Interdependent impacts of inoperability at multi-modal transportation container terminals

Transportation Research Part E 47 (2011) 722–737

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Transportation Research Part E journal homepage: www.elsevier.com/locate/tre

Interdependent impacts of inoperability at multi-modal transportation container terminals Raghav Pant, Kash Barker ⇑, F. Hank Grant, Thomas L. Landers School of Industrial Engineering, University of Oklahoma, Norman, OK, United States

a r t i c l e

i n f o

Article history: Received 27 October 2010 Received in revised form 19 January 2011 Accepted 28 January 2011

Keywords: Inoperability Input–Output Model Inland port Disruptive events Interdependent impacts Multi-regional impacts

a b s t r a c t This work describes the interdependent adverse effects of disruptive events on interregional commodity flows resulting from disruptions at an inland port terminal. To do so we integrate the risk-based Multi-Regional Inoperability Input–Output Model, which measures the cascading regional effects of disruptions to interconnected industries, with models, which simulate port operations such as commodity arrival, unloading, sorting, and distributing. Such models capture three disruption scenarios at the port and provide measures of impact to industries that use the inland port terminal facility. A case study highlights the disruptive effects of a closure of the Port of Catoosa in Oklahoma. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction Many large-scale systems, including infrastructure and industry sectors, are highly interconnected by a number of means, including physical, logical, and geographical relationships (Rinaldi et al., 2001). Critical industries such as transportation, telecommunications, power, and banking share significant resources, and the flow of goods and information constantly takes place among these different industry sectors. Realizing the interdependent nature of US infrastructure and industry sectors, the Department of Homeland Security (DHS) stresses the urgency and need to protect infrastructures (DHS, 2009): ‘‘Attacks on Critical Infrastructure and Key Resources (CIKR) could significantly disrupt the functioning of government and business alike and produce cascading effects far beyond the targeted sector and physical location of the incident. Direct terrorist attacks and natural, manmade, or technological hazards could produce catastrophic losses in terms of human casualties, property destruction, and economic effects, as well as profound damage to public morale and confidence.’’ Hence, interest lies in predicting the adverse impacts of disruptive events in an interdependent economy and evaluating risk management efforts to lessen these impacts. Multi-modal transportation systems, identified by DHS to be among the critical US infrastructures (DHS, 2009), play a significant role in maintaining commodity flows across industries and preserving the functionality of a multi-regional interdependent economy. A disruptive event that causes inoperability of the multi-modal transportation network is propagated to industry demand and supply, thereby causing production losses. For example, in 2002, Oklahoma witnessed the collapse of an I-40 bridge spanning the Arkansas River due to a barge collision with a bridge pylon. The resulting daily detouring of 22,000 vehicles caused congestion, secondary road infrastructure accelerated wear, and other economic losses that persisted ⇑ Corresponding author. Address: School of Industrial Engineering, University of Oklahoma, 202 W. Boyd St., Room 124, Norman, OK 73019, United States. Tel.: +1 405 325 3721; fax: +1 405 325 7555. E-mail address: [email protected] (K. Barker). 1366-5545/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.tre.2011.02.009

R. Pant et al. / Transportation Research Part E 47 (2011) 722–737

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for nearly 2 months as the bridge was repaired (Federal Highway Administration, 2008). Similarly, the I-35W bridge collapse over the Mississippi river in Minneapolis, Minnesota caused the daily rerouting of 140,000 vehicles (Zhu et al., 2009) with a significant adverse economic impact. Events like these make risk analysis of freight disruptions an important research topic. Furthermore, the risks of larger-scale disruptive events, such as earthquakes and malevolent man-made attacks, could result in the protracted closure of key transportation facilities such as rail yards, cargo terminals, airports, seaports, or inland ports. Multi-modal risk assessment studies of various sorts have appeared recently (Sohn et al., 2004; Ham et al., 2005a,b; Tatano and Tsuchiya, 2008; Ishfaq and Sox, 2010); though risk studies of inland port disruptions have been particularly sparse in number. Transfer facilities, such as inland ports, are the locations that are particularly susceptible to disruptions in commodity flows that can cause losses of demand and supply to certain industries, which then propagate among other interdependent intra- and inter-regional industries. Inland port operations that are susceptible to disruptions include commodity arrivals at port, storage at unloading yards, transfer to docks by cranes, loading onto vessels, and departure to destinations. Inland waterways, although prominent in North America, are even more common in the European economy (Rodrigue et al., 2010). Several approaches to quantifying interdependencies among infrastructure and industry sectors have been suggested (O’Reilly et al., 2006; Pederson et al., 2006; Bagheri and Ghorbani, 2007; Lee et al., 2007; Rosato et al., 2008; Tanaka, 2009). This work makes use of an extension of the economic input–output model (Leontief, 1966) that captures the economic equilibrium for supply and demand among interconnected industries. This risk-based interdependency model, the Inoperability Input–Output Model (IIM) (Santos and Haimes, 2004; Santos, 2006), quantifies the propagation of inoperability, or the extent to which industry output will not be produced, through a set of interconnected industry sectors. In particular, this research makes use of the Multi-Regional Inoperability Input–Output Model (MRIIM) (Crowther and Haimes, 2010) framework for studying the cascading effects of inoperability across regions due to disruptions over geography. One significant benefit of the MRIIM is that its parameters are estimable from Bureau of Economic Analysis and Bureau of Transportation Statistics data. In this study, we have modeled the operations at inland ports through simulations as queueing systems capable of quantifying the number of commodities at each point of operation. By comparing the normal port operations with the disrupted port operations, the difference in number of arrivals and departures can be obtained to measure the losses for commodities/ industries that use the port. Quantifying these losses respectively as loss in demand for the exporting region and loss in supply and demand for the importing region provides parameters for the MRIIM. The interdependent nature of the MRIIM then cascades these losses to other industries locally and across regions, thereby providing an estimate for large-scale economic impacts of disruptions at an inland port. The work presented here differs from other transportation disruption studies in that it does not use the traditional network analysis approach. Most of the existing studies in the literature build an optimized transportation network of roads and railways that minimize travel distance across regions and use the economic data to maintain the constraint that the supply is equal to the demand (Ham et al., 2005a,b). Such network approaches are computationally intensive; hence, our analysis of the inflow or outflow of goods through a region using queuing concepts at particular components in a network can reduce the computational burden and help build an efficient means to quantify multi-regional inoperability and economic losses due to disruptive events. In addition, existing studies assume that during a disruption, supply finds alternate paths on the network to meet demand. In practice, this might not be true for short time duration and across all industries. In particular, for port disruptions there are bulk products that are sitting at the port or are off shore for which alternative transportation arrangements are costly or impractical. In light of this perception, a company decision maker may prefer to wait for some time for the port to reopen. This paper is arranged as follows. Section 2 provides background on the IIM and describes the MRIIM framework and resulting metrics for risk assessment. Section 3 discusses the relationship between the MRIIM metrics and transportation hubs (e.g., ports). Section 4 discusses the queueing-based simulation model that describes normal port export and import operations and the adjustments that can be made to incorporate effects of disruptive events. A case study of the exports and imports through the Port of Catoosa in Oklahoma applies the proposed approach in Section 5, and Section 6 provides concluding remarks and points to the future direction of this research. 2. Multi-Regional Inoperability Input–Output Model and its foundations This section provides methodological background on the risk-based multi-regional interdependency model used in this research. 2.1. Input–output model and its multi-regional extension In the traditional economic input–output model (Leontief, 1966), the economy is assumed to consist of a group of n interacting industries, each producing a single commodity. Under a static equilibrium the total output of the ith industry is distributed to all industries and satisfies external demand. The industry i’s output that is used as an input by j is directly proportional to the output of the jth industry. Hence, if zij is the output flow of commodities from industry i to j, then zij = aijxj, where xj is the output of industry j and aij is called the Leontief coefficient or technical coefficient. This equilibrium condition implies Eq. (1), where xi is the output and ci is the external demand for industry i.

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R. Pant et al. / Transportation Research Part E 47 (2011) 722–737 n X

xi ¼

zij þ ci

ð1Þ

j¼1

The formulation in Eq. (2) makes use of the proportionality where x is an n  1 vector of industry outputs xi, c is an n  1 vector of final industry demands ci, and A is an n  n matrix of technical coefficients aij. Data for these parameters are maintained by the Bureau of Economic Analysis (BEA) (2010) annually for 63 industries that make and use products among themselves. n X

xi ¼

aij xj þ ci () x ¼ Ax þ c

ð2Þ

j¼1

For the input–output model of a specific region r, the elements of the A matrix are modified to form the regional input– output matrix Ar in Eq. (3), where li is called the location quotient and is an indicator of how well the industry’s production capacity satisfies the regional local demand (Miller and Blair, 2009).

arij ¼



li aij ; li < 1 aij ;

ð3Þ

li P 1

Mathematically li is defined in Eq. (4), where xri is the output of industry i in region r, xrt is the output of all industries in region r, xi is the output of industry i at the national level, and xt is the output of all industries at the national level.

li ¼

xri =xrt xi =xt

ð4Þ

For multi-regional input–output analysis consisting of p regions, the input–output model is then written as Eq. (5).

2

x1

3

2

6 27 6 6x 7 6 6 . 7¼6 6 . 7 6 4 . 5 6 4 xp

A1

0

0 .. .

A2

0



 ..

.

0

32 3 2 3 0 x1 c1 .. 7 6 x2 7 6 c2 7 7 7 6 6 . 76 7 6 7 76 .. 7 þ 6 .. 7 7 7 0 54 . 5 4 . 5 xp cp Ap

ð5Þ

The system in Eq. (5) does not consider the effects of interdependencies due to the exchange of goods and services between regions. Isard et al. (1998) extended the input–output model to incorporate inter-regional commodity flows. This inter-regional output flow relationship is given in Eq. (6), where zrs ij is the amount of output of industry i in region r that is used s by industry j in region s, zrs i is the amount of output of industry i (i.e., commodity i) that flows from region r to s, and zj is the amount of output of industry i coming from all regions into s that is used as input by industry j. rs s zrs ij ¼ zi zj

ð6Þ

Using assumptions similar to the input–output model it can be said: rs s s rs 1. zrs i is proportional to the total flow of commodity i into region s, fi , from all other regions, i.e., zi ¼ t i fi . s s 2. zsij is proportional to the output of the industry j in region s, i.e. zrs ¼ a x . ij ij j

Hence, from Eq. (6) the inter-regional technical coefficient is found with Eq. (7).

ars ij ¼

zsij zrs s i ¼ trs i aij fis xsj

ð7Þ

The formulation in Eq. (7) provides the basis for the inter-regional input–output flow model in Eq. (8), which is explained in detail in Isard et al. (1998) and Miller and Blair (2009).

xri ¼

p X n X s¼1

s s t rs i aij xj þ

j¼1

p X

r trs i ci

ð8Þ

s¼1

The inter-regional input–output is provided in Eq. (9), where each sub-matrix Trs is an n  n diagonal matrix, whose diagonal elements are the proportions of all commodities t rs i ; 8i 2 f1; 2; . . . ; ng that originated in region r and are consumed in region s.

3 2 11 x1 T 6 .. 7 6 . 4 . 5¼6 4 .. xp Tp1 2

32 1    T1p A 6 .. .. 7 76 .. . . 54 .    Tpp 0

32 3 2 11 x1 T  0 6 . 6 .. .. 7 74 ... 7 6 . þ 5 . . 5 4 . xp Tp1    Ap

32 3 c1    T1p 6 .. .. 7 7 . 7 . . 54 .. 5 cp    Tpp

ð9Þ

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Data for each sub-matrix Trs, called the trade coefficient matrix, are estimated from the Commodity Flow Survey database maintained by the Bureau of Transportation Statistics (BTS) (2010) that documents the annual flow of goods in US dollars using multi-modal transportation across different regions in the United States. Several input–output approaches have been applied to transportation infrastructure investments and disruptions, including spatial economics investigations by Prastacos and Romanos (1987), Rietveld (1994), Zhao and Kockelman (2004), and Cohen (2010). 2.2. Inoperability Input–Output Model and its multi-regional extension The Inoperability Input–Output Model (IIM) (Santos and Haimes, 2004) extends the traditional economic input–output model to quantify how inoperability, not only commodity flows, propagate through interdependent industry sectors. Two metrics that define these risk assessment models are: 1. Inoperability for industry i, qi, refers to the inability of a system to perform its intended functions. In terms of measuring failure in industry sectors, qi is the measure of the loss of production in industry i as a proportion of its original production level, as shown in Eq. (10). The inoperability of a system lies on [0, 1], where qi = 0 is a measure of a perfectly operable industry i, and qi = 1 is a measure of complete failure of industry i.

qi ¼

As planned outputðxi Þ  Perturbed outputð~xi Þ Dxi ¼ As planned outputðxi Þ xi

ð10Þ

2. Demand perturbation for industry i, ci , refers of the change in final demand for industry i due to disruptive events. For economic systems it is the measure of the change in demand as a proportion of the original production level in industry i, as shown in Eq. (11). Demand perturbation can occur due to the inability of the producing sector to meet the demands of the final consumers when there is a failure in the system.

ci ¼

As planned demandðci Þ  Perturbed demandð~ci Þ Dci ¼ As planned outputðxi Þ xi

ð11Þ

Based on these two metrics the IIM is derived from the input–output model without violating the structure and assumptions of the latter. Eq. (12) extends Eq. (2), where A⁄ is now the n  n normalized technical coefficient matrix and diag(x) is the diagonal matrix of the industry outputs.

diagðxÞ1 Dx ¼ ½diagðxÞ1 AdiagðxÞdiagðxÞ1 Dx þ diagðxÞ1 Dc () q ¼ A q þ c

ð12Þ

Santos and Haimes (2004) and Santos (2006) provide more detail to IIM parameters and other foundational aspects of the model. The IIM and some extensions have been deployed in a number of contexts, including analyses of the 2003 Northeast blackout (Anderson et al., 2007), cyber threats (Andrijcic and Horowitz, 2006), biofuel adoption (Santos et al., 2008), workforce losses (Barker and Santos, 2010b; Orsi and Santos, 2010), and supply chain risk (Barker and Santos, 2010a; Wei et al., 2010), among others. Extending the same principles and integrating Eqs. (9) and (12), the Multi-Regional Inoperability Input–Output Model (MRIIM) (Crowther and Haimes, 2010) is provided in Eq. (13), where each of the n  n sub-matrices T⁄rs, 8r; s 2 f1; 2; . . . ; pg is normalized by the diagonal regional output matrices diag(xr), 8r 2 f1; 2; . . . ; pg.

3 2 11 q1 T 6 . 7 6 . 6 . 7¼6 . 4 . 5 4 . Tp1 qp 2

32 1    T1p A 6 .. .. 7 76 .. . . 54 . pp  T 0

32 1 3 2 11 q T 0 6 7 6 .. 7 76 .. 7 þ 6 .. . 54 . 5 4 . Tp1    Ap qp  .. .

32 3 c1    T1p 7 .. .. 76 .. 7 . . 54 . 5 pp cp  T

ð13Þ

3. MRIIM application to transportation facility disruptions Transportation facilities, such as ports, are outlets for commodity flows across regions. Since the multi-regional input– output model quantifies the equilibrium of the imports and exports between regions, port facilities are suitable geographic locations where this equilibrium can be studied. For a port located in region r ðr 2 f1; 2; . . . ; pgÞ exporting to region s ðs 2 f1; 2; . . . ; pg; s – rÞ, the amount of commodity i that arrives at the port is the amount of final demand for that commodity for region r. Hence, Eq. (14) shows how the total final demand, cri , for commodity i in region r is divided, where ðcri Þre is the amount of commodity i that is consumed internally or exported out of other locations except the port, and ðcri sÞpe is the amount of export out of the port into region s.

cri ¼ ðcri Þre þ

X ðcrs i Þpe

ð14Þ

s–r

The amount of commodity i that is shipped to region s is then used by industries in s for their production and for final   Pp rs , contributes towards the total output, xrs consumption. Hence, in region s the amount of import, Dsi r¼1 Di i , of the industry r–s

i and the final demand, csi , for the commodity i. Value ðxrs i Þpi is the amount of industry i output that comes through the port

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R. Pant et al. / Transportation Research Part E 47 (2011) 722–737

from region r, ðxsi Þre is the amount of industry i output in region s coming for sources other than the port import, ðcrs i Þpi is the amount of final demand for commodity i coming from the port into region s, ðcsi Þre is the amount of final demand for commodity i through sources other that the port import.

X

Drs i ¼

r–s

X X ðxrs ðcrs i Þpi þ i Þpi r–s

xsi ¼ ðxsi Þre þ

ð15Þ

r–s

X ðxrs i Þpi

ð16Þ

r–s

csi ¼ ðcsi Þre þ

X ðcrs i Þpi

ð17Þ

r–s

When disruptions result in a change in the amount of arrivals and departures of commodities at the port, they affect the exports and imports of the regions having commerce through the port. It is assumed that the disruptions cause losses in commodity flows only through the port while the rest of the flows are not affected. Hence, Eq. (18) shows that for the entire economy of region r, port disruptions result in a demand perturbation for commodity i, cr i , given by the loss of exports, P rs r ð D c Þ , as a proportion of the total output of commodity i in region, x . s–r i pe i

P

rs s–r ðDc i Þpe r xi

cr i ¼

ð18Þ

For the importing region s, the amount of import loss, P final demand, r–s ðDcrs i Þpi , for commodity i in region s.

X

DDrs i ¼

r–s

P

X X ðDxrs ðDcrs i Þpi þ i Þpi r–s

rs r–s DDi ,

in Eq. (19) results in the loss of output,

P

rs r–s ðDxi Þpe ,

and

ð19Þ

r–s

Thus, for the entire economy of region s, the loss of imports causes an inoperability, qsi , and demand perturbation, cs i , in industry i, provided in Eqs. (20) and (21).

P qsi

¼

rs r–s ðDxi Þpi s xi

ð20Þ

P cs i ¼

rs r–s ðDc i Þpi s xi

ð21Þ

The MRIIM interdependency equation uses the information from Eqs. (18)–(21) as inputs for calculating the inoperabilities and demand perturbations for interconnected industries across regions. If m 2 f1; 2; . . . ; ng different commodities are transported through the port from region r to s, then in the event of a disruption there is a demand perturbation, given by Eq. (18), only for those commodities, while the rest of the commodities experience no demand perturbation. Hence, the demand perturbation vector for region r is found with Eq. (22).

cr j

8P < s–r ðDcrsj Þpe ; j 2 f1; 2; . . . ; mg xrj ¼ : 0; j R f1; 2; . . . ; mg

ð22Þ

Similarly, for the importing region s, there is a demand perturbation for only those commodities imported through the port, while the rest of the commodities experience no perturbation in demand. Combining the information from Eqs. (19)–(21), the demand perturbation vector for the importing region s is calculated in Eq. (23).

cs j

8P < r–s DDrsi  qs ; j 2 f1; 2; . . . ; mg j xsj ¼ : 0; j R f1; 2; . . . ; mg

ð23Þ

Eqs. (22) and (23) combined with the MRIIM in Eq. (13) form a complete solvable system that quantifies the inoperability and demand perturbations for the entire regional economies for interconnected industries. The equations for demand perturbations developed above assume only exports from region r through the port, whereas in actual situations commodities are also imported into r through the port. Therefore, the total demand perturbation for region r is given in Eq. (24).

cr j ¼

8P   > < s–r Dcrsj pe > :

xrj

0;

þ

P s–r xrj

DDsr j

 qrj ; j 2 f1; 2; . . . ; mg j R f1; 2; . . . ; mg

ð24Þ

R. Pant et al. / Transportation Research Part E 47 (2011) 722–737

727

It can be seen that Eq. (24) is the general formulation for quantifying imports and exports through the port located in any of the p regions, while Eqs. (22) and (23) are its sub-cases that deal with only exports and imports, respectively. For non-zero cr j in Eq. (24), the first term quantifies the demand perturbation due to export losses, while the second and third terms quantify the demand perturbation in terms of import losses and industry inoperability arising due to the import losses. 4. Simulation model for port exports and imports A simulation model that provides estimates of the commodity arrivals and departures through the port is a useful tool for estimating the parameters for the MRIIM. Fig. 1 depicts a supply chain model for inland port operations. For the interregional commodity flow analysis we consider a queueing system for freight transfer through the supply chain. Supply chain modeling approaches have been applied in the transportation studies for different types of transfer facilities (Simao and Powell, 1992; Lee et al., 2003; Henesey, 2006; Sacone and Siri, 2009; Lee and Kim, 2010) and have been used in analyzing transportation disruptions (Wilson, 2007). In this study, the components of the different port operations are defined and explained as follows. 1. Delivery/receipt. These operations include the arrival of commodities for exports out of the region and the departure of commodities for imports into the region. 2. Yard operations. These are storage operations for the temporary storage of commodities at the port where they are kept for further transport. 3. Crane operations. Cranes are used at the port to transfer commodities to and from the port docks. 4. Shipment. Freight shipment operations include the departure of commodities for exports and the arrival for imports. A discrete time model, based on concepts developed by Simao and Powell (1992), can be built for simulating the above port operations. Due to different order of the operations, the simulation models for exports and imports will be separate, as shown in Fig. 2. It is assumed that commodities arrive independent of each other at the port, and each commodity is transported through the port operations separately. Hence, for m commodities arriving at the port there are m parallel queueing systems in operation, as depicted in Fig. 2. Considering a time increment of Dt, the discrete time model can capture the evolution of the queueing model at all times t (=0, Dt, 2Dt, . . .). Before developing the iterative equations for the queueing system, some random variables are defined for quantifying different elements of normal port operations: 1. 2. 3. 4.

Yi(t) = The number of units of commodity i arriving at the terminal in the time interval (t  Dt, t]. Ni(t) = Number of units of commodity i in yard storage at time t after commodities have arrived in the interval (t  Dt, t]. Vi(t) = The maximum units of commodity i that can be transferred by the cranes to the docks in the time interval (t, t + Dt]. Wi(t) = The maximum number of imported units of commodity i that can be loaded from the yard to trucks or trains in the time interval (t, t + Dt]. 5. Ui(t) = The number of units of commodity i that are transferred to the dock for shipment in the time interval (t, t + Dt]. 6. Di(t) = The number of units of commodity i departing in the interval (t, t + Dt].

In simulating the commodity arrival process, service capabilities of the transfer cranes and import loading process are known from data describing port annual exports and imports and daily crane operations, respectively. Hence, assuming that Yi(t), Vi(t), and Wi(t) are known, the other variables are calculated by adding and subtracting random variables, as described in the following sections. The same variables are used for formulating the export and import operations as they have the same meaning for both operations. 4.1. Port export operations When commodities arrive at the port, they are stocked at the yard. As shown in Eq. (25), at time t + Dt, the number of units of commodity i at the yard is the sum of the units remaining to be carried by the transfer cranes and the units that arrive.

Fig. 1. Supply-chain model for main inland port operations.

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R. Pant et al. / Transportation Research Part E 47 (2011) 722–737

Fig. 2. Differences in inland port export and import modeling.

Ni ðt þ DtÞ ¼ max½0; Ni ðtÞ  V i ðtÞ þ Y i ðt þ DtÞ

ð25Þ

From Eq. (26), the number of units of commodity i transferred by cranes is the minimum of the number of units at the yard and the crane capacities.

U i ðtÞ ¼ min½Ni ðtÞ; V i ðtÞ

ð26Þ

For normal port operations, the number of units of commodity i exported from the port is equal to the number of units transferred to the docks, as shown in Eq. (27).

Di ðtÞ ¼ U i ðtÞ

ð27Þ

4.2. Port import operations For imports the commodities are now arriving at the docks and transferred from the cranes to the yards. The number of units of commodity i transferred by the cranes becomes that in Eq. (28).

U i ðtÞ ¼ Y i ðt þ DtÞ

ð28Þ

Eq. (29) calculates the number of units of commodity i at the yard as the sum of the units remaining and the units transferred by the cranes.

Ni ðt þ DtÞ ¼ max½0; Ni ðtÞ  W i ðtÞ þ U i ðtÞ

ð29Þ

Under normal port operations, the number of units of commodity i departing the port are equal to the units transferred by the crane, as shown in Eq. (30).

Di ðtÞ ¼ min½Ni ðtÞ; W i ðtÞ

ð30Þ

From the simulation equations it can be seen that the crane operations and departure processes lag the arrival and yard storage operations by Dt time. The above formulations for exports and imports involve the simple additions, subtractions and splitting of random variables. As mentioned before, if the distributions for Yi(t), Vi(t), and Wi(t) are known, then the rest of the distributions of the random variables can be obtained by convolutions of the probability mass or density functions. This allows for estimates of the random variables in the queueing model. Arrivals of the commodities can be modeled as independent non-stationary Poisson processes (with rate ki(t) for commodity i). Similarly, the rate of service for the crane operations at the terminal could be modeled as a Poisson process with time-dependent rates (li(t) for commodity i). 4.3. Modeling disruptive events in export/import simulations A disruptive event such as a man-made attack, an accident, or a natural disaster can cause damage to components of the transportation network. Different scenarios of incorporating disruptive events in the supply chain model can be explored to quantify the amount of loss incurred due to damages. In this study we investigate how disruptions can affect the parameters in the queueing system simulation model. Some situations considered are as follows. 1. Terminal closure. A disruptive event, such as a storm, tornado, or attack, may cause the closure of the terminal for some time DT. In this case there are no arrivals over the period of the storm, but normal service is resumed once the event subsides. In the simulation algorithm this is modeled as Eq. (31).

R. Pant et al. / Transportation Research Part E 47 (2011) 722–737

Y i ðtÞ ¼ 0; 8t 2 ðt; t þ DT

729

ð31Þ

Such an event is a special case of the scenario where there is a partial disruption in the arrival of commodities due to a disruptive event. Using the assumption of time-dependent Poisson arrival rate of commodities, Eq. (32) quantifies how the rates of arrival for commodity i change in the simulations, where are ki the disrupted arrival rates and ki(t) are the arrival rates under normal port operations.

~ki ðtÞ ¼



ki ðtÞ; t 2 ðt; t þ DT ki ðtÞ;

ð32Þ

t R ðt; t þ DT

2. Crane outage. Disruptive events and normal wear and tear that damage some of the cranes may limit the number of commodities that are transferred to and away from the docks. Hence, if the disruption lasts for a time DT, in the simulation e i is the capacity limit on the amount of units of commodity i model the condition imposed is governed by Eq. (33), where U that can be transported by the cranes.

e i; U i ðtÞ 6 U

t 2 ðt; t þ DT

ð33Þ

A generalized simulation modeling scenario for such events could be the change in the time-dependent service rates of crane operations, as shown in Eq. (34), where li ðtÞ are the disrupted crane service rates and li(t) are the service rates under normal port operations.

l~ i ðtÞ ¼



li ðtÞ; t 2 ðt; t þ DT li ðtÞ; t R ðt; t þ DT

ð34Þ

3. Departure stoppage. Similar to arrival disruptions, hazards such as floods in the river or barge accidents can cause disruptions in the departure of commodities for exports and imports. For commodity i, such disruptions over time DT change the number of units departed with Eq. (35), where hðtÞ 2 ½0; 1Þ; 8t 2 ðt; t þ DT is the factor representing the reduction in departing commodity.

e i ðtÞ ¼ D



hðtÞDi ðtÞ; t 2 ðt; t þ DT Di ðtÞ;

ð35Þ

t R ðt; t þ DT

The above three modeling formulations for disruptive events provide different scenarios for calculating the losses over the period of analysis. Some or all of these scenarios can occur in an actual port disaster. Each scenario can be incorporated easily into the queueing model while preserving the simple arithmetic of addition, subtraction, and splitting on the random variables. 5. Case study: inland port disruption The concepts of the MRIIM and port disruption models are applied to a case study of the Port of Catoosa in Tulsa, Oklahoma. Spread over an area of approximately 2500 acres, in terms of area, Catoosa is the largest inland port in the United States. Annual freight volume of 2.2 million tons is sent and received through the Port of Catoosa along the Arkansas River. There are approximately 70 companies using the port from which about 4000 people earn their livelihood (Tulsa Port of Catoosa, 2010). Table 1 lists the names of the industries that do the most commerce through Catoosa and Table 2 lists the combined estimates for the annual exports and imports in tons of these industries among the states that do the most commerce using the port. These estimates are obtained from different databases (US Army Corps of Engineers, 2010; Tulsa Port of Catoosa, 2010; Commodity Flow Survey, 2010). These sectors/commodities are the inputs for the simulation model, with each commodity having its separate queue from arrival until departure. 5.1. Case study simulation results This case study considers a 2-week closure of the Port of Catoosa, similar to the closure experienced following the collapse of an I-40 bridge spanning the Arkansas River in eastern Oklahoma in 2002. The Port of Catoosa was affected by this incident Table 1 Names and NAICS codes for main industries using the Port of Catoosa. Industry name

NAICS code

Food and beverage and tobacco products Petroleum and coal products Chemical products Nonmetallic mineral products Primary metals Fabricated metal products Machinery Miscellaneous manufacturing

311 324 325 327 331 332 333 339

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Table 2 Estimates of annual tonnage of exports and import through the Port of Catoosa for 2007. State

Industry 311

Exports from OK AL 36,247 IL KY LA 547,496 MS TX Imports to OK AL AR IA IL LA MS OH Total

Total 324

325

327

331

332

333

339

38,267 60,000 127,057

3200 237,900

20,967

8236 153,068

12,595

86,090

6917

1600

165,663 7620 6426 11,479 585,761 5377 54,312

7620 6426 4269 8488

45,928

7210 438,338 5377

602,926

193,952

748,825

45,887

50,399

3973

289,557

23,485

36,247 38,267 60,000 677,753 237,900 30,803

11,436

1600

1917,668

for about 2 weeks as all transport through the port was stopped. Using the 2007 import–export data, we investigate the effect of this scenario occurring, its effect on the exports and imports through the port, and the ensuing losses to the interdependent industries in the states involved. The Tulsa Port of Catoosa (2010) also provides information on the monthly tonnage of exports and imports through the port. Taking the ratio of total monthly export–import with the total annual export–import and multiplying it by the annual export–import for each industry the monthly export–import tonnage per industry/commodity is obtained. Assuming that the port is open for 5 days a week from Monday to Friday, the total monthly flow of each industry is converted to a daily flow by dividing it equally among the number of working days in the month. Since there is randomness in the daily flow, it is assumed that each daily flow obtained from the data calculations is the mean of a Poisson arrival process. As an example, Table 3 shows the mean daily arrival rates for each working day of every month. The simulation starts at the first day of the year with Dt = 1 day and runs until the last day of the year to obtain the estimates of the annual arrivals and departures through the port as exports and imports. For port operations, it is assumed that the cranes have a very large capacity, which makes certain that all commodities arriving at the port are shipped the next business day. The disruption scenario reflecting the I-40 bridge collapse corresponds to the terminal closure scenario, the first of the three disruptive scenarios in Section 4.3. It is assumed that the port is closed for 2 weeks due to the bridge collapse and regular operations resume as normal after those 2 weeks. In addition, for simplicity it is assumed that the companies that use the port are able to deliver products to assigned destinations on normal lead-time after exiting the port, which means that there are no other sources of disruption in any of the surrounding states in Table 2. Fig. 3a–d illustrates one realization of the simulated daily behavior of normal port operations for an entire year and disrupted for 2 weeks beginning May 26 (or day 146). The plots in (a)–(d) describe port operations for the daily number of tons of arrivals, yard storage, crane transfers, and departures, respectively, for Farm and Beverage and Tobacco products being shipped from Oklahoma to Alabama. Simulations for exports to other states and imports coming to the port show similar behavior. As illustrated in Fig. 3a under normal port operations the daily tonnage arriving at the port is finite for the 5 working days of the week and is zero on the weekends. During the disruption time window this tonnage becomes zero for all the Table 3 Mean daily arrival rates for each working day of the week of every month of Food and Beverage and Tobacco products shipped from Oklahoma to Alabama. Month

Mean daily commodity arrival rate (tons)

January February March April May June July August September October November December

131.54 229.02 182.38 147.62 115.46 109.04 35.97 79.76 97.12 166.25 159.79 222.67

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Table 4 Structure of the non-zero values for the demand perturbation vector of Eq. (13). The numerical values are the mean estimates (103) of losses due to export and imports as a proportion of the total industry output in the state. State AL AR IL

Industry 311 0:0395 

324

0.0022

IA KY

0.0062

LA

0:5788  qLA 311

TX

327

0.0303

0.0193 0:0027  qIL 327

331

332

333

339

0.5275

0.2215

2.0549

0.1962

0:2576  qLA 333

0.0781 6:7095  qOK 331

0.0166 0:4880  qOK 332

0.4821

0.3208

0:0626  qTX 333

0:0408  qTX 339

0:0654  qKY 325 0:0134  qLA 324

MS OH OK

325

qAL 311

0:1781  qLA 325 0:6572  qMS 325

0:8320  qOK 311

0:1625  qOK 324

5:4405  qOK 325

0:0021  qTX 324

0:0648  qOK 327

Fig. 3. Simulation behavior for exports of any commodity showing the daily number of units (a) arriving at the port, (b) stored in the yard, (c) transferred by the cranes to the docks, and (d) departing the port. The plots show that the flows are affected for a few days when the port terminal is closed for 2 weeks.

days the port is shut down. Arrivals for the month of July are lower than the rest of the year because it is a lean month for commerce across the port. In Fig. 3b for weekends and during the disruption time window the daily tonnage at the yard remains constant and equal to the number of units before the closure. For the remaining days of normal port operations the tonnage of yard storage depends upon the tonnage arriving, since the cranes have enough capacity to transfer all the units arriving. Fig. 3c and d reflects the same behavior as Fig. 3a with a lag of 1 day, because the cranes are able to transfer all commodities that arrive the previous day and are not in operation during weekends and port closure (Fig. 3c), which leads to commodities departing on all days except on weekends and during port closure (Fig. 3b). 5.2. Economic loss estimates from simulations For each commodity export and import through the port we run 1000 simulations for each case: with or without the disruption, based on the estimates of standard error of the mean (Pritsker and O’Reilly, 1999). For commerce between Oklahoma and any of other states, each simulation provides us with estimates of the first two non-zero terms of Eq. (24) depending upon whether the commodity counts as an export or import. Fig. 4a–d shows the distribution for the perturbation

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in exports and imports, expressed as a proportion of the total industry output, of the Primary Metals industry (NAICS-331) for four states. As seen in Table 2, Primary Metals are exported from Alabama, Louisiana and Ohio into Oklahoma. Hence, due to port closure the demand perturbation ðcr j Þ for Alabama, Louisiana and Ohio is directly equal to loss of exports, which is the first non-zero term in Eq. (24). Since Oklahoma imports Primary Metals the demand perturbation for Oklahoma is expressed in terms of the loss of imports and inoperability (second and third non-zero terms in Eq. (24)), because imports contribute towards the demand perturbation and inoperability of the industry in Oklahoma. The MRIIM of Eq. (13), for which the simulation results supply the ðcr j Þ inputs, represents the equilibruim model for 10 states each having 62 industry sectors based on the combination of the BEA and CFS datasets. Hence, in Eq. (13) T⁄rs and A⁄r are 62  62 matrices that are assembled to form 620  620 inter-regional trade and interdependency matrices respectively, while the industry output and demand perturbation are 620  1 vectors. Table 4 shows the structure for the non-zero terms of the demand perturbation vector that is input into the MRIIM of Eq. (13), expressed using Eq. (24), for each industry corresponding to the state in which it is located. The numerical values are the mean estimates (103) of the loss in exports and imports as a proportion of the total output for the industry in the state. All other demand perturbations values are zero based r on Eq. (24) formulations. It can be seen that some of the cr j values are expressed in terms of the inoperabilities ðqj Þ due to the industry sector imports. Also, since the Port of Catoosa is located in Oklahoma it has the highest perturbations in exports and imports because its industries are engaged in both export and import with most of the states. Based on Table 4 mean estimates of the proportional losses of exports and imports for the industries in each state, the values of the mean total direct losses incurred by these industries in the states are calculated to be $62.2 million. The Primary Metals (NAICS-331), Chemical products (NAICS-325), Food and Beverage and Tobacco products (NAICS 311) in descending order are the top three industries that are the most affected due to the port closure. The Primary Metals industry incurs an estimated export–import mean loss of $21.6 million over all the states, because primary metals represent the third most significant export and import through the port accounting for both tonnage and prices. As expected, Oklahoma industries suffer the most losses in export or import (mean estimate of $31.1 million) because they are most dependent on the port compared to other states. Based on the demand perturbation metric obtained from simulation model and its subsequent use in the MRIIM analysis the industry output economic losses across states shows that the closure of the Port of Catoosa for 2 weeks causes losses to the industries that do commerce through it and is considerably cascaded to other interdependent industries that are not using the port. The results generated in this section provide risk planning insight for (i) industries who use inland waterways

Fig. 4. Distribution of loss of exports for (a) Alabama (b) Louisiana (c) Ohio and loss of imports for (d) Oklahoma, expressed as a fraction of the industry output in the respective states, for the Primary metals industry (NAICS-331) due to 2-week port closure.

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or who rely upon industries that do, in order to develop strategies for minimizing losses, and (ii) inland port authorities, in order to measure the efficacy of risk management across stakeholders from various industries and various geographical locations. The estimates provided below show the losses that occur when the port is closed for 2 weeks in May, using 2007 economic data. The MRIIM in Eq. (13) provides estimates of the industry inoperabilities across all the states. Fig. 5 shows the mean and 95% confidence interval estimates for the total inoperability in entire states economies due to 2 weeks of port closure. The total inoperability in a state is due to the cascading of the demand perturbations for the industries directly affected by the port closure to the other interdependent industries in the state. Oklahoma industries suffer the most due to a port closure, as measured by the mean economic inoperability (0.0041). Louisiana, Mississippi and Alabama are the three states doing the most trade through Catoosa as reflected in the inoperability values. A useful insight into the MRIIM effects is gained by comparing the import–export losses for the industries using the port with their respective output losses. Fig. 6 shows the mean and 95% confidence interval estimates for total losses in industry export–imports and outputs for the eight industries that use the port. The combined average output losses across these industries are $37.9 million, of which the Primary Metals (NAICS-331) industry contributes the most with losses of $14.2 million. The inter-regional T⁄rs matrices in general make sure that for any industry only a fraction of the entire demand perturbation effect is transferred to its output inoperability, as the output losses incurred are smaller compared to demand perturbation losses. Hence, the export–import losses for each industry in Fig. 6 tend to be greater than their output losses. The strength of the MRIIM lies in its capability to propagate the demand perturbations of a few industry sectors across all the inter-regional interdependent industries. This property is highlighted in Fig. 7, which shows the mean and 95% confidence estimates for the direct total demand perturbations losses for all the port’s industries in each state and the corresponding indirect output losses incurred across all the 62 statewide industries. The cumulative mean industry demand losses of $48.6 million across all regions result in cumulative mean output losses of $101.9 million. As seen in the MRIIM Eq. (13) the inoperability of each regional industry is expressed in terms of all the other inter-regional industry outputs and demand perturbations. Each demand perturbation is distributed across all industries connected across the regions. Hence, a state in which the industry demand perturbations are minimal will experience some amount of inoperability in all its industries due to the interconnectedness. The cumulative effect produces larger output losses compared to demand losses for most of the states even when they have almost zero demand losses. Texas exemplifies this effect the best as average demand losses of $0.13 million result in aggregated output losses of $23.6 million. Oklahoma is the only state for which the industries have demand losses ($24.3 million) greater than the output losses ($11.9 million), which, as explained previously, is due to the effect of the T⁄rs transferring only fractions of larger demand losses to output losses. Similar effect are seen to some degree for Louisiana and Alabama as these states also have substantial demand losses. The impact of port closure on the 10 states can become greater when the traffic through the port is heavier. During the 2002 bridge collapse industries were able to sustain minimal impact of port closure because May is considered a lean month for port usage. For other periods of greater traffic, this might not be the case. Fig. 8 illustrates the estimates for the mean and

Fig. 5. Mean and 95% confidence interval estimates for total inoperability in state economies due to a 2-week disruption at the Port of Catoosa.

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Fig. 6. Mean and 95% confidence interval estimates of total losses for industries using the Port of Catoosa (in 106 dollars).

Fig. 7. Mean and 95% confidence interval estimates for direct total port demand losses and indirect total output losses for all industries in each state (in 106 dollars).

95% confidence bounds of economic losses for the total economy of the 10 states for a 2-week port closure occurring on the 15th day of each month. Large losses occur for the period of October–March when the port imports and exports are the largest. Hence, losses due to port closure can go up to approximately $190 million (for the month of March), which highlights the severity of the event. A sensitivity analysis of the effect of the length of port closure on economic losses helps in further highlighting the severity of such an event. Fig. 9 illustrates the mean and 95% interval estimates for the combined economic losses to the 10 states as the duration of port closure extends from 2 weeks up to 10 weeks starting the 15th of January. Since, the MRIIM is a linear model and the port traffic rate during this duration remains almost constant, the economic losses show a linear incremental behavior. Losses amount up to $760 million for a 10-week port closure, although in reality it is expected that companies would be looking for alternate shipping strategies to reduce export–import losses.

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Fig. 8. Mean and 95% confidence interval estimates for total economic losses across all 10 states due to disruption at Port of Catoosa (in 106 dollars).

Fig. 9. Mean and 95% interval estimates for the total economic losses across 10 states for varying durations of closure of the Port of Catoosa (in 106 dollars).

5.3. Risk management insights from the port case study The results generated in this study highlight the use of the proposed integration of the MRIIM with a simulation of port operations to model the severity of losses suffered by the different industry sectors and different states following a closure of the Port of Catoosa. These losses can be greatly magnified if the period of inoperability extends beyond 2 weeks. Further the losses to the state economies show that due to interdependence small disruptions magnify the industry outputs and economic losses. If such disruptions occur at critical times of the year then they can result in widespread adverse impacts across regions. Critical insights are provided by the study that can be useful for the both the port and the industries using the port. As illustrated through the case study, the Primary Metal industry suffers maximum losses in export–import, which lead to maximum output losses. Hence, interest lies for the shippers of primary metals to invest in safeguarding the port against dam-

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ages because such products are also transported in bulk across waterways more conveniently. In addition, from Table 2 data it can be seen that three states export Primary Metals into Oklahoma, which shows that the industry is affected across four states. Maintaining waterway transport across the four states would benefit port authorities in limiting the damages due to disruptions. The interdependent effects on the economy quantified by the MRIIM provide valuable estimates into the spreading out of the disruptive effects across state economies. As Fig. 7 illustrates, the Texas economy is greatly affected even due to small demand losses for the state. Consequently, industries in Texas should be interested in looking at contingency plans, e.g., maintaining inventory to safeguard against the effects of the port transport disruptions. Estimates of the losses for different months and for longer durations can help companies plan their monthly shipping schedules and invest in exploring contingency shipping strategies. Port authorities are interested in assuring that the port opens as soon as possible. For lean months of trade the impacts of port are much less, but for high traffic months having security measures in place helps prevent port closure and speed recovery from port closure. 6. Concluding remarks Multi-modal transportation systems are vital to the shipment of commodities among interdependent industries and across multiple regions, and freight disruptions at a number of nodes along the transportation system can have adverse impacts on the flow of commodities. One such node is an inland waterway port, whose risk studies in the literature have been sparse. This paper provides a novel approach for modeling the adverse impact across interdependent industries and across multiple regions, resulting from a disruption in the operations of an inland port. The risk-based approach integrates the Multi-Regional Inoperability Input–Output Model (MRIIM) with a simulation model of inland port operations to quantify the impact of real disruptions in inter-regional commodity flow connected by a single terminal of usage in a multi-modal transportation system. The study considers three different disruption scenarios (terminal closure, crane outage, and departure stoppage) and quantifies interdependent impact in terms of inoperability (extent to which output is not being shipped and produced), and economic losses (dollar value of port inoperability). The modeling approach depends upon existing and estimated data sources. The MRIIM is parameterized from commodity flow databases from the Bureau of Economic Analysis and the Bureau of Transportation Statistics, and the simulation model is parameterized by commodity flow data describing the operations of the inland port. The analysis using and integrated inland port simulation model and the MRIIM quantifies adverse impacts of a 2-week terminal closure scenario in the month of May for the Port of Catoosa, located on the Arkansas River navigation system near Tulsa, Oklahoma. For this scenario, the mean loss estimate is $37.9 million for the eight industries across ten primary states that use the port. The mean loss estimate cascades to $101.9 million across the entire economies of the 10 states when industry interdependencies are considered. For busier months of commerce, a 2-week disruption at the port can result in $190 million losses across these states. The contributions of this paper are several. First, we broaden the scope of the MRIIM scheme (Crowther and Haimes, 2010) with the novel integration of the approach with multi-modal transportation systems for analyzing the interdependent adverse impacts of an inland port disruption. Second, our queuing model provides a much simpler analysis approach of tracking freight movement through the port compared to other discrete models (Simao and Powell, 1992). We also show how the components of our queuing model are altered due to disruptions, often ignored in much of the literature. Finally, the ultimate usefulness of our risk-based approach lies in its ability to measure the efficacy of risk management options. That is, investments in port protection (e.g., security, system hardening) may result in reduced initial effects of a disruption, and investments in preparedness (e.g., contingency routing options) may result in reduced downtime of a port. The approach described here is also useful to measure the interdependent and inter-regional benefit of implementing these risk management investments. Although this case study has been descriptive in nature, prescriptive uses of the model may be more useful and powerful. Several opportunities for further research will be explored, including relaxing the equilibrium assumption of the MRIIM to include a dynamic analysis of inoperability and economic losses, and exploring more complex scenarios of port disruptions that highlight the realistic nature of man-made attacks, accidents, and natural disasters. Acknowledgements This work was supported in part by the U.S. Federal Highway Administration, under awards SAFTEA-LU 1934 and SAFTEA-LU 1702, and the National Science Foundation, Division of Civil, Mechanical, and Manufacturing Innovation, under award 0927299. References Anderson, C.W., Santos, J.R., Haimes, Y.Y., 2007. 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