A discrete-continuous model
of freight mode and shipment
size choice
Megersa Abate (presenter), The Swedish
National Road and Transport Research Institute
(VTI);
Inge Vierth, VTI ; Gerard de Jong, Significance,
Uni. of Leeds, CTS, Stockholm
Introduction – The Swedish National Freight
Model
• The main feature of the Swedish freight transport model
(SAMGODS) is incorporation of a logistic model component
in the traditional freight demand modeling framework
• The SAMGODS model consists of
1. Product specific demand PC-matrices (producers-consumers)
2. Logistics model (LOGMOD)
3. Network model
Structure of SAMGODS model: ADA
ADA model based on de Jong and Ben-Akiva (2007)
Aggregate flows
PWC flows
Disaggregation
OD Flows
A
C Aggregation
B
Disaggregate firms
and shipments
Firms
(agents)
Shipments
Logistic
decisions
Assignment
Introduction: Deterministic cost minimization
• The current logistic model is based on a deterministic cost
minimization model where firms are assumed to minimize
annual total logistic cost [G(.)]
argmin 𝐺 .
• The cost trade-off involves order costs; transport,
consolidation and distribution costs; cost of deterioration
and damage during transit; capital holding cost; inventory
cost; stock-out costs
Limitation of the current logistic model
• The current logistic model lacks two mains elements:
1. other determinants of shipment size and transport chain choice
( decisions are solely based on cost)
2. stochastic element ( it is deterministic)
Objective of the current project
• This project is a first step towards estimating a full
random/stochastic utility logistic model
• We formulate econometric models to analyze the determinants
of firms’ transport chain and shipment size choices
• Parameter estimates from this model will later be used to set-up
a stochastic logistic model
• Estimation of elasticity for policy analysis
Stochastic logistic model
•
A full random utility logistic model was planned but has
not yet been estimated on disaggregate data ( de Jong and
Ben-Akiva, 2007)
• The model is specified as:
Ul = -Gl – l
where Ul is the utility derived from logistics and transport chain choice,
Gl is logistics cost, and l is a random variable
Modeling framework
• The main econometric work involves modeling the
interdependence between shipment size and transport chain
choices
• This interdependence implies the use of a joint ( e.g.
discrete-continuous) econometric model to account for the
simultaneity problem
Econometric model
Discrete-Continues econometric set-up
Ul = 1X + G + 1
(1)
SS2 = 2X + 2
(2)
Where Ul is a utility form a mode choice and SS is shipment
size, X and G are vectors of explanatory variables that determine
SS the choice of transport chain,
Modeling approaches in the literature
1. An independent discrete mode choice model (which is the most
common formulation)
Ul = 1X + 1
(1)
2. A joint model with discrete mode and discrete shipment size choice
(e.g. Chiang et al. 1981; de Jong, 2007; Windisch et al. 2009)
Ul = 1X + G + 1
(1’)
3. A joint model with discrete mode and continuous shipment size
choice ( Abate and de Jong, 2013; Johnson and de Jong, 2010; Dubin and
McFadden 1984; Abdelwahab and Sargious,1992;Holguín-Veras ,2002)
Ul = 1X + G + 1
(1)
SS2 = 2X + 2
(2)
Determinants of shipment size/transport chain
choice
Variables (in X and G)
Effect on SS
Effect on mode/chain choice
Transport Cost
Negative
Transport Time
Negative
Value Density
Negative
?
Access to Rail/Quay
?
?
Firm Characteristics
?
?
Network Characteristics
?
?
Data
Main data source :
- National Commodity Flow Survey 2004/05 (CFS) based on
the US CFS
- Network data – mainly transport time and cost variables from
the logistics module of SAMGODS
Descriptive Statistics
Variable
Rail Access
Quay Access
Mean/%
2%
0.4%
Shipment Weight (KG)
26010.6
Shipment Value (SEK)
37121.9
Value Density (SEK/KG)
Transport Costs (105 SEK)
Transport Time (hours)
1231.4
1129.6
13.5
2,897,175
No. of Obervation
Major commodities - outgoing shipments
Swedish CFS 2004/05
Freq.
Share
(%)
Live Animals
Foodstuff and animal
fodder
Metal products
128136
4.42
Avg. value
Avg.
density
Value
Avg. weight (value/weight)
(SEK)
(KG)
(SEK/KG)
29081.90
3542.29
10.24
304956
39235
10.53
1.35
20788.93
39147.35
1181.89
6472.73
3162.02
32.20
Leather and textile
178744
6.17
14364.23
490.89
2511.12
Timber
Machineries
1481862
231748
51.15
8.00
8863.77
27381.46
34123.72
280.67
0.26
7920.00
Total
2364681
81.62
Total shipments in CFS
2897010
Commodity
There are 28 commodity groups in the CFS based on the SAMGODS classification,
and 6 commodities make up 80% of the shipment
Transportation Costs and Commodity value –
Metal Products
Variable
Average Values
From CFS ( values per shipment)
Weight (kg)
6556.49
Value (SEK)
31942.84
Tonne-Kilometer
7071.12
Value/Tonne (SEK/KG)
24.38
From Network Data based on all available choices
Distance/shipment (KM)
591.41
Transport Cost (SEK)
3.92e+07
Transport Tim (hours)
10.24
Transport Chain Type Definitions
Chains
% Share
Truck
96
Truck-Truck-Truck
0.01
Truck-Vessel-Truck
1.66
Truck-Ferry- Truck
0.50
Truck-Rail-Vessel-Truck
0.20
Truck-Rail-Truck
0.22
Truck-Air-Truck
0.53
Shipment size categories
Category
1
2
3
4
5
6
7
8
9
10
11
From (kg)
0
51
201
801
3001
7501
12501
20001
30001
35001
40001
To (kg)
50
200
800
3000
7500
12500
20000
30000
35000
40000
45000
Freq.
703,939
153,222
160,420
157,891
136,884
127,583
161,688
210,919
207,622
344,695
340,498
Percent
24.36
5.3
5.55
5.46
4.74
4.42
5.6
7.3
7.19
11.93
11.78
12
45001
100000
153,857
5.32
13
100001
200000
10,835
0.37
14
200001
400000
7,238
0.25
15
16
400001
800001
800000
-
6,417
5,641
0.22
0.2
2,889,349
100
Total
Results
Estimation results for a Nested Logit model for discrete mode and
discrete shipment size choice (2004/5 CFS)
Results
Nest Structure of mode and chain
Mode
Chains
Truck
Truck
Truck-Truck-Truck
Truck-Vessel-Truck
Truck-Ferry- Truck
Truck-Vessel
Water
Rail
Truck-Rail-Vessel-Truck
Truck-Rail-Truck
Air
Truck-Air-Truck
Results
NL for discrete mode and discrete shipment size choice from
2004/5 CFS (Windisch et al. 2009)
Variable
Relevant alternatives
Proxy to Rail/Quay
Rail/Vessel
7.02***
Value density in SEK/kg
All modes: all smallest
shipment sizes
1.11***
Transport cost in SEK/shipment
All
Number of observations: 2.225.150
Pseudo rho-squared w.r.t. zero: 0.73
Pseudo rho-squared w.r.t. constants: 0.32
NL
Coefficient
-0.0012***
Results: Estimation results for mixed multinomial logit model including
estimated shipment size at instrumental variable (Johnson and de Jong,
2009)
Variable
Relevant
alternatives
Coefficient t-ratio
Road constant
Rail constant
Water constant
Company is in biggest size class
(sector-dependent)
Commodity type is metal products
Road
Rail
Water
Rail
3.169
-1.107
-1.385
.279
126.6
-21.1
-22.6
8.1
Rail
-.471
-9.3
Commodity type is chemical products
Rail
-.0338
-.6
Absolute difference between estimated All
and average observed shipment size Vl
-.240
-63.0
Transport cost in SEK/shipment
Road, rail,
water, air
-.0000240
Transport time in hours (*10)
Transport time in hours (*10)
Road
Rail
-.00745
-.00317
Transport time in hours (*10)
Air
-.328
Number of observations: 744860
Final log likelihood value: -124835.5142
Pseudo rho-squared w.r.t. zero: .8791
Pseudo rho-squared w.r.t. constants: .0529
Distribution
(standard
deviation)
t-ratio
-35.2
-.0000142
-54.5
-32.2
-17.1
.0000918
.000132
.5
.5
-20.4
.167
19.2
A joint model with discrete mode and continuous
shipment size choice: Metal Products
A joint model with discrete mode and continuous shipment size choice
(Dubin and McFadden 1984 )
SS2 = 2X + 2
(1)
Ul = 1X + G + 1
(2)
Results: Shipment Size model preliminary results
VARIABLES
Log. Value Density
Access to Rail at Origin
International Shipment
Total Shipments
Summer
Log. Distance
Container mindre än 20 fot
Pallastat (pallagt,palletiserat) gods
Okänd
Observations
R-squared
Dependent Variable
Log-shipment size (kg)
-1.925***
(0.0389)
2.117***
(0.485)
1.921***
(0.155)
-0.000695***
(1.55e-05)
0.302***
(0.0485)
0.385***
(0.0224)
-2.100
(2.816)
-0.980**
(0.407)
-0.374
(1.812)
33,121
0.230
Results: MNL model for metal products CFS 04/05
Log. Cost
Log. Time
Constant
Truck-RailTruck
Truck-Ferry- TruckTruck
Vessel-Truck
0.74***
0.46***
3.5***
(0.037)
(0.036)
(0.52)
0.26***
1.71***
6.31***
(0.049)
(0.116)
(1.46)
-12.04***
-13.88***
-84.92***
(0.445)
(0.53)
(14.37)
Observations
33183
Pseudo R-squared
0.4249
Results: Marginal Effects of cost – Truck
-.6
-.4
-.2
0
Average Marginal Effects of logcost
0
2
4
6
8
10
logcost
12
14
16
18
Results: Marginal Effects of cost – Truck-Rail-Truck
0
.2
.4
.6
.8
Average Marginal Effects of logcost
0
2
4
6
8
10
logcost
12
14
16
18
Results: Marginal Effects of cost – Truck-Ferry-Truck
-.2
0
.2
.4
.6
Average Marginal Effects of logcost
0
2
4
6
8
10
logcost
12
14
16
18
Results: Marginal Effects of cost – Truck-Vessel-Truck
2.8
3
3.2
3.4
3.6
Average Marginal Effects of logcost
0
2
4
6
8
10
logcost
12
14
16
18
Results: Conditional shipment quantity model using the Dubin-McFadden
Method
Log. Value Density
Log. Total Shipments
Access to Rail
International
Summer
Cargo Type
Firm Size
Select_Truck
Select_Rail
Select_Ferry
Select_Vessel
Constant
Observations
Truck
Rail
Ferry
Vessel
-0.937***
-0.187***
-0.0379
0.0270**
0.139*
-0.411***
Included
Included
-0.264*
1.685***
-0.108
0.0356
-1.266
0.224
-0.116
Included
Included
0.0993
0.141
-7.914***
0.217
Included
Included
-0.189
-2.940
-3.641*
6.904***
0.536
Included
Included
-3.678***
-28.38***
19.40**
16.62
8.117***
2.114***
-2.288***
12.40***
7.398***
2.910*
13.54***
31,412
1,526
130
115
Results: Elasticity Comparison ( Johnson and de Jong,
2009)
Independent
mode choice
Discrete shipment
size and mode
Continuous
shipment size and
discrete mode
Road cost
-0.002
-0.030
-0.003
Rail cost
-0.438
-0.126
-0.393
Water cost
-0.920
-0.073
-0.639
Air cost
-0.311
-0.001
-0.198
Road time
-0.040
-
-0.025
Rail time
-0.447
-
-0.302
Air time
-1.391
-0.871
-1.454
Conclusions
 Transport Cost , Transport Time and Firm characteristics such
as access to rail and quay at origin are important determinants
of transport chain and shipment size choices.
 Low elasticity for road (truck) transport cost
 It is important to handle the simultaneous nature of the
decisions on mode/transport chain and shipment size choices
 Due to large data, estimation can be difficult to utilize the most
theoretically sound model
Thank you for your attention !
Contact: megersa.abate@vti.se
https://sites.google.com/site/megersabate/
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