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 OD Flows Assignment

Disaggregation A C Aggregation

B

Disaggregate firms Firms Shipments

and shipments (agents)

Logistic

decisions

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 Mean/%

Rail Access 2%

Quay Access 0.4%

Shipment Weight (KG) 26010.6

Shipment Value (SEK) 37121.9

Value Density (SEK/KG) 1231.4

Transport Costs (105 SEK) 1129.6

Transport Time (hours) 13.5

No. of Obervation 2,897,175

Major commodities - outgoing shipments

Swedish CFS 2004/05

There are 28 commodity groups in the CFS based on the SAMGODS classification,

and 6 commodities make up 80% of the shipment

Commodity Freq.

Share

(%)

Avg.

Value Avg. weight

Avg. value

density

(value/weight)

(SEK) (KG) (SEK/KG)

Live Animals 128136 4.42 29081.90 3542.29 10.24

Foodstuff and animal

fodder 304956 10.53 20788.93 1181.89 3162.02

Metal products 39235 1.35 39147.35 6472.73 32.20

Leather and textile 178744 6.17 14364.23 490.89 2511.12

Timber 1481862 51.15 8863.77 34123.72 0.26

Machineries 231748 8.00 27381.46 280.67 7920.00

Total 2364681 81.62

Total shipments in CFS 2897010

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 From (kg) To (kg) Freq. Percent

1 0 50 703,939 24.36

2 51 200 153,222 5.3

3 201 800 160,420 5.55

4 801 3000 157,891 5.46

5 3001 7500 136,884 4.74

6 7501 12500 127,583 4.42

7 12501 20000 161,688 5.6

8 20001 30000 210,919 7.3

9 30001 35000 207,622 7.19

10 35001 40000 344,695 11.93

11 40001 45000 340,498 11.78

12 45001 100000 153,857 5.32

13 100001 200000 10,835 0.37

14 200001 400000 7,238 0.25

15 400001 800000 6,417 0.22

16 800001 - 5,641 0.2

Total 2,889,349 100

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

Water Truck-Vessel-Truck

Truck-Ferry- Truck

Truck-Vessel

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 NL

Coefficient

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 -0.0012***

Number of observations: 2.225.150

Pseudo rho-squared w.r.t. zero: 0.73

Pseudo rho-squared w.r.t. constants: 0.32

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 Distribution

(standard

deviation)

t-ratio

Road constant Road 3.169 126.6

Rail constant Rail -1.107 -21.1

Water constant Water -1.385 -22.6

Company is in biggest size class

(sector-dependent)

Rail .279 8.1

Commodity type is metal products Rail -.471 -9.3

Commodity type is chemical products Rail -.0338 -.6

Absolute difference between estimated

and average observed shipment size Vl

All -.240 -63.0

Transport cost in SEK/shipment Road, rail,

water, air

-.0000240 -35.2 -.0000142

-54.5

Transport time in hours (*10) Road -.00745 -32.2 .0000918 .5

Transport time in hours (*10) Rail -.00317

-17.1 .000132 .5

Transport time in hours (*10) Air -.328 -20.4 .167 19.2

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

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

Dependent Variable

VARIABLES Log-shipment size (kg)

Log. Value Density -1.925***

(0.0389)

Access to Rail at Origin 2.117***

(0.485)

International Shipment 1.921***

(0.155)

Total Shipments -0.000695***

(1.55e-05)

Summer 0.302***

(0.0485)

Log. Distance 0.385***

(0.0224)

Container mindre än 20 fot -2.100

(2.816)

Pallastat (pallagt,palletiserat) gods -0.980**

(0.407)

Okänd -0.374

(1.812)

Observations 33,121

R-squared 0.230

Results: MNL model for metal products CFS 04/05

Truck-Rail-

Truck

Truck-Ferry-

Truck

Truck-

Vessel-Truck

Log. Cost 0.74*** 0.46*** 3.5***

(0.037) (0.036) (0.52)

Log. Time 0.26*** 1.71*** 6.31***

(0.049) (0.116) (1.46)

Constant -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

Effects

on P

r(M

od

echa

in_S

==

1)

0 2 4 6 8 10 12 14 16 18logcost

Average Marginal Effects of logcost

Results: Marginal Effects of cost – Truck-Rail-Truck

0.2

.4.6

.8

Effects

on P

r(M

od

echa

in_S

==

121

)

0 2 4 6 8 10 12 14 16 18logcost

Average Marginal Effects of logcost

Results: Marginal Effects of cost – Truck-Ferry-Truck

-.2

0.2

.4.6

Effects

on P

r(M

od

echa

in_S

==

131

)

0 2 4 6 8 10 12 14 16 18logcost

Average Marginal Effects of logcost

Results: Marginal Effects of cost – Truck-Vessel-Truck

2.8

33.2

3.4

3.6

Effects

on P

r(M

od

echa

in_S

==

141

)

0 2 4 6 8 10 12 14 16 18logcost

Average Marginal Effects of logcost

Results: Conditional shipment quantity model using the Dubin-McFadden

Method

Truck Rail Ferry Vessel

Log. Value Density -0.937*** -0.0379 -0.108 -1.266

Log. Total Shipments -0.187*** 0.0270** 0.0356 0.224

Access to Rail 0.139*

International 0.536 -0.411*** -0.116 0.217

Summer Included Included Included Included

Cargo Type Included Included Included Included

Firm Size -3.678*** -0.264* 0.0993 -0.189

Select_Truck 1.685*** 0.141 -2.940

Select_Rail -28.38*** -7.914*** -3.641*

Select_Ferry 19.40** 2.114*** 6.904***

Select_Vessel 16.62 -2.288*** 7.398***

Constant 8.117*** 12.40*** 2.910* 13.54***

Observations 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/

References

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