 568 mi (9 hrs.) for Truck #2
You may choose to accept one, both, or none of the shipments offered. If you choose both, it is possible to use Truck #1 for both moves. Shipment Empty Miles (Travel Time) to Origin 1 90 mi (2hrs.) 1&2
Loaded Miles (Travel Time) Empty Miles (Travel Loaded Miles (Travel to Des2na2on 1 Time) to Origin 2 Time) to Des2na2on 2 295 mi (5 hrs.) 107 mi (2 hrs.) 568 mi (9 hrs.)
Below are your options for which shipment(s) and at what payment (for the linehaul portion of the trip) you choose to accept from the shipper. Please choose the best available option. Choose only one. a) Shipment (1) only for $1000 ($3.39 per mile) – using Truck #1 for the move; b) Shipment (2) only for $600 ($1.06 per mile) – using Truck #2 for the move; c) Shipments (1) and (2) for $1520 (Combined $1.76 per mile) – using either Truck #1 for both moves, or both Trucks #1 and #2 individually; d) None. I will pass on this shipper and wait for something better.
§ Submitted to approximately 400 truckload carriers with a response rate ≈ 11% § Each respondent evaluated 9 pricing scenarios 32
- N = 45; J = 9;
N x J = 405 observations
Randomized Survey Design Pricing Scenario Data
Carrier Submits Preliminary Information
Database Query via Web Service
Base Shipment Data v Origin-Destination of Shipments 1 & 2 v Current truck locations v Loaded and empty miles Random Shipment Data v Price of Shipments 1 & 2 v Bundle discount v Lead time
Carrier Completes Randomized Pricing Scenarios
Randomized Pricing Scenarios
• Respondent enters preliminary information • Web service places a call to a relational database consisting of base pricing scenarios • Base pricing scenarios are shipment O-Ds and current locations of the carrier’s hypothetical trucks
• Web service randomizes shipment attribute data for all scenarios and returns them to the online survey tool Survey administered using Qualtrics (www.Qualtrics.com)
End Time 33
Variables Derived from Survey Results Variable
Definition
Shipment Variables Loaded Miles
Number of miles shipment is actually transported
Empty Miles
Number of miles associated with a shipment not related to its actual transport
Cross Empty Miles
Number of miles from the drop-off location of one shipment and the delivery location of the next shipment
Demographic Variables
34
Individual experience
Number of years a respondent has been in the logistics industry
Firm size
Size of the carrier by number of employees
Firm fleet size
Number of vehicles under control by the carrier
Firm tenure
Number of years a firm has been in the logistics industry
Survey Summary Statistics Single Shipment Offers Variable Loaded Miles Empty Miles Price per Mile Price
Lead Time
Min. 300 0 0.49 212
Bundle Offers
Mean
Max.
397 31.9 1.39 547
Same Day 177
Variable
577 126 2.76 1,417
1 Day 344
2 Days 163
Min.
Loaded Miles Cross Empty Miles Price per Mile Price
600 0 0.73 587
Mean 793 112 1.33 1,049
Same Day 169
Lead Time
Definition and Frequency by Category Variable Experience Firm Size Firm Fleet Size Firm Tenure
35
Low
Moderate
High
Less than 7 years
7 to 10 years
More than 10 years
Less than 250 employees
250 to 500 employees
More than 500 employees
Less than 250 trucks
250 to 1,000 trucks
More than 1,000 trucks
Less than 7 years
7 to 10 years
More than 10 years
Variable
Low
Individual Experience
0.103
0.342
0.526
Firm Size
0.237
0.237
0.526
Firm Fleet Size
0.579
0.211
0.158
0.0263
0.395
0.579
Firm Tenure
Moderate
Max.
High
1,090 213 2.31 2,120
1 Day 2 Days 163 --
Characterizing Carrier Behavior § Reservation price is the least price at which carrier k is willing to sell a transportation service, in our case capacity k m j
denotes the pricing scenario
Pm
denotes the price of alternative m
p
Compensation offered to motor carrier k to provide transportation service S
denotes the Carrier Alternative available to carrier k as part of the offer
(1) U mk (S, p) −U ( 0, 0) ≡ 0
The reservation price, Rk(p), is the price at which motor carrier k sells the transportation service and nets a zero gain in utility
{
}
1 (2) p − R k ( p ) ≥ max p − R k (P1 ),..., PM − R k (PM )
(3) p ≥ R k (p )
{
Offer price must exceed the reservation price
}
(4) max p1 − R k (P1 ),..., PM − R k (PM ) < 0
36
Surplus must be greater than all other alternatives
Carrier will refrain from all alternatives if they do not offer more utility than the ‘No choice’ option
Jedidi, K. and Zhang, Z.J. (2002) Augmenting Conjoint Analysis to Estimate Consumer Reservation Price. Management Science 48 (10).
Random Parameters Mixed Logit for Panel Data U kmj = Vkmj + ukmj
Utility yielded to motor carrier k from the surplus of alternative m
ukmj ~ i.i.d . Gumbel
Random portion of utility is distributed iid Gumbel
Jk
Conditional likelihood of motor carrier k selecting among the four alternatives in price scenario Jk
Lk | β = ∏ Qkmj j =1
Qkij = e
β `xkij
∑e
β `xkmj
Logit probability of the i th is selected
m
Lk = ∫ (Lk | β )⋅ f (β )dβ β
2 ⎛ c11 Ω = C C = ⎜⎜ ⎝ c11c12 T
c11c12 ⎞ ⎟ 2 2 ⎟ c12 + c 22 ⎠
1 Train, K. (1998)
37
Unconditional likelihood of the observed choice sequence for carrier k • Allowing β to vary across the population induces correlation across alternatives and scenarios • Additionally, we allow for correlation among the random parameters • Coefficients for Price, and for Loaded Miles specified as random
Recreation Demand Models with Taste Differences Over People. Land Economics 74 (2). Estimation of multinomial logit models in R: The mlogit Packages.
2 Croissant, Y. (2013)
Variable Types and Definitions Variable
Type
Model 1
Model 2
Single
Indicator
ü
ü
ü
Bundle
Indicator
ü
ü
ü
Price
Continuous
ü
ü
ü
Loaded Miles
Continuous
ü
ü
ü
Cross Empty Miles
Continuous
ü
ü
ü
Lead Time
Categorical (Same day, 1 day, 2 days)
ü
ü
ü
Experience
Categorical (Low, Moderate, High)
ü
ü
ü
Firm Size
Categorical (Small, Moderate, Large)
ü
Fleet Size
Categorical (Small, Moderate, Large)
Tenure
Categorical (Low, Moderate, High)
ü
Note: Underlined categories denote the reference levels in the discrete choice analysis. 38
Model 3
ü
Deterministic Utility Specifications Model 1
Model 3
Variable 1-Shipment Bundle Price Price * Low Experience Price * Mod. Experience Loaded Miles
Parameter βSingle βBundle βPrice βPrice-LE βPrice-ME βLoaded Miles
Parameter βSingle βBundle βPrice βPrice-LE βPrice-ME βLoaded Miles
βSingle βBundle βPrice βPrice-LE βPrice-ME βLoaded Miles
Loaded Miles * Mod.-Sized Firm Loaded Miles * Large-Sized Firm Loaded Miles * Mod.-Size Fleet Loaded Miles * Large-Size Fleet
βLoaded Miles-MF βLoaded Miles-LF ---
--βLoaded Miles-FM βLoaded Miles-FL
-----
Loaded Miles * Mod. Firm Tenure --
--
βLoaded Miles-TM
Loaded Miles * High Firm Tenure --
--
βLoaded Miles-TL
Cross Empty Miles * Bundle Lead Time 1-Day Lead Time 2-Days 39
Model 2
Parameter
βCross Empty Miles βCross Empty Miles βCross Empty Miles βOne-Day Lead βOne-Day Lead βOne-Day Lead βTwo-Day Lead βTwo-Day Lead βTwo-Day Lead
Discrete Choice Analysis Results Model 1
Model 2
Model 3
Significance
Significance
Significance
**** ****
* **** ****
****
****
Loaded Miles * Mod.-Sized Firm
--
--
LoadedMiles * Large-Sized Firm
--
--
**
--
Variable 1-Shipment Bundle Price Price * Low Experience Price * Mod. Experience Loaded Miles
**** * *** ****
LoadedMiles * Mod.-Size Fleet
--
Loaded Miles * Large-Size Fleet
--
Loaded Miles * Mod. Firm Tenure
--
--
Loaded Miles * High Firm Tenure Cross Empty Miles * Bundle Lead Time 1-Day Lead Time 2-Days Log-Likelihood LRI
--
--
-263.91 0.360
-262.94 0.363
§
Results statistically significant at the 5% level or better
§
Indicate that carriers are most influenced by offered payment and amount of loaded miles - Single shipment elasticities for ‘Price’ and ‘Loaded Miles’ are 0.0011 and -0.0022 - Bundled shipment elasticities are 0.0002 and -0.0004
-****
§
Results are intuitive - Offer price reflects a carrier’s revenue for transporting a shipment
-330.64 0.199
Significance codes: [0, 0.001) = ‘****’, [0.001, 0.01) = ‘***’, [0.01, 0.05) = ‘**’, [0.05, 0.1) = ‘*’. 40
- Distance is the primary driver of operational costs.
Discrete Choice Analysis Results Model 1 Variable
Model 2
Coefficient Std. Error
1-‐Shipment Bundle Price
Sig.
Coefficient
Model 3
Std. Error Sig.
Coefficient
Std. Error Sig.
0.269
0.895
0.503
0.904
-‐0.363
0.886
1.24
1.68
1.59
1.68
3.13
1.64
0.0108
0.00146
***
0.0224
0.00226 ***
0.00385
0.00099
***
-‐0.00367
0.00104 ***
0.000427
0.00069
0.0105
0.00143 ***
Price * Low Experience
0.00188
0.00097
.
Price * Mod. Experience
0.00204
0.00071 **
0.00076
0.00056
Loaded Miles
-‐0.0203
0.00331 ***
-‐0.0217
0.00349
LoadedMiles * Mod.-‐Sized Firm
0.00154
0.00104
-‐-‐
-‐-‐
-‐-‐
-‐-‐
-‐-‐
-‐-‐
LoadedMiles * Large-‐Sized Firm
-‐0.00131
0.00105
-‐-‐
-‐-‐
-‐-‐
-‐-‐
-‐-‐
-‐-‐
-‐-‐
-‐-‐
-‐-‐
-‐-‐
-‐-‐
-‐-‐
***
-‐0.0398
0.00436 ***
LoadedMiles * Mod.-‐Size Fleet -‐-‐
-‐-‐
-‐-‐
-‐0.00217
0.00095
Loaded Miles * Large-‐Size Fleet -‐-‐
-‐-‐
-‐-‐
0.00096
0.00107
LoadedMiles * Mod. Firm Tenure
-‐-‐
-‐-‐
-‐-‐
-‐-‐
-‐-‐
-‐-‐
0.00910
0.00164 ***
Loaded Miles * High Firm Tenure
-‐-‐
-‐-‐
-‐-‐
-‐-‐
-‐-‐
-‐-‐
0.00205
0.00143
Cross Empty Miles * Bundle
*
.
-‐0.00320
0.00299
-‐0.00326
0.00298
-‐0.00071
0.00306
Lead Time 1-‐Day
-‐0.0939
0.299
-‐0.115
0.302
0.0318
0.290
Lead Time 2-‐Days
0.0262
0.435
-‐0.0194
0.435
0.532
0.434
cor(Price) cor(Price, Loaded Miles) cor(LoadedMiles) Log-‐Likelihood LRI
-‐0.00722
0.00188 ***
-‐0.00705
0.00173
***
0.0564
0.00829 ***
0.0141
0.00316 ***
0.015
0.003
***
-‐0.102
0.0144 ***
0.00626
0.00093 ***
0.006
0.001
***
-‐0.00786
0.00108 ***
-‐263.91
-‐262.94
-‐330.64
0.360
0.363
0.199
Significance codes: [0, 0.001) = ‘***’, [0.001, 0.01) = ‘**’, [0.01, 0.05) = ‘*’, [0.05, 0.1) = ‘.’.
Calculating Reservation Price § Recall that the primary goal is to estimate reservation prices - Let W define the set of non-price parameters, where w = 1 … W. - Let zw denote the non-price variables, and β Price and βW denote the price and non-price parameters, respectively Rkmj
W
⎞ β z = ⎛⎜ − 1 w w β Pr ice ⎟⎠∑ ⎝ w
» Reservation prices are inferred by taking the sum of the non-price parameters and multiplying by the reciprocal of the appropriate price parameter(s).
42
Reservation Price Validation Procedure § Decision Rule: Carriers select the option that yields the highest utility (i.e. surplus) § Criterion: Reproduce observed choice frequencies over several hundred simulations § Validation procedure 1. Delineate Training and Holdout data sets of carrier choice scenarios 1. Training data – 30 respondents (270 obs.); Holdout data – 15 respondents (135 obs.)
43
2.
Draw values for random parameters and error terms from their respective distributions
3.
Calculate utility for all choice alternatives presented to carriers in the Holdout data set
4.
Determine the preferred alternative based on the decision rule
5.
Repeat steps 2-4 several hundred times
6.
Calculate the simulated choice frequencies
Reservation Price Validation Results Shipment 1
Shipment 2
Bundle
None
Observed Choice Frequencies 0.0815
0.189
0.211
0.519
Simulated Choice Frequencies Model 1
0.0900
0.151
0.170
0.588
Model 2
0.0820
0.148
0.185
0.585
Model 3
0.132
0.174
0.344
0.350
Note: Density of choice frequencies for Model 1 depicted in the figures.
44
Primary Implications: Carrier-segmented Reservation Price Functions
2000 1800
§ LE
Price ($)
1600
ME
1400
LE-‐MF
1200
LE-‐LF ME-‐MF
1000
ME-‐LF
800
MF
600
LF HE-‐SF
400 300
375
450
525
600
675
750
825
§ § § § § § § §
Model 1 Carrier Segments LE = Low Experience (Not Mod.- or LargeSize Firm) ME = Mod. Experience (Not Mod.- or LargeSize Firm) LE-MF = Low Experience + Mod.-Size Firm LE-LF = Low Experience + Large-Size Firm ME-MF = Mod. Experience + Mod.-Size Firm ME-LF = Mod. Experience + Large-Size Firm MF = Mod.-Size Firm (Not Low or Mod.Experience Respondent) LF = Large-Size Firm (Not Low or Mod.Experience Respondent) HE-SF = High Experience + Small-Size Firm
900
Loaded Miles
Carrier Segment
Reservation Price Function
LE
Rkj = {-1/(βPrice + βPrice-LE)} * (βLoaded Miles*Loaded Milesj + βOne-Day Lead*1-Day Lead Timej)
ME
Rkj = {-1/(βPrice + βPrice-ME)} * (βLoaded Miles*Loaded Milesj + βOne-Day Lead*1-Day Lead Timej)
LE-MF
Rkj = {-1/(βPrice + βPrice-LE)} * (βLoaded Miles*Loaded Milesj + βLoaded Miles-MF*Loaded Milesj * Mod. Firm Sizej + βOne-Day Lead*1-Day Lead Timej)
…
…
45
Primary Implications: Bundled Offers may be Less Expensive 2500
§
Reservation price functions for bundles are similarly developed
§
Generally exhibit lower pershipment reservation prices
§
May be an important source of cost savings for shippers while offering benefits to carriers
LE
2000
Price ($)
ME LE-‐MF
1500
LE-‐LF ME-‐MF
1000
ME-‐LF 500
MF LF
0 300
375
450
525
600
675
750
825
900
General
Loaded Miles
Carrier Segment
Reservation Price Function
LE
Rkj = {-1/(βPrice + βPrice-LE)} * (βLoaded Miles*Loaded Milesj + βOne-Day Lead*1-Day Lead Timej)
ME
Rkj = {-1/(βPrice + βPrice-ME)} * (βLoaded Miles*Loaded Milesj + βOne-Day Lead*1-Day Lead Timej)
LE-MF
Rkj = {-1/(βPrice + βPrice-LE)} * (βLoaded Miles*Loaded Milesj + βLoaded Miles-MF*Loaded Milesj * Mod. Firm Sizej + βOne-Day Lead*1-Day Lead Timej)
…
…
46
Key Findings and Limitations § The speculative nature of the spot market has considerable behavioral dynamics that are important to capture § 3PLs can develop effective revenue management strategies based on carriers’ different valuations of spot market shipments. § Offering multiple shipments simultaneously on the spot market (bundling) can create cost savings for 3PLs. § Limitations - Ability to capture real-world, as opposed to experimental reservation prices • Because of the spot market’s volatility, the framing of the experiment changes in substantial and un-modeled ways over time.
- Magnitude: A larger field experiment with many more carriers would yield richer insights and the ability to improve carrier segmentation 47
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Elasticities Single Shipment Variable Price Respondents with low Price * Low Experience experience among the Price * Mod. Experience most price-sensitive. Loaded Miles Loaded Miles * Mod.-Sized Firm Loaded Miles * Large-Sized Firm Loaded Miles * Mod.-Size Fleet Loaded Miles * Large-Size Fleet Loaded Miles * Mod. Firm Tenure Loaded Miles * High Firm Tenure Variable Price Price * Low Experience Firms with moderate Price * Mod. Experience tenure among the mostLoaded Miles Loaded Miles * Mod.-Sized Firm distance-sensitive. Loaded Miles * Large-Sized Firm Loaded Miles * Mod.-Size Fleet Loaded Miles * Large-Size Fleet
Model 1 Elasticity 0.0011 0.0031 0.0034 -0.0022 -0.0034 -0.0014
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Model 2 Elasticity 0.0010 0.0065 0.0015 -0.0019
---
-- Model 1 Elasticity 0.0002 0.0016 0.0019 -0.0004 -0.0012 -0.0002
---
---0.0001 -0.0005
---
---0.0032
-0.0134 -0.0017
Model 2 Elasticity 0.0001 0.0058 0.0003 -0.0003
---
Model 3 Elasticity 0.0005 0.0001 0.0006 -0.0008 -----
-0.0009 -0.0026
---
Bundle
Loaded Miles * Mod. Firm Tenure Loaded Miles * High Firm Tenure Cross Empty Miles * Bundle
-0.0033
Model 3 Elasticity 0.0002 0.000003 0.0003 -0.0003 -----0.0279 -0.0014 -0.0007
Probability Curves & Reservation Price Functions Probability Curves Calculated using the following assumptions » 1 day of lead time and mean values of all variables » Alternatives treated as separate binary choices (e.g. zero utility values for the unselected alternatives)
Reservation Price Functions
§ Let W define the set of non-price parameters, where w = 1 … W. § Let zw denote the non-price variables, and β Price and βW denote the price and non-price parameters, respectively rkmj
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W
⎞ β z = ⎛⎜ − 1 w w β Pr ice ⎟⎠∑ ⎝ w
Reservation prices are inferred by taking the sum of the non-price parameters and multiplying by the reciprocal of the appropriate price parameter(s).
Single Shipment Probability Curves
1
0.8
LE
0.7
ME
0.6
LE-‐MF
0.5
LE-‐LF
0.4
ME-‐MF
0.3
ME-‐LF
0.2
MF
0.1
LF 900
870
840
810
780
750
720
690
660
630
600
570
540
510
480
450
420
390
360
HE-‐SF 330
0
300
Probability of Acceptance
0.9
Model 1 Carrier Segments v LE = Low Experience (Not Mod.- or LargeSize Firm) v ME = Mod. Experience (Not Mod.- or LargeSize Firm) v LE-MF = Low Experience + Mod.-Size Firm v LE-LF = Low Experience + Large-Size Firm v ME-MF = Mod. Experience + Mod.-Size Firm v ME-LF = Mod. Experience + Large-Size Firm v MF = Mod.-Size Firm (Not Low or Mod.Experience Respondent) v LF = Large-Size Firm (Not Low or Mod.Experience Respondent) v HE-SF = High Experience + Small-Size Firm
Offer Price ($)
Carrier Segment
Deterministic Utility
LE
Vkj = βSingle*Singlej + βPrice*Pricej + βPrice-LE*Pricej * Low Experiencek + βLoaded Miles*Loaded Milesj + βOne-Day Lead*1-Day Lead Timej
ME
Vkj = βSingle*Singlej + βPrice*Pricej + βPrice-ME*Pricej * Mod. Experiencek + βLoaded Miles*Loaded Milesj + βOne-Day Lead*1-Day Lead Timej
LE-MF
Vkj = βSingle*Singlej + βPrice*Pricej + βPrice-LE*Pricej * Low Experiencek + βLoaded Miles*Loaded Milesj + βLoaded Miles-MF*Loaded Milesj * Mod. Firm Sizej + βOne-Day Lead*1-Day Lead Timej
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