estimating an origin–destination table for us imports of waterborne containerized freight

Transportation Research Part E 45 (2009) 611–626

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Transportation Research Part E

journal homepage: www.elsevier .com/locate / t re

Estimating an origin–destination table for US imports of waterbornecontainerized freight

Brian Levine a, Linda Nozick a,*, Dean Jones b,1

a School of Civil and Environmental Engineering, Cornell University, Hollister Hall, Ithaca, NY 14853, United Statesb Sandia National Laboratories, P.O. Box 5800 MS 1138, Albuquerque, NM 87185-1138, United States

a r t i c l e i n f o

Article history:Received 5 March 2008Received in revised form 23 June 2008Accepted 15 November 2008

Keywords:Origin–destination tableContainerized freightOptimizationGravity model

1366-5545/$ - see front matter � 2008 Elsevier Ltddoi:10.1016/j.tre.2008.11.001

* Corresponding author. Tel.: +1 607 255 6496.E-mail addresses: [email protected] (B. Levine), L

1 Tel.: +1 505 284 4886.

a b s t r a c t

Containerized freight imports into the US are growing at an average of 10% per year. Thistraffic is concentrated at a small number of US seaports. It is therefore important to have anaccurate understanding of the flow of containers from their origin country through theseseaports to their final destination. This paper develops an optimization model to estimateroute flows and a corresponding multi-modal origin–destination table for containers bysynthesizing data on international trade and railcar movements with a gravity model forthe demand of container traffic. This analysis provides insights into the balance of railand truck inland transportation from each port.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

In 2006, almost 18.5 million twenty-foot equivalent units (TEUs) of goods entered the United States through US containerports (US Maritime Administration, 2007). On average, containerized import volumes have been growing at about 10% peryear over the last decade. Fig. 1 gives the total number of containers (in millions of TEUs) imported, as well as the numberthat entered through the four largest container ports from 1997 to 2006. In 2006, approximately 23% of containers enteredthrough the port of Los Angeles, which has experienced a growth rate of about 14% per year over the last decade. The secondlargest container port is Long Beach, which handled about 20% of imported containers in 2006 and has been experiencing agrowth rate of about 20% per year over the last decade. It is clear from the figure that container traffic is highly concentratedat a small number of ports. Almost 88% of total containerized imports (measured in TEUs) enter through the 10 largest ports.These ports are Los Angeles, Long Beach, New York, Charleston, Savannah, Norfolk, Oakland, Seattle, Tacoma, and Houston.

Fig. 2 gives the number of containers imported into the US in 1997, 2000, 2003, and 2006 from the 10 largest importingcountries (US Maritime Administration, 2007). China is the largest, representing over 45% of containers imported in 2006 andexperiencing more than a 20% annual growth rate over the last decade.

Total waterborne imports in 2004 were worth approximately 716 billion dollars, of which waterborne containerized im-ports are worth 423 billion dollars and represent commodities such as furniture, electronics, machinery, toys and games,and beverages (US Maritime Administration, 2004). Clearly, these imports are of vital economic concern to the United States.Also, several container ports are in areas threatened by natural disasters. During the 1989 Loma Prieta earthquake in the SanFrancisco Bay Area, the Port of Oakland sustained significant damage from earthquake induced settlement and liquefaction

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[email protected] (L. Nozick), [email protected] (D. Jones).

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612 B. Levine et al. / Transportation Research Part E 45 (2009) 611–626

resulting in damage to rail lines, cranes, and wharf piles. Given the growth rate of imports experienced at US container ports,the concentration of traffic at a small number of seaports, and the vulnerability of some of these seaports to natural hazards, itis important to have an accurate understanding of the flow of containers from their origin country through US seaports to theirfinal destination in the United States, so that investments in port capacity and other transportation infrastructure can be madeconsistent with the needs generated by this traffic.

This paper focuses on the estimation of the number of containers (measured in TEUs) that are shipped from foreign coun-tries through international ports to US ports via sea links, and then via truck and rail from US ports to aggregations of Bureauof Economic Analysis (BEA) economic areas in the United States. BEA areas are geographic regions, composed of a collectionof counties, which represent centers of regional economic activity. There are 177 of these regions in the United States. Toestimate the multi-modal origin–destination table, we have developed an optimization model that synthesizes data on(1) international trade available from PIERS Global Intelligence Solutions and (2) the Carload Waybill Sample of domesticrailcar movements available from the Surface Transportation Board (STB), with a gravity model of the demand for the trans-portation of international sea containers.

B. Levine et al. / Transportation Research Part E 45 (2009) 611–626 613

Luo and Grigalunas (2003) use the Waterborne Databank for US containerized imports and distribute those flows (whichare based on weight) to each state based on population to create an estimate of an origin–destination table. We extend thisconcept by integrating additional relevant data and a gravity model. We focus on the PIERS data on international trade incontrast to the Waterborne Databank because it reports the number of containers rather than just weight. Also by usingthe railcar movement data we have a mechanism to understand the spatial distribution of some of those flows into the Uni-ted States, allowing for some calibration of a gravity model. We also have a more disaggregated representation for the ship-ment originations and destinations. We use 67 countries in contrast to 6 international regions and 84 regions in thecontinental US instead of 48 states.

The next section focuses on the development of an optimization model to estimate a multi-modal origin–destinationmodel for containerized traffic. The third section describes the insights gained from the application of that model to USwaterborne containerized imports for 2004. The fourth section discusses conclusions, contributions to the literature, andopportunities for future research.

2. Model formulation

We formulate the multi-modal origin–destination table estimation problem as a linear program where the origins are 1 of67 foreign countries, the destinations are aggregations of BEA economic areas which form 84 regions, and the freight maytravel via either rail or truck within the United States. As mentioned in Section 1, we integrate two types of data into theoptimization: the PIERS dataset on international trade from 2004 and the Carload Waybill sample of domestic railcar move-ments from 2003. We also integrate a gravity model into the mathematical formulation. The goal is to synthesize a multi-modal origin-destination table that matches the datasets and the gravity model as closely as possible.

Fig. 3 presents a map of the 67 countries that are considered container origins and a graphical representation of the num-ber of containers they export to the US. These 67 countries represent about 98% of the containers that entered the US in 2004.In Fig. 3, the container volumes for China and Hong Kong have been grouped together (though not in the model) and rep-resent more than 39% and 7% of containers imported (as measured in TEU containers) in 2004, respectively. From thismap, it is clear that the largest export countries can be grouped into three distinct regions: Asia, Europe, and Central & SouthAmerica. Asia represents 72% of the exports with almost 11 million TEUs, Europe represents 16.9% with approximately 2.5million TEUs, while Central & South America only represent 11.1% with 1.67 million TEUs.

The 84 regions we refer to as Transportation Analysis Zones (TAZs) are illustrated in Fig. 4 and cover the entire continentalUS. Each TAZ is composed of one or more BEA economic areas. The BEA economic areas are indicated by the dashed lines inthe figure, whereas the solid lines indicate the TAZs. For example, TAZ 152 is composed of BEA Economic Areas 110–113. This

Fig. 3. Origin countries.

112

110113

111TAZ 152

Fig. 4. Transportation analysis zones.


TAZ contains most of the state of North Dakota, including the city of Fargo, and the north-western portion of Minnesota,including the city of Moorhead. Since the countries are considered the origins and the TAZs are the destinations, the numberof loaded containers to be moved by rail and by truck (over some defined period of time) can each be summarized by a67 � 84 table. For this analysis, we use the 2004 PIERS international trade-data, the 2003 STB Waybill, and economic datafrom 2004; hence, the estimated origin–destination table is for 2004.

The model estimates the OD table by determining route flows for each mode of transportation within the United States,denoted by fr. The route flow is the number of containers that travel on a route from a specific origin country to a specificTAZ. In this model, a route r consists of an origin country o, foreign departure port p0, US port p, destination TAZ d, and modem. The mode m refers to the domestic portion of the movement. It can be either truck or rail. All movements are via ship fromthe country of origin to a US port. Fig. 5 illustrates links contained in four sample routes from the country of Germany to theTAZ that includes Houston, TX. The first route goes through the Port of Lisbon in Portugal, the Port of New York, and then viatruck to the TAZ that includes Houston, TX. The second route uses the same first two links but then goes via rail to the TAZthat includes Houston, TX. The third route goes through the port of Bremerhaven in Germany, the Port of New York, and thenvia truck to the TAZ that includes Houston, TX. The fourth route uses the same first two links but then goes via rail to the TAZthat includes Houston, TX. Note there is a distinction between origin country o and what we call departure country o0, thecountry where the cargo is loaded onto a ship destined for the US. Therefore, each departure country o0 has a collection ofports p0 associated with it. As seen in Fig. 5, the departure country o0 may or may not be the same as the origin country o.There are thus four types of nodes in this model: nodes that represent the foreign countries (of which there are 67), nodesthat represent the foreign ports (of which there are 455), nodes that represent the US ports (of which there are 32) and nodesthat represent each traffic analysis zone (of which there are 84).

The network described above also consists of a set of links (i, j) that connect nodes in the network. There are four types oflinks in the network, the first three of which we have observations for: (1) links starting at an origin country o and ending atdeparture port p0; (2) links starting at departure port p0 and ending at US port p; (3R) rail links starting at US port p and end-ing at a TAZ d; and (3T) truck links starting at US port p and ending at a TAZ d. We also have observations for groups of linksof type 3R, for which all links in a particular group start at the same port p but end at different TAZs d.

Observations of flows on links of type (1), top0 , and (2), lp0p, come directly from the 2004 PIERS dataset. Both types of linkflows are hoped to be known with certainty, but deviations are allowed when either conflicts arise with the gravity model orare implied by differences with observations on other links.

Observations of flows on links of type (3R), np~d, where ~d is a single TAZ or a group of TAZs, come from the 2003 CarloadWaybill Sample. The STB Waybill is approximately a 3% sample of rail traffic and therefore provides a detailed picture of railmovements over the rail network each year. Wolfe and Linde (1997) provide a useful description of the Waybill Sample andexplain how it can be effectively used. The 2003 STB Carload Waybill Sample provides a lower bound on the flow for rail linksin 2004. The 2003 STB Carload Waybill Sample can also be used to provide an upper bound on the flow for rail links in 2004by inflating each Waybill entry by a growth rate. This allows some flexibility in the model to assign rail flows.

Fig. 5. Sample links in routes in the network.


Again, we allow deviations in these flows where inconsistencies arise. It is also important to note that the STB Waybilldoes not explicitly identify both the number of international containers transported and the port at which the containersoriginate. Rather, the STB Waybill identifies the number of carloads for STCC commodity code 46 transported from onecounty to another. This designation corresponds to mixed freight, which is used for intermodal shipments. From the numberof railcars, we can determine the number of TEU containers transported by using conversion factors, and we can also attemptto infer which of these flows actually originated at a seaport based on the originating county of these flows.

In 2003, approximately 6 million TEU containers were imported through the Ports of Los Angeles and Long Beach. Leach-man (2005) estimates, based on 2004 data, that rail traffic has about a 40% share from the Ports of Los Angeles and LongBeach. They also estimate that another 5% of containers from these two ports are trans-loaded near the port into 53 foot con-tainers for rail shipment. Since the ports of Los Angeles and Long Beach are both in Los Angeles County, for the purposes ofextracting flows of rail cars from the 2003 STB Waybill, these ports are considered together. According to the 2003 STB Way-bill, 1886000 rail carloads of STCC 46 originated in Los Angeles County. Thus, if we assume that there are about 1.7 contain-ers per railcar (Intermodal Association of North America, 2007), and that there are about 1.79 TEUs per container handled atthese two ports (Pacific Maritime Association, 2007), this implies that about 5.7 million TEU containers originate in Los Ange-les country. Using the insights from Leachman (2005) only, about 2.7 million of the TEU containers that originate in LosAngeles County originate at the ports.

Table 1 gives estimates of the number of containers (measured in TEUs and rounded to the nearest thousand) moved byrail from 12 of the largest ports. Miami is not included because the 2003 STB Waybill reports no rail carloads of STCC 46originating in Miami-Dade County. It is not clear why this is the case, although the 2005 STB Waybill does have originationsfrom Miami-Dade County. Leachman (2005) also provides estimates for the rail share from the Ports of Oakland, Seattle, andTacoma. These have also been incorporated into the estimates of the number of containers moved by rail from each of these

Table 1Estimated container originations by Port.

Port Counties TEU containers moved by rail

LA/Long Beach Los Angeles 2700 000Oakland Alameda/Contra Costa/San Joaquin 365000Seattle/Tacoma King/Peirce 864000New York Hudson, Union, Bergen, Essex 843000Baltimore Baltimore 101000Norfolk Norfolk, Portsmouth 296000Charleston Charleston 160000Savannah Savannah 140000Port Everglades Broward 66000Houston Harris 450000


ports given below. For the remainder of the ports, we have no data to indicate what the share of rail might be. However, thenumber of TEU container originations implied by the rail carload originations in these counties is less than the number ofcontainers handled at the ports, so it is reasonable to assume that all of the rail carloads originate at the ports themselves.

Using this information, we can estimate the spatial distribution of trips originating at each port. The fraction of the totalnumber of TEU containers estimated to originate by rail in each county (or counties) associated with a given port can be ap-plied to each observation in the STB Waybill originating in the county (or counties). This gives an estimate of how many TEUcontainers travel between a port and each TAZ by rail. Fig. 6 gives these estimates for the Port of Los Angeles and Long Beachand the Port of New York. For example, this process implies that 370000 containers (in TEUs) are bound for the Dallas areafrom the Ports of Los Angeles and Long Beach. It is useful to notice the large number of containers that are estimated to bebound for Chicago, and to a lesser extent, Memphis. These are likely a result of the practice of ‘‘rebilling” on transcontinentalrail movements, as discussed by Wolfe and Linde (1997). This occurs when carloads are interchanged between two railroadsand therefore two separate waybills are generated, one for each segment of the movement. Since there is no mechanism toidentify the follow-on movement, rebilling leads to over-estimates of the traffic that terminates at interchange points suchas Chicago and Memphis. To account for the practice of rebilling in the model, we assume that for ports on the east coast,observations of TEU containers into the TAZs that include Chicago and Memphis really reflect the flow of TEU containersbound for those TAZs as well as TAZs to the west. Similarly, for ports on the west coast, observations of TEU container flowsfor the TAZs that include Chicago and Memphis are assumed to be bound for those TAZs as well the TAZs to the east. Theseassumptions are reasonable given both the practice of rebilling and the fact that shippers tend to minimize their shippingcosts which tends to reduce circuitry; therefore, the follow-on movement is likely in the same general direction.

Before describing the model in more detail, we present the following sets and parameters. Let (i, j) be the set of all linkswhere i is the origin node of the link and j is the destination node of the link. As mentioned before, each node is a foreigncountry, a foreign port, a US port, or a TAZ. Let r be an index over the set of all routes. Let m be an index over the set of trans-portation modes in the US (e.g. truck and rail). Let p be an index over the set of all US ports. Let p0 be an index over the set ofall foreign ports. Let p0(r) be the set of all routes that use foreign port p0. Let rij be the set of all routes that include link (i,j). Letp(r) be the set of all routes that include US port p. Let Rod be the set of all routes connecting origin o with destination d. LetM(r) be the mode associated with the domestic portion of route r.

The key decision variables in this model are the number of containers on route r, fr, where each route is a path from anorigin country o, through a foreign port p0, to a US port p, to a TAZ d, and where the movement from US port p to TAZ d is bymode m. These variables are constrained to be non-negative. The route flows can then be translated into an origin–destina-tion table by summing the route flows which have the same origin country and destination TAZ. These route flows can alsobe translated into an origin–destination table for both rail and truck by summing the route flows which have the same origincountry o, destination TAZ d, and mode M(r).

The PIERS international trade dataset gives the number of containers (in TEUs) that travel along each link from origin o toforeign port p0, top0 . The first term on the left-hand side of Eq. (1) is the sum of the route flows that use both origin country o

Fig. 6. Rail flows from the Port of LA/Long Beach and the Port of New York to each TAZ based on the 2003 STB Waybill.


and foreign port p0. The next two terms are variables that represent the amount by which the route flows are lower or greaterthan that implied by the PIERS data. uþop0 is constrained to be non-negative and u�op0 is constrained to be non-positive. There-fore constraint (1) attempts to identify route flows that are as consistent as possible with the number of containers (in TEUs)shipped from each origin country to each foreign port of export.
X
r�rij ji¼o;j¼p0fr þ uþop0 þ u�op0 ¼ top0 8o; p0 ð1Þ

The PIERS dataset also gives the total number of containers (in TEUs) that are shipped from each foreign port p0 to each USport p, lp0p. The first term on the left-hand side of Eq. (2) is the sum of the route flows that use both foreign port p0 and domes-tic port p. The next two terms are variables that represent the amount by which the route flows are lower or greater than thatimplied by the PIERS data. gþp0p is constrained to be non-negative and g�p0p is constrained to be non-positive. Therefore con-straint (2) attempts to identify route flows that are as consistent as possible with the number of containers (in TEUs) shippedfrom each foreign port to each US port.
X
r�rij ji¼p0 ;j¼p

fr þ gþp0p þ g�p0p ¼ lp0p 8p0;p ð2Þ

Given the link flow observations lp0p from the PIERS data, it is possible to compute the total number of containers (in TEUs)that depart each foreign port p0, bp0 . Constraint (3) attempts to identify values for the route flows, fr, that match the PIERS datafor the number of containers that pass through each foreign port. However, deviations are allowed. eþp0 is a variable that rep-resents the amount by which the flows, fr, are smaller than that expected based on the PIERS data and e�p0 is a variable thatrepresents the amount by which the flows, fr, are larger than expected. eþp0 is constrained to be non-negative and e�p0 is con-strained to be non-positive
X
r�p0ðrÞfr þ eþp0 þ e�p0 ¼ bp0 8p0 ð3Þ

Additionally, given the same link flow observations lp0p from the PIERS data, it is also possible to compute the total numberof containers (in TEUs) that enter each US port p, mp, and then penalize deviations from these values. Constraint (4) encour-ages solutions that match the container volumes entering each US port, but deviations are allowed. hþp is a variable repre-sents the amount by which the flows, fr, are smaller than that expected based on the PIERS data and h�p is a variable thatrepresents the amount by which the flows, fr, are larger than expected. hþp is constrained to be non-negative and h�p is con-strained to be non-positive
X
r�pðrÞfr þ hþp þ h�p ¼ mp 8p ð4Þ

Constraints (5) and (6) incorporate observations of container flows from the 2003 STB Waybill data. Each observation inthe waybill applies to a group of rail links (i, j) starting from a US port and ending at a TAZ or group of TAZs. The set ~d may becomposed of a single destination TAZ or a collection of destination TAZs. The total number of TEU containers shipped acrossthose links by rail must be at least as large as that implied by the 2003 STB Waybill data, np~d, where p is the port and ~d is theset of TAZ destinations that the observation pertains to. The observations in the STB Waybill are lower limits on the rail linkflows since we are using the 2003 STB Waybill rather than the 2004 dataset. Containerized traffic has been growing at about8% per year, therefore we can expect that the 2004 values for the flows from the Waybill are generally greater than those inthe 2003 STB Waybill (Intermodal Association of North America, 2007). The first term on the left-hand side of Eq. (5) is thesum of the route flows that use US port p and terminate at a TAZ in the set ~d, and use rail for movement from the US port tothe TAZ. The right-hand side is the total number of TEU containers indicated by the 2003 STB Waybill that enter a port p andterminate at one of the TAZs in the set ~d. kþpd is a variable that represents the amount by which the flows, fr, are smaller thansuggested by the STB Waybill. kþpd is constrained to be non-negative

Xr�rij ji¼p;j�~d;MðrÞ¼rail

fr þ kþp~d � np~d 8p; ~d ð5Þ

For all TAZs, except the ones that include Chicago and Memphis, the observations in the STB Waybill pertain to a singledestination TAZ. We do not write a lower limit for the TAZ that includes Chicago or the TAZ that includes Memphis sepa-rately from each port. Rather, if the port is on the west coast, we write a lower limit constraint that pertains to all TAZsto the east of the Mississippi River. If the port is on the east coast, we write a lower limit that pertains to all TAZs westof the Mississippi River plus the TAZs that include Chicago and Memphis. We compute this lower limit by summing the flowsgiven in the Waybill from that particular port to each of the TAZs that the constraint pertains to. This allows the model to re-distribute the containers that the Waybill associates with Memphis and Chicago to other TAZs in the appropriate group fromeach port. The ports designated as ‘‘East Coast Ports” are Baltimore, Charleston, New York, Norfolk, Port Everglades, andSavannah. The ports designated as ‘‘West Coast Ports” are Los Angeles/Long Beach, Oakland, and Seattle/Tacoma. Houstonis the only port for which there are 2003 STB Waybill observations that do not fall into either category. Therefore, for thePort of Houston, we write constraint (5) for all destination TAZs.


We can also create upper bounds on the rail flows from the ports to the TAZs using the 2003 STB Waybill. Eq. (6) followsthe same format as Eq. (5) except that Eq. (6) is an upper bound constraint whereas equation (5) was a lower bound con-straint, and in equation (6) the right-hand side is multiplied by an inflation factor, cp. The inflation factor can be used to rep-resent the amount above the values in the STB Waybill for which deviations are considered acceptable. It can also be used tocompensate for the growth that has occurred between the time period of the PIERS international trade data and the STBWaybill. We use the growth that occurred between 2003 and 2004 at each of the ports as estimated by the US MaritimeAdministration (US Maritime Administration, 2007)

Xr�rij ji¼p;j�~d;MðrÞ¼rail

fr þ k�p~d � cpnp~d 8p; ~d ð6Þ

Again, for all TAZs, except the ones that include Chicago and Memphis, the observations in the STB Waybill pertain to asingle destination TAZ, and Eq. (6) is written for each of these port-TAZ pairs. The exception to this is for individual linksbetween ports on the East Coast and TAZs on the West Coast, and links between ports on the West Coast and TAZs onthe East Coast. Since Eq. (5) allows the model to redistribute containers on these rail links, the number of TEU containersmay be higher than the observation in the STB Waybill. Hence, we do not write Eq. (6) for these port-TAZ pairs.

As before, for the TAZ that includes Chicago and the TAZ that includes Memphis we do not write an upper limit constraintseparately from each port. Rather, if the port is on the west coast, we write an upper limit constraint that pertains to all TAZsto the east of the Mississippi River. If the port is on the east coast, we write an upper limit constraint that pertains to all TAZswest of the Mississippi River plus the TAZs that include Chicago and Memphis. We compute this upper limit by summing theflows given in the Waybill from that particular port to each of the TAZs that the constraint pertains to, and multiplying thisfigure by the inflation factor, cp, for that port.

Since rail is substantially more likely as distance from the port increases, it is reasonable to assume that containers enter-ing the US through west coast ports would primarily move by rail if the destination TAZ is in the east. Similarly, it is reason-able to assume that containers entering the US through east coast ports move primarily by rail if the destination TAZ is in thewest. Since we are assuming all containers travelling from east coast ports to TAZs west of the Mississippi and from westcoast ports to TAZs east of the Mississippi do so by rail only, we can then constrain truck flow on these links to be 0. Finally,note that if the Waybill observation for link (i, j) is equal to zero then the combination of the lower bound constraint (5) andupper bound constraint (6) effectively sets the rail flow on this link equal to zero.

In order to give the model additional guidance as to how to determine the route flows and therefore the origin–destina-tion table, we incorporate a gravity model into the mathematical formulation. Constraint (7) is a gravity model for the move-ment of waterborne containerized freight imports from origin country o to TAZ d

Bod ¼ KoWoGdd�kod 8o;d ð7Þ

where Bod is the number of containers (in TEUs) shipped from origin country o to TAZ d, Wo is the value of container ship-ments from origin country o to the US as given in the Waterborne Databank (US Maritime Administration, 2004), Gd is theearnings in TAZ d (US Department of Commerce, 2004), dod is the distance o to d and Ko is a country specific variable (what iscommonly referred to as a K-factor in the freight demand modeling literature). Eq. (7) can be simplified because Ko and Wo

can be grouped together, since they are constant for a particular origin. If we then assume that dod is the shortest route from oto d measured in travel time, and that k is a constant, then d�k

od is a constant for each origin–destination pair. The simplifi-cation is then given as Eq. (8) below, where K̂o and Bod are the two decision variables, both of which are constrained tobe non-negative

Bod ¼ bK oGdd�kod 8o;d ð8Þ

This equation implies that the number of containers that flow from origin country o to destination TAZ d is proportional toboth the earnings of the destination TAZ d and the distance from country o to TAZ d. These are reasonable assumptions fortwo reasons. First, much of what is transported in waterborne containers are retail goods and the consumption of thesegoods is reasonably assumed to be proportional to economic activity. Second, distance has a negative impact on the demandfor transportation. It is also important to realize that the PIERS international trade data provides substantial information onthe total number of TEUs imported from each country. Hence, there is substantial information on the sum of the Bod variablesfor a given o. This information is integrated into the model through Eq. (1).

We use oceanic distance and an average sailing speed to measure the travel time between the foreign port of export andthe US port of import. This is analogous to Malchow and Kanafani’s (2004) use of shortest oceanic distance to measure dis-tance in their analysis. Luo and Grigalunas (2003) and Leachman (2005) also use the same ocean distance measure in theiranalysis. Alternatively, we could have used average shipping time across the schedules used by all vessels that visited eachpair of ports on the same voyage during a fixed time period. This information is contained the Global Transport Analyzeravailable from Pacific Shipper. There are significant challenges with acquiring this data for the large number of foreign port– US port pairs in a form useful for inclusion in the model, hence we use the simpler measure used by other authors.

Ashtakala and Murthy (1988, 1993) use a similar gravity model for land-based freight transportation and find that valueof k varies from 0.25 to 1.0 depending on the commodity. Ashtakala and Murthy (1988) also observe that higher exponentvalues are associated with the transportation of lower value goods. They reference two other studies that draw the same


conclusion (Chisholm and O’Sullivan (1973) and Black (1971)). Since this model focuses on international waterborne ship-ments and the associated domestic land movement, it is unclear what an effective value of the exponent will be. One strategyto address this is to use different values for the exponent and select the one that appears to fit the data best; that is, generatesthe least amount of discrepancies with the data in the PIERS international trade dataset, the STB Waybill, and the resultantgravity model.

Constraint (9) allows the model to select route flows that deviate from the gravity model given in Eq. (8). This is done byattempting to match the sum of the route flows from a given country o to a TAZ d to the gravity model estimate for the sumof those route flows, Bod. Again, we include error terms to allow for deviations. qþod is a variable represents the amount bywhich the flows, fr, are smaller than that expected based on the gravity model and q�od is a variable that represents theamount by which the flows, fr, are larger than expected. qþod is constrained to be non-negative and q�od is constrained to benon-positive
X
r�Rod

fr þ qþod þ q�od ¼ Bod 8o; d ð9Þ

The goal of constraints (1)–(9) is to identify route flows for containerized international freight traffic that enters the USthrough seaports which is as consistent as possible with: (1) observations of flows from each foreign origin country to eachforeign port of export; (2) observations of flows from each foreign port to each US port; (3) the total freight leaving eachforeign seaport that is destined for the US; (4) the total freight entering each US port; (5) the lower bound on the numberof containers shipped by rail from US seaports to each TAZ or group of TAZs; (6) the upper bound on the number of contain-ers shipped by rail from US seaports to each TAZ or group of TAZs; and (7) a gravity model between origin country o and TAZd based on total value of all goods shipped by water for each foreign country to the US, earnings for each TAZ, and the dis-tance between them. (1)–(4) is obtained from the 2004 PIERS international trade dataset and (5) and (6) is obtained from the2003 STB Waybill.

The objective is given in Eq. (10). The first term in the objective penalizes deviations from estimates of the number ofcontainers that are exported from each foreign country through each foreign port. The second term penalizes deviations fromthe flows of containers from each foreign port to each US port. The third term in the objective penalizes deviations from esti-mates of the number of containers that are exported from each foreign port to the US. The fourth term penalizes deviationsfrom estimates of the number of containers that are imported through each US port. The fifth term penalizes rail flows thatare lower than that implied by the 2003 STB Waybill from each US port to each TAZ or group of TAZs. The sixth term penal-izes rail flows that are higher than that implied by the 2003 STB Waybill and the associated port growth rate from each USport to each TAZ or group of TAZs. The seventh term penalizes deviations from the gravity model. The final term in the objec-tive minimizes the total distance represented by all of the route flows where Dr is the distance of the rth route. We includethis term to encourage the use of shorter routes, when possible, because this will produce a more reasonable solution. Thecoefficient b is assumed to be very small and serves as a ‘‘tie breaker” between all solutions that minimize the remainder ofthe terms in the objective
X
ðo;p0 Þa0ðuþop0 � u�op0 Þ þ

Xðp0 ;pÞ

a1ðgþp0p � g�p0pÞ þX

p0a2ðeþp0 � e�p0 Þ þ

Xp

a3ðhþp � h�p Þ þ a4

Xp~d

kþp~d

� a5

Xp~d

k�p~d þXðo;dÞ

a6ðqþod � q�odÞ þ bX

r

frDr ð10Þ

where a0, a1, a2, a3, a4, a5 and a6 are coefficients that reflect the relative importance of deviations from each set of constraints,and b is a per container mile penalty for travel distance. We penalize separately (1) deviations from expected total port con-tainer volumes at foreign ports and US ports; (2) deviations from the observations of flows from individual foreign countriesto individual foreign ports; and (3) deviations from the observations of flows from individual foreign ports to individual USports, because generally it is more important to match the total volumes at each port than it is to match the flows of con-tainers between specific ports. It is also likely that the observations of total volumes at ports are more reliable than those onindividual foreign port to US port movements. By setting the coefficients a2 and a3 higher than a0 and a1, this can be achievedquite easily when there are inconsistencies with other data or the gravity model. Since the data that support the first fourterms is derived from the PIERS international trade data, and that data is internally consistent, the trade-off in the objectiveis really between the first four terms, and the fifth and sixth which come from the 2003 STB Waybill. If violations are to occurwith the PIERS data it is preferable that these violations are more heavily focused on the link observations rather than theport volume observations. The distance term has the lowest penalty (b = 0.00001) because it is simply used to choose be-tween alternative optimal solutions to the remainder of the terms in the objective. The other weights are all equal to 1, ex-cept for a6 = 2.5. Since there were no errors associated with a0, a1, a2, a3 using higher weights on these coefficients would notchange the model results for these data sets.

3. Insights from the model

In order to identify an effective value for the exponent k of the distance term in the gravity model (Eq. (8)), the optimi-zation was run for values of k from 0 to 9 in increments of 0.2. Fig. 7 shows a graph of a measure of the error as a function of k.

0%

2%

4%

6%

8%

10%

12%

14%

16%

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9Lambda

% E

rror

Fig. 7. Percent error of model results as compared to origin–destination table.


The measure used is the ratio of the value of the objective function (excluding the last term) and the sum of the entries in theresultant origin-destination table, expressed as a percentage. From the figure, it can be seen that values of k which are asso-ciated with very small errors are between 1.2 and 3.2. For each of these values, the total percent error is less than 2% and theestimated solutions are very similar. Therefore, we chose to use a k of 1.2, since that value is close to what other studies haveestimated for k.

When k is 1.2, the estimated origin-destination table is consistent with both the 2004 PIERS international trade data forcontainerized imports and the gravity model. However, there is one inconsistency with the observations in the 2003 STBWaybill that were used to generate lower bound constraints (Eq. (5)), and one inconsistency with the observations in the2003 STB Waybill that were used to generate upper bound constraints (Eq. (6)). These discrepancies are given in Table 2.The only discrepancy of significant magnitude is that from the Port of Houston to Los Angeles. The estimated route flowsfrom the model imply that about 190000 TEU containers enter at the Port of Houston and are bound for the Los Angeles area.The 2003 STB Waybill implies there are about 347000 TEU containers that are shipped from the Port of Houston to the LosAngeles area by rail. Hence, there is a discrepancy of about 157000 TEU containers. The 347000 TEU containers reported inthe Waybill represents about 77% of all TEU containers imported through the Port of Houston in 2003. While there is no evi-dence to discount this observation in the Waybill, the magnitude of the observation is somewhat inconsistent with theremainder of the traffic at the Port of Houston (which is more local in nature). The other discrepancy arises from a violationof the upper bound constraint. The 2003 STB Waybill and the growth rate at the ports of Los Angeles and Long Beach from2003 to 2004 imply that about 1.8 million TEU containers travel from the ports of Los Angeles and Long Beach to all TAZ eastof the Mississippi River, whereas the model estimates that this number is low by about 62000 TEU containers. However, thisrepresents an error of only about 3.5%.

From the route flows variables in the model, the flow of TEU containers can be tracked through the network. If we con-sider the traffic originating abroad in China, about 95% of TEU containers exported from Mainland China are shipped througheight Mainland Chinese ports, the Port of Hong Kong, the Port in Busan, South Korea and through the Port of Kaohsiung, Tai-wan. These ports and the TEU containers imported are illustrated in Fig. 8. It is useful to notice the concentration of activityat the Shanghai and Hong Kong port areas. The region from Shanghai to Hong Kong is a special economic zone with substan-tial financial incentives spurring tremendous growth. Historically, Hong Kong has been the dominant port, second only toSingapore. However, with the rapid growth in this special economic zone in China, the ports of Yantian and Shanghai haveattracted substantial traffic. Today Shanghai is the second largest port in the world next to Singapore (Asian Economic News,2007), with Hong Kong third.

Once TEU containers, originating in China, are exported through the collection of Asian ports mentioned above, the TEUsarrive at US ports. Fig. 9 gives the number of TEU containers imported from China through the six US ports with the highestvolume. Together, these six ports represent about 94% of the total number of containers imported from China. As expected,the majority of the TEU containers are imported through West Coast ports, but it is interesting to note that about 17% of thetotal number of TEU containers imported does so through the Ports of New York, Savannah, and Norfolk. Fig. 8 also shows thefraction of TEU containers through each of the ports that originates in China. It is not surprising that the West Coast ports

Table 2Discrepancies in model results with 2003 STB Waybill.

Constraint Error

Port of Houston to Los Angeles TAZ Lower bound, Eq. (5) 157000Ports of LA & Long Beach to TAZs East of Mississippi Upper bound, Eq. (6) �62000

Fig. 8. Export port volumes (in TEU Containers) from China.

0

500

1000

1500

2000

2500

3000

3500

4000

LA-LO

NG BEACH

SEATTLE-TACOMA

NEW YORK

SAVANNAH

OAKLAND

NORFOLK

U.S. Port

TEU

Con

tain

ers

( in

thou

sand

s)

0

0.1

0.2

0.3

0.4

0.5

0.6

TEU ContainersFraction from China

Fig. 9. US port volumes (in TEU Containers) from China.



have a high percentage of traffic coming from China, but perhaps it is more surprising that East Coast ports, such as Savannahand Norfolk, have almost 50% and 30% of their traffic originating in China, respectively.

Fig. 10 gives an estimate of the number of TEU containers imported from China that are destined for each TAZ by bothtruck and rail. Notice that the large economic areas in the US attract a large number of TEUs. For example, there are almost600000 TEUs destined for the New York City TAZ from China. The model estimates that about 35% enters the US through thePort of New York and travels locally via truck, and about 65% through the Ports of Los Angeles and Long Beach and travels viarail. On the other hand, shipments from China headed to the TAZs near Savannah and Norfolk enter almost exclusivelythrough nearby ports and are served via truck. These conclusions should be used with some caution. This formulation hassignificantly more decision variables than equations, and linear programs tend to produce solutions that have relativelysmall numbers of variables that take on positive values, thereby producing ‘‘lumpy solutions”. Therefore, individual TAZsmay be served by a larger number of ports than indicated in the solution, though there is a strong basis to believe thatthe ports indicated in the solution do provide significant service.

Fig. 11 gives the total estimated number of TEU containers (by truck and rail) destined for each TAZ from the Ports of LosAngeles and Long Beach, the Port of Oakland, and the Ports of Seattle and Tacoma. Given that all but one upper bound con-straint was honored in the model, we can infer that all of the container volumes destined for TAZs east of the MississippiRiver were achieved with rail service. It is interesting to notice that the Ports of Los Angeles and Long Beach are estimatedto provide significant service across the US, with the exception of the southeast, whereas the Ports of Seattle and Tacomaprovide service mainly in the north.

Fig. 12 gives the total estimated number of TEU containers (by truck and rail) destined for each TAZ from the Ports of NewYork, Charleston, Norfolk and Savannah. It is interesting to notice that the vast majority of the containers that enter the USthrough these ports are destined for TAZs on the east coast. Very few containers travel west of the Mississippi River. This is incontrast to the ports on the West Coast, which service a large portion of the continental US.

Fig. 13 shows the estimated TEU container rail flows from both the Ports of Seattle and Tacoma and the Ports of Los Ange-les and Long Beach to TAZs east of the Mississippi River, and that were indicated as terminating at Chicago or Memphis in theSTB Waybill. The model concludes that some of this traffic does indeed terminate at the TAZs that include Chicago and Mem-phis, but much of it is destined for other TAZs. For example, the 2003 STB Waybill indicates that from the Ports of Seattle andTacoma, about 600000 TEU containers are destined for the TAZ that includes Chicago and about 35000 are destined for theTAZ that includes Memphis. The model indicates that much of this traffic is really destined for the Northeast US with signif-icant concentrations in New York City, Michigan, and Ohio. On the other hand, the 2003 STB Waybill indicates that from thePorts of Los Angeles and Long Beach about 1090000 TEUs are destined for the TAZ that includes Chicago and about 400000TEUs are destined for the TAZ that includes Memphis. The model indicates that, just like the Seattle ports, much of this trafficis really destined for other TAZs east of the Mississippi River. Given the larger role of Memphis for the Ports of Los Angeles

Fig. 10. Estimated Number of TEU containers Imported from China to each TAZ by rail and truck.

Fig. 11. Flow of containers from key West Coast Ports to TAZs.

Fig. 12. Flow of containers from key East Coast Ports to TAZs.


and Long Beach in comparison to the Ports of Seattle and Tacoma, substantial traffic is estimated to be destined for TAZs inthe South.

Fig. 14 gives the truck flow in TEU containers from the Port of NY/ NJ and LA and Long Beach. In 2005, a total of 2.2 millionTEU containers of US imports were handled by the Port of NY and NJ. As indicated in Table 1, a total of 843000 of these con-tainers are sent by rail. Therefore 1.4 million TEU containers (approximately 65%) are sent by truck to their final destination.

Fig. 13. Estimated rail flows in TEU containers from the Ports of Seattle and Tacoma and the Ports of Los Angeles and Long Beach that STB Waybill Reportsas terminating in Memphis or Chicago.

Fig. 14. Estimated truck flows in TEU containers from the Port of New York and New Jersey and from the Ports of Los Angeles and Long Beach.


Fig. 14 indicates that a large percentage of the containers sent by truck have their final destination in the tri-state area (NY,NJ, and Connecticut). A smaller percentage of containers is sent to Boston via truck. Truck traffic from the ports of LA andLong Beach is concentrated in the state of California, but is also estimated to travel further distances to reach their finaldestination.

Fig. 15. Distribution of TEU containers across regions of origin for each TAZ.


Fig. 15 gives the total number of containers that are destined for each TAZ by originating region of the world (Asia, Europe,Central & South America, other). Clearly, Asia is the dominant region. Perhaps the most interesting observations in this figureis how constant the balance is between the four regions of the world across the continental US. Certainly, there is a slightincrease in the percentage from Asia in the west, Europe in the east, and Central & South America in the south and gulf coast,but these shifts are still quite minor. For example, the TAZs with the largest percentage share from Asia are in California,Seattle, Oregon, Montana, Utah, and Idaho (percentages in the low eighties), whereas the TAZs with the smallest percentageshare from Asia (percentages in the low sixties and among the highest from Europe) are in Maine, Florida, Georgia, SouthCarolina, Massachusetts, Pennsylvania, etc. Imports from Central & South America are relatively larger in Florida, Georgia,South Carolina, and the Gulf Coast Region (percentages in the mid-teens).

4. Conclusions and future research

This paper contributes to the literature by providing a method, using optimization, to synthesize information on US inter-national trade, the Carload Waybill from the Surface Transportation Board, and economic information to estimate an inter-national multi-modal origin–destination table for containerized imports. Using this model we observe that the estimatedorigin-destination table is consistent with the PIERS international trade data, a gravity model for the transportation of inter-national sea containers based on economic data, and the impedance computed from travel times, and is nearly consistentwith the STB Carload Waybill. This is the first time these datasets have been effectively integrated and the underlying impli-cations for US imports of waterborne containers made available for detailed analysis. This method has also allowed for someinsight to be developed about the balance between rail and truck inland transportation from each port.

This research can be extended in a few different directions. First, it is possible that additional data could be developed toaugment the optimization. These data could be improvements to the types of data already included, or it could be the iden-tification of new datasets to complement the data included. Second, the gravity model could be refined. Currently, we focuson aggregate measures of economic activity, but there is the opportunity to create other gravity models that might, poten-tially, be more representative of the demand for the transportation of waterborne sea containers. Third, as in most origin–destination estimation models based on synthesizing link count information, there are a large number of solutions to thisoptimization model which have very similar values for the objective function. It could be interesting and useful to under-stand the patterns that exist in these solutions and possibly to develop a representation for the origin–destination table thatis probabilistic based on these solutions. Fourth, the PIERS data contains substantial information about the movements ofindividual commodities which could be effectively used if it could be complemented with other commodity specific infor-mation. This additional data could be in the form of transportation demand models at the commodity level or data that indi-cates the spatial demand for those commodities inside the US. Finally, it is also important to develop an origin–destinationtable for US exports through container seaports. This analysis is readily adaptable to the development of this table.


While not a direct extension of this research, the product of this research can be used to address a variety of importantissues. For instance and as mentioned previously, container seaport traffic is growing at about 10% per year. With this level ofgrowth, port expansions will be and are needed. This model provides important insights that can be used to manage thatexpansion. As another example, labor shortages arise intermittently at either the ports themselves or at the railroads fora variety of reasons. These shortages can have a profound impact on the speed with which containers are handled at theports. As an illustration, during the summer of 2004, the UP did not have enough trained workers (largely resulting froma change in federal labor law that triggered increased retirements) to handle the level of container traffic coming throughLos Angeles/Long Beach and moving east by rail (Machalaba, 2004). The problem was exacerbated by a shortage of long-shoremen in the port itself. The rail yards near Los Angeles became clogged; then the congestion reached back into the con-tainer storage areas in the port; and eventually ships backed up in the anchorage waiting to unload. By September of thatyear, truckers were reporting long delays in the terminal to pick up containers (Mongelluzzo, 2004), and queues of more than30 ships anchored off the coast waiting for berths were reported (Johansson, 2004). The origin–destination table developedthrough this research can be used to understand the volume of traffic and the extent of the impact on container traffic. It canalso be used with a logistics model like that in Leachman (2005) to predict what diversions might occur in response to anincrease in travel time caused by these types of labor shortages. Finally, the origin–destination table developed in this re-search can be integrated with the type of logit models developed in Malchow and Kanafani (2004). Malchow and Kanafani(2004) estimate a logit model to select the US port of export for four commodity types, one of which is manufactured goods,for a select set of foreign countries. They obtain the shipment origins from customs declarations as part of the PIERS exportdataset. Unfortunately, the origin given in the customs declarations is often not the true location at which the shipment orig-inates, but either where the load was created near the port or the address of the company. The origin–destination tabledeveloped in this model would allow for the correction of these issues in the customs declaration documents, potentiallyimproving the analysis. Their analysis was done for US exports, but the same analysis could be done for US imports. Similarly,the model developed in this paper could be adapted to estimate an origin–destination table for US exports.

References

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Practice 27 (5), 373–382.Asian Economic News, 2007. Hong Kong port throughput slips to 3rd after Singapore, Shanghai: A report. April 23rd, 2007.Black, W.R., 1971. The utility of the gravity model and estimates of its parameters in commodity flow studies. Proceedings of the Association of American

Geographers, 28–32.Chisolm, M., O’Sullivan, P., 1973. Freight Flows and Spatial Aspects of the British Economy. Cambridge University Press, London.Intermodal Association of North America, 2007. Intermodal Industry Statistics. <http://www.intermodal.org/statistics_files/stats5.shtml>.Johansson, C., 2004. In delays, their ship comes in. Orange County Register (September 9th, 2004).Leachman, R.C., 2005. Final Report: Port and Modal Elasticity Study. Piedmont, Southern California Association of Governments, California.Luo, M., Grigalunas, T.A., 2003. A spatial-economic multimodal transportation simulation model for US coastal container ports. Maritime Economics &

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estimating an origin–destination table for us imports of waterborne containerized freight

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