Paper: Two Interdependence Models                                              Ping Chen, 5/24/2010



Demand Driven and S...
Paper: Two Interdependence Models                                                     Ping Chen, 5/24/2010



Key word: In...
Paper: Two Interdependence Models                                             Ping Chen, 5/24/2010




1. Introduction
Inf...
Paper: Two Interdependence Models                                             Ping Chen, 5/24/2010



services that are fu...
Paper: Two Interdependence Models                                             Ping Chen, 5/24/2010




According to [Paeli...
Paper: Two Interdependence Models                                             Ping Chen, 5/24/2010



The paper is organiz...
Paper: Two Interdependence Models                                               Ping Chen, 5/24/2010




2. Dependence Ind...
Paper: Two Interdependence Models                                                   Ping Chen, 5/24/2010




     Downstre...
Paper: Two Interdependence Models                                             Ping Chen, 5/24/2010



encouragement of the...
Paper: Two Interdependence Models                                             Ping Chen, 5/24/2010



propagated perturbat...
Paper: Two Interdependence Models                                            Ping Chen, 5/24/2010




3. Economic Input-Ou...
Paper: Two Interdependence Models                                                     Ping Chen, 5/24/2010




        Ind...
Paper: Two Interdependence Models                                              Ping Chen, 5/24/2010



and Use tables retu...
Paper: Two Interdependence Models                                             Ping Chen, 5/24/2010



355 various sectors ...
Paper: Two Interdependence Models                                                                                         ...
Paper: Two Interdependence Models                                               Ping Chen, 5/24/2010



   are fundamental...
Paper: Two Interdependence Models                                              Ping Chen, 5/24/2010




4. Economic Input-...
Paper: Two Interdependence Models                                                                                         ...
Paper: Two Interdependence Models                                                Ping Chen, 5/24/2010



v j – Value added...
Paper: Two Interdependence Models                                            Ping Chen, 5/24/2010



                     ...
Paper: Two Interdependence Models                                                         Ping Chen, 5/24/2010



Leontief...
Paper: Two Interdependence Models                                                        Ping Chen, 5/24/2010



DoC’s 485...
Paper: Two Interdependence Models                                                      Ping Chen, 5/24/2010



on electric...
Paper: Two Interdependence Models                                              Ping Chen, 5/24/2010




5. Extensions to I...
Paper: Two Interdependence Models                                              Ping Chen, 5/24/2010



infrastructure inop...
Paper: Two Interdependence Models                                              Ping Chen, 5/24/2010



interdependence equ...
Paper: Two Interdependence Models                                              Ping Chen, 5/24/2010



                   ...
Paper: Two Interdependence Models                                             Ping Chen, 5/24/2010



sector’s inoperabili...
Paper: Two Interdependence Models                                            Ping Chen, 5/24/2010




6. Experiments: Dema...
Paper: Two Interdependence Models                                                                                         ...
Paper: Two Interdependence Models                                                                                         ...
Paper: Two Interdependence Models                                                                                         ...
Paper: Two Interdependence Models                                                                                         ...
Paper: Two Interdependence Models                                             Ping Chen, 5/24/2010



power plant is the i...
Paper: Two Interdependence Models                                             Ping Chen, 5/24/2010




7. Typical Supply S...
Paper: Two Interdependence Models                                             Ping Chen, 5/24/2010




Tables 7 and 8 comp...
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
Leontief and Ghosh 2..
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  1. 1. Paper: Two Interdependence Models Ping Chen, 5/24/2010 Demand Driven and Supply Constrained Input-Output Models for Infrastructure Interdependence Analysis Abstract Unknown and unmanaged interdependence among infrastructure sectors could cause severe problems and long lasting impacts on productivity and economic activity. Understanding and evaluating the security of national infrastructure systems need requires systematic and inclusive analysis. This paper reviews and examines the interdependence among these critical infrastructures by investigating the supply chain connections among them. In this paper, infrastructure interdependence related disruptions have been classified into two types: demand driven and supply constrained. Two economic input-output models that can be extended to address these two interdependence related problems are introduced. As the demand driven problem based on the Leontief economic input-output model has received much attention, this paper focuses on reviewing and evaluating the counterpart of the Leontief model: the Ghoshian model, which can be used to estimate the impact from constrained supply. Extensions of these two models that can be applied in interdependence analysis are discussed in the paper. It is found that various sectors can be characterized as either a typical supply or demand sector according to their impact on the entire economy. The proposed method of classifying these infrastructure sectors and the features of the typical supply and demand sector are presented. At the end of the paper, we discuss the implications of having these two types of models. They are suitable appropriate for the assessment of various dependence related disruption problems. The combined application of these two models enables a comprehensive analysis of the vulnerability of individual infrastructure sectors and it facilitates the detection of sensitive sectors that are prone to the disturbance from other infrastructure sectors and the sectors whose stable supply or demand are crucial for the entire economy. The prioritization and optimization of resource allocation strategies based on the output from these two models makes decision making and policy design more rational. 1
  2. 2. Paper: Two Interdependence Models Ping Chen, 5/24/2010 Key word: Interdependence Analysis, Economic Input-Output Model, Critical Infrastructure Sectors, Demand Driven, Supply Constrained 2
  3. 3. Paper: Two Interdependence Models Ping Chen, 5/24/2010 1. Introduction Infrastructure systems are generally manmade systems that function collaboratively and synergistically to produce and distribute a continuous flow of essential goods and services that interact with people’s daily life and everyday economic activities [Heller 2002]. Critical infrastructures, such as those that supply water, oil and gas, power, telecommunications, transportation, etc. are foundations of today’s society. They support and maintain the economic operations and activities of our communities. Aside from being productive and in high demand, the increased operational complexity and excessive utilization of these infrastructure systems have made them more vulnerable than in the past [Zimmerman 2001] [Haimes 2005(c)]. The reliability and safety of the services provided by these infrastructure sectors are under threat of from many potential factors. Little [2002] has identified a number of them: natural disasters, terrorist attacks, design faults, excessively prolonged service lives, aging materials, and inadequate maintenance. More diversified sources that can bring unexpected disruptions with large-scale and long- term impacts also exist, such as a power outage, a labor strike, and so on. To carry out the critical services that are needed, infrastructure systems themselves are physically connected to each other to fulfill the requirement of the service/commodity from one sector as a necessary input/aid to facilitate the production in another. As an example, electricity is required in almost every economic sector and the rapid development of the economy further intensifies this requirement. The increased buildup of interdependencies can be found as the result of promoting convenient and efficient services, such as the encouragement of the companies to incorporate information technology in modern production processes under the pressure of intense competition and rapidly increased demand. The consequence from this interdependence is that the fluctuation of supply or demand in any sector which is part of an interconnected system can disturb the normal production of others. Moreover, this effect could ripple through their interconnections and increase the total impact. Interruptions in one infrastructure sector can cascade to others. This has become an important factor that can cause critical infrastructures to reduce their operational productivity and even fail to provide necessary 3
  4. 4. Paper: Two Interdependence Models Ping Chen, 5/24/2010 services that are fundamental for economic vitality and sustainability. The U.S. Department of Energy and the Office of Science and Technology Policy, for example, underscored in their report, that “the issue of interdependencies among critical infrastructures is a fundamental dimension of critical infrastructure protection” [Zimmerman 2001]. Cascading failure has been identified as the main source of vulnerability in critical infrastructure systems [Amin 2000]. To protect these sectors effectively and efficiently, we need to first identify and understand these interdependencies and, understand how the interdependence-induced disruptions get spread and measure their impacts.. Research on interdependencies has been conducted mostly within the realm of qualitative methods. Some research has attempted to quantitatively evaluate the interdependencies among some of the sectors. For example, an agent-based Complex Adaptive System (CAS) approach has represented the interactions among economic and societal factors and the operation of several infrastructures by assuming each system as one agent interacting with another and studying the behaviors and responses of these systems by changing the connection conditions among them [Wildberger 1997]. In addition, Heal and Kunreuther [2004] has introduced the concept of Interdependent Security (IDS) using game-theoretic models as a way of investigating how interdependence affects individual choices about security expenditures in interdependent systems. The advantage of these approaches is that they can characterize multiple aspects of interdependencies. However, because of the complexity of each pair of dependent infrastructure sectors, these models can only include a limited number of infrastructure sectors. The ripple effects among the collection of complete infrastructure sectors cannot be represented appropriately. “The analytical capacities in understanding infrastructure interconnections and interdependencies have not been developed to a point where their interactions can be easily managed. One reason for the complexity of these interdependencies is the many combinations and metrics used to characterize either the interactions or their impacts, and analytical models to simulate these conditions have not yet been developed” [Zimmerman 2001] 4
  5. 5. Paper: Two Interdependence Models Ping Chen, 5/24/2010 According to [Paelinck and Nijkamp 1976], one way to measure the degree of interdependence of various industries is through input-output tables. In measuring the extent to which any one industry interacts with others, a distinction should be made between two kinds of linkage effects, called the backward effects and the forward effects. The distinction should be made based on the recognition of two mechanisms. First, the input provision induces the attempt to supply. Tracking this input function back to the original supplier constitutes a backward connection. Secondly, various products are consumed to feed the demand of an upstream activity; this generates a forward connection [Paelinck and Nijkamp 1976]. However, there have been very few continuing attempts that integrate these two supply-demand effects. In this research, we are going to investigate two modifications made on the economic input-output models to obtain models that can evaluate interdependence and recognize both supply and demand propagations within an interdependent economic network that is composed of a complete collection of economic sectors including these infrastructure sectors. The research presented here uses input-output transaction data based connections to interpret the interdependencies among a large collection of various economic sectors. As the sectors defined in the input-output tables tie each other together through their demand and supply relations, this supply chain connection has evolved into an important linkage that connects the critical infrastructure sectors to each other and could, as well, propagate the damage of any of them to the others. Santos and Haimes [2004] have explored how to use demand reduction derived impact to quantify their interdependency. However, his study reviewed only the impact from the demand provision side, leaving the impact from the supplier side untouched. As interdependence analysis is about the evaluation of the impact from both the supply side and the demand side, this is an incomplete assessment method. This paper presents another impact mechanism which is counterpart of his and reveals the implications importance and vulnerability ofon the selected infrastructure sectors by considering both of these two impact mechanisms. 5
  6. 6. Paper: Two Interdependence Models Ping Chen, 5/24/2010 The paper is organized as follows: (1) introduction and explanation of two types of dependence induced disruption problems; (2) introduction of two classical input-output (I-O) models to lay the foundation for an economic loss and inoperability interdependence model that are designed to address these two types of interruption problems; (3) interpretation and comparison of the impacts derived from these two models for assumed interruptions on selected infrastructure sectors; (4) identification and characterization of two major types of infrastructure sectors: typical supply and typical demand sectors; (5) identification of vulnerable infrastructure sectors and critical infrastructure sectors; (6) discussion of potential applications of the proposed interdependence model. 6
  7. 7. Paper: Two Interdependence Models Ping Chen, 5/24/2010 2. Dependence Induced Disruption Problem Type In a physically interconnected economy, each sector typically functions as both a supplier and consumer. Therefore, dDemand and supply constitute the main forces that sustain the normal operations of each individual sector. Material/Goods/Service moves from one sector to the other. The consumer sector becomes the downstream side of the transaction; the supplier becomes the upstream side of the transaction. The spread of interdependence induced disruptions thereafter can be classified into two ways: either being borne by its the downstream upstream sectors as the result of a disturbance applied onproduced at its a supply sector or borne by itsthe downstream upstream sectors as the result of a disturbance applied on itsproduced at a demand sector,. or a mixed effect of these two. That isNamely, whatever the initial disruption cause is and whichever the initially affected sector would be, the spread of disruptions has only two directions: forward propagation from the upstream to the downstream; and backward propagation from the downstream to the upstream. In other words, it is eitherThe former is a supply or a demand-driven a supply constrained disruption. and the latter is a demand driven disruption. Figure 1 shows these two types of disruption propagation processes where the arrow indicates the direction of physical connection from the supply sector to the demand sector. The starting end of the arrow represents the upstream sector of a supply demand connection while the finishing end of the arrow represents the downstream sector. The solid box represents the initially disturbed sector and the shaded box represents the sector directly or indirectly affected after the initial disruption on the solid-box sector occurs. The following details the classification of these two types of disruptions.Therefore, we have two sets of flow here, one is the flow of the material, service, etc, which is always from the upstream sector to the downstream sector; the other is the flow of disruptions. In the demand driven disruption case, the disruption effects propagate from the downstream sector to the upstream sector; in the case of supply constrained disruption, the disruption effects propagate from the upstream sector to the downstream sector. Discussion after this graph details and examplifies the classification of these two types of disruptions. 7
  8. 8. Paper: Two Interdependence Models Ping Chen, 5/24/2010 Downstream Upstream Downstream Upstream Demand-driven Supply-constrained Figure 1 Illustration of Two Dependence Related Disruption Type 1. Demand-driven Disruption: This type of indirect interruption is caused by changed demand in a one sector and; the consequences of reduced demand are borne by its supply sectors. For example, the 9/11 terrorist attack greatly reduced the confidence of travelers in the safety of airlines; therefore, quite a few passengers changed their choice of travel modes. Consequently, the supply sectors to the air transportation sector (e.g., petroleum supply sector, etc) lost their production request from these airline companies and their productivities output were reduceddropped even through there was increased demand on other types of products / services for the same reason, i.e., the increased demand on its substitutes, such as highway transportation services. The Other causes that can bring about this changedemand-driven interruptions may include technology reformation, reduced customer interests, etc. Sometimes, demand-driven disruption has support from psychological belief, like the one statedexample in Haimes [2005(b)] that “psychological factors mirror the physical destruction delivered by terrorism and other extreme disasters”. Because humans serve as the final requester for all kindsconsumer of many types of production activitiesoutputs, any factors that could affect human choice would become a reason that the demand level of intermediate or final products is affected. Technology reform could also bring higher demand in one sector and reduced interest in other sectors. This type of disruption is related more to changes in physical requirements instead of the psychological concerns. An example could be the technology change in certain industries, such as requested from environmental inspection. The dis- 8
  9. 9. Paper: Two Interdependence Models Ping Chen, 5/24/2010 encouragement of the public from using fossil fuels to generate electricity will unavoidably inevitably force the power plants to choose renewable clean energy sources or install innovative cleaning technologies. Such changes may cause the related fossil fuel supply sectors to reduce their production, while at the same time driving up the production level in these new technology providing sectors. 2. Supply-drivenSupply-constrained Disruption – Most of this type of disruptionThis type of indirect disruptions is initially caused by reduced production in one sector, for a variety of reasons; and the consequences are borne by the sectors that have direct or indirect demand on the deficient supply sectors. Therefore, it may be more appropriate to call it “supply constrained disruptions”. For example, the attack on a power plant could possibly break down the production of other sectors whose operations can not continue without electricity. This is because the demand on the affected sector won’t decrease even though its service becomes unsecured or less reliable as people have less flexibility of switching to an alternative product or service. The causes of such disruptions may include system failure, natural disaster, etc, on the supply sectors. These kinds of chained disruptions happen only when the output from the economic sectors is curtailed by a reason that is not a result of reduced demand. For example, equipment failure, natural disaster, accidental accidents, etc, which cause the reduction of production in the supply sector and does not necessarily cause an immediate change in the demand for the services or products from the demand sectors. What always happens is that tThe indirectly affected sectors have planned demand and the disruptions are caused because their production capacity is not ablecan not to be fully realized because ofdue to their inability to acquire insufficient acquisition quantities of limited products or services from their supply side. A terrorist attack could cause supply-drivensupply-constrained disruptions as well as the demand driven disruptions.. Therefore, tThe question of evaluating infrastructure interdependence becomes howis equivalent to estimate the impact of a disruption using calibrated, scalable measurement through the interconnections among these infrastructure sectors. Two issues are raised when evaluating the interdependence related impacts: (1) how to classify whether one 9
  10. 10. Paper: Two Interdependence Models Ping Chen, 5/24/2010 propagated perturbation creates a demand-driven or supply-drivensupply-constrained impact or both. Given both of them are possible to occur, which one should be addressed first;; (2) how to estimate the direct and indirect impacts through the supply chain induced due to some initial disruptions problems. Related to the first issue, we need to identify the type of disruptions that could happen after a particular sector is exposed to an initial interruption. As the connections among these sectors are determined by their input- output relations, we need criteria to determine which sectors are prone to generate supply drivensupply constrained impacts and which sectors are prone to generator demand driven impacts. Related to the second issue, we need to compute the economic loss due to a supply or demand interruption and take into account both direct and indirect effects. The following sections will illustrate the insights that have been gained by employing economic input-output data and economic input-output models to address these two issues. 10
  11. 11. Paper: Two Interdependence Models Ping Chen, 5/24/2010 3. Economic Input-Output (EIO) Data The United States economic input-output (EIO) transaction data have been collected and reported for over 50 years. EIO data are presented in the form of transactions measured by dollar amount. These data describe the monetary transactions between various economic sectors, defined according to a standard classification system developed by the US Department of Commerce to categorize business activities. The Bureau of Economic Analysis (BEA) publishes the transaction data covering two aspects: the Make table depicts what commodities and how much of each commodity is produced by each industry; the Use table explains what commodities and how much of each commodity is consumed by each industry to implement its own production level. In this study, we chose the 1997 commodity-by-industry Use table and industry-by-commodity Make table as our base data set, which is the most recent benchmark collection of data available. Benchmark tables are collected only every five years and released five years later than the benchmark year. In the Use table, each row represents one distinct commodity and each column represents one industry. Each cell entry represents the amount of the row commodity that is bought and used by the column industry. In the Make table, each row represents one distinct industry and each column represents one distinct commodity. Each cell entry represents the amount of the column commodity that is made and sold by the row industry. The 1997 data use a new classification system that is based on the North American Industry Classification System (NAICS) 511 IO sectors are included in the 1997 data and they are defined according to this classification system. Among them, eleven critical infrastructure sectors are identified for further study. Their NAICS code number and sector name are listed in Table 2 Table 1. 11
  12. 12. Paper: Two Interdependence Models Ping Chen, 5/24/2010 Index NAICS Sector Name 19 211000 Oil and gas extraction 30 221100 Power generation and supply 142 324110 Petroleum refineries 391 481000 Air transportation 392 482000 Rail transportation 393 483000 Water transportation 394 484000 Truck transportation 396 486000 Pipeline transportation 412 514100 Information services 419 52A000 Monetary authorities and depository credit intermediation 468 7211A0 Hotels and motels, including casino hotels 470 722000 Food services and drinking places Table 1 Infrastructure Sectors selected from 1997 EIO Table The classification of demand-driven and supply-drivensupply-constrained disruptions requires us to explain whether the sectors are prone to better classified as one of the two disruption types. One way of doing so is to characterize each sector by comparing its supply and demand features, which is whether or not these sectors contribute “more” as a supplier or contribute “more” as a consumer. Here, the comparison could be based on either the monetary value or the amount of consumers and suppliers among their entire supply and demand transactions. The following is an experiment we conducted to identify supply and demand sectors via the EIO Use and Make tables. Since the Use and Make tables represent only the relationship between industry and commodity, to investigate the inter-transactions from one industry to another industry, an industry-by- industry transaction table is created using the following method: the commodity-by- industry Use table is first normalized at each column by dividing each element in that column by the total sum purchase made by that column sector; the industry-by- commodity Make table is normalized at each row by dividing each element in that row by the total sum of sales made by that row industry. The product of the normalized Make 12
  13. 13. Paper: Two Interdependence Models Ping Chen, 5/24/2010 and Use tables return a normalized industry-by-industry matrix. This normalized industry-by-industry matrix is different from the direct requirement matrix in that the direct requirement matrix is the column normalized Use table and it doesn’t consider which sectors the used commodities is made from. By integrating the Use table and Make table, the portion of output that is produced from a supply sector to a demand sector is determined. By multiplying this the industry-by-industry matrix with the total industry output from each sector, we can obtain the industry-by-industry table. [Haimes 2005(a)] adapted the same method to obtain the industry-by-industry input output table. There are 511 sectors included in the generated 1997 industry-by-industry table by using the Use and Make tables. Among them, 12 sectors are special industry sectors, 13 are final uses sectors; 3 are value added sectors. As these sectors don’t have clearly defined product or service, they are excluded from the following classification analysis. Therefore, only 483 sectors are used for the classification purposeexercise. Two criteria related to this industry-by-industry transaction table have been designed to differentiate classify a sector into a typical supply sector from or a typical demand sector: • Criteria I: Number of connections. This criteria needs toC count the number of different sectors that one particular sector buys from or sells to out of the 483 sectors from Industry-by-Industry Transaction Table. If the total number of sectors buying the product/service from this sector is higher than the amount of sectors it buys from, this sector is classified as a supply sector, otherwise it is a demand sector; • Criteria II: Monetary value of transactions. This criteria needs to cCount the total dollar value of the commodities one particular sector buys and sells from Industry-by- Industry Transaction Table. If the total amount is higher from the purchase side, the sector is recognized to be demand sector; otherwise it is a supply sector; Table 2 shows the classification outcome for the infrastructure sectors under one of the two criteria defined above, where “SUPPLY” indicates that the sector contributes more as a supply sector than as a demand sector, or “DEMAND” otherwise under one of the two criteria defined above. Overall, most of the infrastructure sectors are classified as “SUPPLY” sectors. As an example of a supply sector, the power sector purchases from 13
  14. 14. Paper: Two Interdependence Models Ping Chen, 5/24/2010 355 various sectors in a total amount of $79.7 Billion and sells to 479 sectors in a total amount of $100.2 Billion. As there are more sectors requesting electricity and for a larger amount of dollar value, we classify the power sector as a supply sector. Food services and drinking is one example of a demand sector under Criteria II. The purchase and sale for this sector in 1997 are $174.5 Billion and $57.3 Billion which has a larger amount dollar value of input transactions than the output from its inter-sector transactions. The Air Transportation sector is an example of a demand sector under Criteria II, also. The total purchase and sale in this sector in 1997 is $65 Billion and $46.0 Billion, respectively, and the amount of suppliers and demanders are 344 and 481 each. The Pipeline Transaction sector is a special example of discrepancy between the classification under Criteria I and Criteria II. Pipeline Transportation sector is classified as a demand sector under Criteria I. There are 332 different sectors that make commodities or provide services for the pipeline transportation industry and 194 sectors that use the service from this sector. However, when the actual monetary transaction is taken into account, the actual sale from this sector to these 194 demand sectors was $24.8 Billion in 1997, which is much higher than the 18.8 Billion of purchases it made in 1997 from its supply sectors. 14
  15. 15. Paper: Two Interdependence Models Ping Chen, 5/24/2010 Ind-by-Ind Transaction Table Index NAICS Sector Name Number of Connections Amount of Transaction Purchase Sale Suppliers Demanders Classification Classification ($Million) ($Million) 19 211000 Oil and gas extraction 331 481 SUPPLY $54,137 $147,600 SUPPLY 30 221100 Power generation and supply 355 479 SUPPLY $79,725 $100,210 SUPPLY 142 324110 Petroleum refineries 375 482 SUPPLY $140,090 $86,222 DEMAND 391 481000 Air transportation 344 481 SUPPLY $65,012 $46,049 DEMAND 392 482000 Rail transportation 353 482 SUPPLY $16,404 $25,529 SUPPLY 393 483000 Water transportation 359 481 SUPPLY $14,947 $5,377 DEMAND 394 484000 Truck transportation 341 482 SUPPLY $86,401 $109,760 SUPPLY 396 486000 Pipeline transportation 332 194 DEMAND $18,771 $24,803 SUPPLY 412 514100 Information services 348 477 SUPPLY $4,677 $6,535 SUPPLY 419 52A000 Monetary authorities and depository credit intermediation 342 481 SUPPLY $92,607 $109,080 SUPPLY 468 7211A0 Hotels and motels, including casino hotels 404 481 SUPPLY $20,789 $24,284 SUPPLY 470 722000 Food services and drinking places 417 476 SUPPLY $174,510 $57,256 DEMAND NAICS Sector Name Number of Connections Amount of Transaction Purchase Sale Suppliers Demanders Classification Classification ($Billion) ($Billion) 211000 Oil and gas extraction 331 481 SUPPLY $54.1 $147.6 SUPPLY 221100 Power generation and supply 355 479 SUPPLY $79.7 $100.2 SUPPLY 324110 Petroleum refineries 375 482 SUPPLY $140.1 $86.2 DEMAND 481000 Air transportation 344 481 SUPPLY $65.0 $46.0 DEMAND 482000 Rail transportation 353 482 SUPPLY $16.4 $25.5 SUPPLY 483000 Water transportation 359 481 SUPPLY $14.9 $5.4 DEMAND 484000 Truck transportation 341 482 SUPPLY $86.4 $109.8 SUPPLY 486000 Pipeline transportation 332 194 DEMAND $18.8 $24.8 SUPPLY 514100 Information services 348 477 SUPPLY $4.7 $6.5 SUPPLY 52A000 Monetary authorities and depository credit intermediation 342 481 SUPPLY $92.6 $109.1 SUPPLY 7211A0 Hotels and motels, including casino hotels 404 481 SUPPLY $20.8 $24.3 SUPPLY 722000 Food services and drinking places 417 476 SUPPLY $174.5 $57.3 DEMAND Table 2 Classification of Supply Sector vs. Demand Sector based on Direct Transactions Looking atIn addition to the infrastructure classification result as shown in Table 2 more closely, we see:, we have also compared the overall classification outcome by using these two methods on the whole collection of economic sectors. Here is a summary of these findings: (1) Criteria I identified 321 supply sectors and 164 demand sectors; Criteria II identified 256 supply sectors and 229 demand sectors, there are a higher proportion of supply sectors than demand sectors according to the above defined criteria; (2) Criteria I identified 321 supply sectors and 164 demand sectors; Criteria II identified 256 supply sectors and 229 demand sectors, there are a higher proportion of supply sectors than demand sectors according to the above defined criteria; (3) Both of these classification methods show identify that most of these designatedthe selected infrastructure sectors used in practice, i.e., those recognized in Table 1 are supply sectors and. This is reasonable as we think that the services from these sectors 15
  16. 16. Paper: Two Interdependence Models Ping Chen, 5/24/2010 are fundamental for a large number of and varied number kinds of economic activities in addition to the huge amount of requirement; (4) Criteria I and II agree in most situations for classifying these infrastructure sectors. For sectors which they disagree, The observation that there are a broader sectors have identical classification outcomes by these two criteria partially attributes to the fact that a typical supply sector will supply to a large number of sectors and the total dollar value of these supplies are high and a typical demand sector have requirement from a large number of supply sectors and the total dollar value of these supplies are high. (5) Criteria I and II agree in most situations for classifying these infrastructure sectors. For sectors which they disagree, the discrepancy comes in two types. Some of the sectors consume a higher amount of products / services from a relatively small amount of different suppliers, such as air transportation, petroleum refineries, water transportation and food service sector, etc. Some of the sectors supply to a small amount of different consumers but with a high amount of dollar values, such as pipeline transportation service sector; Since there are a large number of sectors classified as supply sectors, it is important to study the impact of losing the supply from these sectors as one part of interdependence analysis. In the following sections, we will review the demand-driven impact model that was studied by Haimes and propose its counterpart Ghosh model for studying the supply- constrained impact. 16
  17. 17. Paper: Two Interdependence Models Ping Chen, 5/24/2010 4. Economic Input-Output Models As mentioned before, one apparent feature of supply chain connections is that the influence of an initial perturbation on any sector can be spread to another other sectors through direct and indirect linkages. As indirect effects are the major manners mechanism tothat spread the initially disturbed services to other seemingly unrelated sectors, it is important that an interdependence model is capable of exploring the indirect impacts as well as the direct ones. There are two similar interdependence modeling methods that use economic input-output data and take into account both the direct and the indirect effect: the Leontief model and the Ghosh model. Both of these models were originally created to study the degree of inter-connections among various economic sectors. Both models assume that the economy consists of nN interconnected economic sectors. Each sector employs the output from part or all of these sectors, as well as additional primary input, called value added value here, to satisfy the needs of the final demand and intermediate requirements. The total output from each industry is composed of two parts: the supply from that sector to the inter-industry activities, in addition to the supply to the final demand, such as human consumptions. Similarly, the total input into each industry is also composed of two parts: the input that is from the inter-industry activities, as well as the supply from the primary input, or added value, such as labor input etc. The summation of the supply from one sector contributed to the inter-industry activities, together with their supply to the final demand, constitute the total output from that sector. The inter-industry input going into that sector, together with the supply from the primary input, or added value, constitute the total input into that industry. Table 3 depicts these items, their names and their relationships through in an input-output table. 17
  18. 18. Paper: Two Interdependence Models Ping Chen, 5/24/2010 Input to Industry Intermediate Final Output Total Input Infrastructure Non-infrastructure Output (O) (c) Output (X) Output from Industry 1 2 3 n (1) 1 X11 X12 X13 X1n O1 c1 X1 Infrastructure (1) 2 X21 X22 X23 X2n O2 c2 X2 (1) Non- 3 X31 X32 X33 X3n O3 c3 X3 infrastructure n Xn1 Xn2 Xn3 Xnn On cn (1) Xn Intermediate Input (I) I1 I2 I3 In Value Added or Primary v1 v2 v3 vn GDP Input (v) T (1) (1) (1) (1) Total Industry Input (X ) X1 X2 X3 Xn Input to industries Exogenous Demand or Intermediate Total Industry Final Output (c) Infrastructures Non-Infrastructures Ouput (O) output (X) Output from industries 1 2 3 n 1 2 q 1 X11 X12 X13 X1n O1 c 11 c 12 c 1q X 1(1) Infrastructures 2 X21 X22 X23 X2n O2 c 21 c 22 c 2q X 2(1) Non- 3 X31 X32 X33 X3n O3 c 31 c 32 c 3q X 3(1) Infrastructures n Xn1 Xn2 Xn3 Xnn On c n1 c n2 c nq Xn (1) Intermediate input (I) I1 I2 I3 In Value Added 1 v 11 v 12 v 13 v 1n or Primary 2 v 21 v 22 v 23 v 2n GDP Input (v) p v 31 v 32 v 33 v 3n T (1) (1) (1) (1) Total Industry input (X ) X1 X2 X3 Xn Table 3 Economic Input-Output Table Illustration The variables used in the economic input-output table (Table 3) include: n – The number of defined industries; X i – Total output of industry i (i = 1, 2, …, n); X j T – Total input to industry j (j = 1, 2, …, n); X ij – Input of industry i to the production output of industry j (intermediate consumption); q – The amount of different category of final demand; ci – Final demand (or final consumption) for industry i’s output in Final Demand category k (k=1…q); p – The amount of different category of primary input; 18
  19. 19. Paper: Two Interdependence Models Ping Chen, 5/24/2010 v j – Value added (or primary input) for industry j’s input in the category l of the added value (l = 1…p); Input-Output analysis conducted on these transaction data creates a picture of a regional or national economy describing flows to and from industries and institutions which can be used to predict changes in overall economic activity as a result of trigger change in the local or national economy. To facilitate the analysis, here are the assumptions for performing the input-output analysis: (1) The activities of these economic sectors are within an open static economic input- output system that has a balanced input and output; (2) Fixed proportions technology: each output is produced via a unique combination of inputs. There is no substitution among inputs which can give us the same commodity as output; (3) The demand from sector j to sector i is proportional to the total input to sector j. xij = aij x j (∀i, j ) aij – Proportion of industry i’s input to j, with respect to total production output of industry j; (4) The supply from sector i to sector j is proportional to the total output from sector i. xij = xi bij (∀i, j ) bij – Proportion of industry i’s input to j, with respect to the total input from industry i; (5) Constant returns to scale: doubling inputs doubles all outputs, no more and no less. Furthermore, the following balance eEquation and suggests that the total output of industry i is consumed either as intermediate consumption (i.e., xi j ), or as final consumption ( ci ); the total input to industry j is composed of inter-industry supply (i.e., xi j ) and the primary input ( v j ): 19
  20. 20. Paper: Two Interdependence Models Ping Chen, 5/24/2010 n n xi = ∑ xij + ci = ∑ aij x j + ci j =1 j =1 n n x j = ∑ xij + v j = ∑ xi bij + v j i =1 i =1 The matrix format of the equation becomes x = Ax + c x' = x'B +v' The Leontief model and Ghosh model are established using these input-output balance equations. The solution of total industry input (output) X to the above equations and forms the Leontief and Ghosh model respectively: x = ( I − A) −1 c x ' = v '( I − B ) −1 The Leontief model is a demand-oriented driven EIO model. Similarly, a supply- drivensupply-constrained input-output model was formulated by Ghosh (1958) to first describe certain aspects of centrally planned economies [Oosterhaven 1988]. Compared with the Leontief model, the Ghoshian model does precisely the opposite. It starts with the input identity and complements it with the assumption of fixed output coefficients, also called allocation coefficients, which is symbolized by B here. The following equationEquation shows the connection between the two sets of coefficients where A (called the direct requirement matrix) is the coefficient matrix in the 20
  21. 21. Paper: Two Interdependence Models Ping Chen, 5/24/2010 Leontief’s model and B (called the direct supply matrix) is the coefficient matrix in the  Ghosh model and x is the vector of the total output per industry. Also, the A or B matrix can be acquired by normalizing the transaction matrix by column or row with regard to the total output from each sector which was proposed by Oosterhaven [1988].   B = [diag ( x )]* A *[diag ( x )]−1 Another way of expanding the result of X can explain how the total impact is counted: x = ( I − A) −1 c = Ic + Ac + A2 c + A3c + .... x ' = v '( I − B ) −1 = v ' I + v ' B + v ' B 2 + v ' B 3 + ... Where Ic + Ac represents the direct requirement on each sector from the final demand c; A 2 c represents the first level indirect requirement and A 3 c represents the second level indirect requirement and so on. Where v ' I + v ' B represents the direct supply to all the sectors as an effect of primary input (value added), v ' B 2 represents the first level indirect supply and v ' B 3 represents the second level supply and so on. Following are two examples of performing Leontief and Ghosh input-outputIO analysis on how the final demand and primary input drive the production and allocation in these economic sectors. According to the published 1997 US input-output benchmark transaction tabledata, to produce $1 Million of electricity from the power generation and supply sector, $21,700 is demanded from the petroleum refinery industry; $ 30,500 from the rail transportation industry and $33,600 from the pipeline transportation industry as a direct input. An example of running the Leontief model on the generation of $1 Million of electricity is conducted through the EIO-LCA website [EIOLCA 2005]. The Economic Input-Output Life Cycle Assessment software developed by Carnegie Mellon traces various economic transactions and resource requirements for a particular product or service. The model captures various manufacturing, transportation, and related requirements to produce a product or service. The results are based upon the 491 by 491 sector direct requirement matrix published by Department of Commerce, which includes around 483 commodities. 21
  22. 22. Paper: Two Interdependence Models Ping Chen, 5/24/2010 DoC’s 485x 485 commodity input-output model of the U.S. economy. Table 4 shows the top 10 sectors and their output in dollar amount that are required to support the generation of $1 Million of electricity through the total supply chain. Total Economic Direct Economic Direct Economic Sector NAICS ($ Million) (%) ($ Million) Total for all sectors 1.7300 79.8 1.3805 221100 Power generation and supply 1.0072 99.3 1.0001 211000 Oil and gas extraction 0.0983 71.0 0.0698 212100 Coal mining 0.0782 90.6 0.0709 486000 Pipeline transportation 0.0336 93.2 0.0313 482000 Rail transportation 0.0305 87.8 0.0267 420000 Wholesale trade 0.0253 32.5 0.0082 533000 Lessors of nonfinancial intangible assets 0.0232 3.0 0.0007 324110 Petroleum refineries 0.0217 43.5 0.0094 541100 Legal services 0.0200 75.7 0.0151 531000 Real estate 0.0194 37.5 0.0073 Table 4 Top 10 Sectors that are demanded for generating $1Million Power Supply (Example Output from Leontief Model. Source: [EIO-LCA 2005]) By running the Ghosh model on the consumption of $1 Million of generated electricity, it can be determined that the electricity will be allocated as follows: $23,000 to petroleum refinery industry and $38,500 to the food service and drinking places, directly. Table 5 shows how the generation of $1.007 Million electricity is allocated to various sectors through their supply chain. The total amount of allocation ($1.007 Million) is higher than the original $1 Million because during the successive production processes, more demand 22
  23. 23. Paper: Two Interdependence Models Ping Chen, 5/24/2010 on electricity is generated. The top 10 sectors that acquire electricity directly or indirectly are listed in Table 5 as well as the total amount of usage of electricity in that sector which is computed from the Ghosh model and the 1997 EIO data. Total Economic Direct Economic Direct Economic Sector NAICS ($ Million) (%) ($ Million) Total for all sectors 2.0464 23.7 0.4851 221100 Power generation and supply 1.0072 99.3 1.0001 531000 Real estate 0.0759 83.1 0.0631 4A0000 Retail trade 0.0656 69.5 0.0456 722000 Food services and drinking places 0.0385 59.6 0.0229 420000 Wholesale trade 0.0346 55.9 0.0194 324110 Petroleum refineries 0.0230 36.2 0.0083 550000 Management of companies and enterprises 0.0215 73.0 0.0157 336300 Motor vehicle parts manufacturing 0.0201 26.8 0.0054 336110 Automobile and light truck manufacturing 0.0187 9.1 0.0017 622000 Hospitals 0.0181 46.0 0.0083 Table 5 Top 10 Sectors that are supplied by $1Million Power Supply (Example Output from Ghosh Model) 23
  24. 24. Paper: Two Interdependence Models Ping Chen, 5/24/2010 5. Extensions to Infrastructure Interdependence Model An economic input-output model explains how the final demand drives the total output and how the primary input is allocated into different industries’ production needs. It demonstrates the economic connections among infrastructure sectors. However, to evaluate infrastructure dependency, especially to estimate the dependency induced impact explicitly and efficiently, we need a scalable measurement of the impact and need to extend the original IO model to be able to assess these impacts. Variations of the Leontief model have been applied in estimating the economic impact as a result of demand-driven interconnections. One of the few attempts for creating such a model is to estimate the demand reduction input-output inoperability due to terrorism of interconnected infrastructures [Haimes 2004]. This model is developed to estimate the terrorist related infrastructure vulnerability under the assumption that the loss of confidence in the attacked infrastructure sector would bring loss of demand in that sector and therefore bring production losses to the downstream supply sectors. It can be used to estimate the accumulated losses among all economic sectors by assuming that the losses could mount up among all these sectors following their input-output connections. To assess interdependence oriented vulnerability, it is necessary to explore and measure how disturbances of production in one infrastructure sector propagate to other sectors, either as a result of naturally caused or human induced threat. The interdependence effect occurs when an infrastructure disruption spreads beyond itself to cause appreciable impact on other infrastructures, which in turn cause more effects on still other infrastructures [Little 2002]. Therefore, estimation of the consequence of dependence induced interruptions that is brought to one infrastructure sector from an initially disturbed sector becomes a good measurement of the tightness of interdependence between these two. Haimes [2004] introduced two measurements for quantitatively describing the tightness of interdependency: economic loss and inoperability. Economic loss is the monetary representation of lost production in the measured sector and 24
  25. 25. Paper: Two Interdependence Models Ping Chen, 5/24/2010 infrastructure inoperability is the ratio of the lost production capacity to its planned production level. For example, an economic loss of $10,000 means that the lost production level in the affected sector is equivalent to $10,000. 10% inoperability means that 10% of the planned production capacity in the sector of interest is unavailable for some reason. As economic loss is not indicative of the capacity of the sector’s real production level, inoperability would be a better alternative assessment as it takes into account whether that loss is significant compared to the planned production in that sector. For example, a $1 Million loss would be significant for a plant having $2 Million of planned production every year, but is not so significant for a plant having $200 Million of planned production every year. The demand-driven inoperability (economic loss) input-output model created by Santos and Haimes [2004], the extension of the initial Leontief model, is used to estimate the inoperability in all sectors after the initial shock and the model is given as below: q = A*q + c* Where q is the accumulated inoperability vector; A* is the inoperability interdependency matrix where the cell entry of row i, column j represents the inoperability that is brought to sector i if we assume that sector j loses its complete productions and this value is between 0 and 1; c* is the demand-side perturbation vector. The solution to the overall impact on each sector is the following: q = ( I − A* ) −1 ⋅ c* As an example of applying this inoperability interdependence model, suppose that we have a system that is composed of four sectors: the power sector, the transportation sector, the water and the telecommunication sector. Suppose that the A* matrix is determined using Equation and the unexpected events in the transportation sector cause their consumers to lessen their demand by 10%. We can set up the inoperability 25
  26. 26. Paper: Two Interdependence Models Ping Chen, 5/24/2010 interdependence equation as shown in Equation . By solving this equation, we can acquire the supply chain induced total inoperability impact in each sector (q1, q2, q3, q4).  q1   0.2 0.1 0.2 0   q1   0   q   0.3 0.1 0 0.2   q2   0.1  2 =   +   q3   0.1 0.4 0.1 0.1  q3   0          q4   0 0.2 0 0.1  q4   0  The solution for the above equation is (q1, q2, q3, q4) = (0.03, 0.13, 0.06, 0.03), which means that when the demand on the service from the transportation sector is decreased by 10%, due to the supply chain connections among them determined by the A matrix in Equation , the total loss of demand from the power sector, the transportation sector, the water and the communication sector is around 3%, 13%, 6% and 3%, respectively. Similarly, we can establish the extension of the Ghosh model that can be applied to supply drivensupply constrained infrastructure interdependence problem. The supply constrained interdependence model is derived similarly to the Ghosh input-output model: q ' = q ' B* + v*' Where, v* is a supply-side perturbation vector; B* is the supply-drivensupply-constrained interdependency matrix; q is the accumulated inoperability vector. Therefore, the total inoperability after the shortage of primary supply can be represented as q ' = v*' ⋅ ( I − B* ) −1 As an example of applying this supply constrained inoperability interdependence model, suppose that the B* matrix is determined using Equation and the initial disruption in the transportation sector causes it to lessen its available supply by 10%. We can set up the inoperability interdependence equation as shown in . By solving this equation, we can acquire the supply chain induced total inoperability impact in each sector (q1, q2, q3, q4). 26
  27. 27. Paper: Two Interdependence Models Ping Chen, 5/24/2010  0.1 0 0.3 0.2   0.2 0.1 0.1 0  [ q1 q2 q3 q4 ] = [ q1 q2 q3 q4 ]   0.3 0.1 0 0.1  + [ 0 0.1 0 0]    0.1 0.2 0 0.1 The solution for the above equation is that (q1, q2, q3, q4) = (0.03, 0.12, 0.02, 0.01), which means the when the supply of service from the transportation sector is decreased by 10%, due to the supply chain connections among them determined by the B matrix in Equation , the total loss of production from the power sector, the transportation sector, the water and the communication sector is around 3%, 12%, 2% and 1%, respectively. Although matrix A* in Equation and matrix B* in Equation have very similar format, they share completely different meanings. For example, the second row and first column in the A* matrix, which is 0.3, means that if 10% production in the column sector is disabled, the row sector, which is a supply sector to the column sector, will lose its productivity by 0.3*10%=3%. In contrast, the second row and first column in B* matrix, which is 0.2, means that if 10% production in the column sector is disabled, the row sector, as a demand sector of electricity, will lose its productivity by 0.2*10%=2%. The B* matrix and A* matrix have to be created separately and they are not normally equal to each other. Haimes [2005 (a)] proposed to compute the inoperability matrix A* as:   A* = [diag ( x )]−1 ⋅ A ⋅ [diag ( x )] That is, employing the original Leontief input-output model, but restating the final demand in that model (c in Equation) as a decreased demand (c* in Equation) caused by unexpected perturbations will return from the model the consequent resulting economic loss (q in Equation), instead of necessary economic input (x in Equation), from all the supply sectors measured in monetary value. By normalizing this monetary loss with regard to the annual output of the supply sector gives us the inoperability that is represented by a percentage number. Therefore, the inoperability matrix in Equation can be represented by first retrieving the economic loss that is represented by the demand 27
  28. 28. Paper: Two Interdependence Models Ping Chen, 5/24/2010 sector’s inoperability and then normalized by the annual productivity of the supply sector as shown in Equation. Similarly, to acquire the impact in the form of inoperability for the supply constrained interdependence model, a new interdependence matrix B* needs to be created which modifies the economic interdependence matrix with each sector’s as- planned productivity, as:   B* = [diag ( x )] ⋅ B ⋅ [diag ( x )]−1 According to Haimes [2004], the as-planned productivity, which is assumed to be equal   to the total output from each industry, is denoted as x . diag ( x ) creates a square matrix  which has x all along its diagonal and zero on the off-diagonal positions. Each element bij in the interdependence matrix B measures the economic loss in jth sector when the ith sector loses its total output supply by $1 Million dollar. To gain the interdependence  xi  matrix measured by inoperability B , bij is normalized by a factor of  where xi * xj  represents the as-planned productivity from the supply sector (ith sector) and x j represents the as-planned productivity from consumer sector (jth sector). Therefore, bij* from the inoperability interdependence matrix B* measures the reduced productivity in jth sector when the ith sector loses its productivity by 100%. We use these two interdependence matrix to measure the impact in the following analysis. 28
  29. 29. Paper: Two Interdependence Models Ping Chen, 5/24/2010 6. Experiments: Demand Driven vs. Supply Constrained Impact The rest of this section describes an experiment to calculate the economic dependencies among 12 infrastructure sectors using the extended Ghosh model. The 12 infrastructure sectors considered are selected from Table 1. Compared with the original full economic input-output model (Table 3), this experiment maintains only the input output transactions among these infrastructure sectors and leaves the contribution inter-industry transactions from related to these the non-infrastructure sectors as part of the new added value (z) or the new final demand (e) (Table 6). The total input, output from each industry stays the same comparing with the full economic input output model (Table 3). This 12 by 12 infrastructure sector matrix maintains the intermediate transactions among these 12 sectors. The final demand and added value parts of this matrix are higher than the ones in the original full scale EIO model because the intermediate output from the non-infrastructure sectors is added to the final demand and added value parts of that matrix. The total industry input (output) remains the same in both the original full-scale EIO model and the reduced infrastructure sector only model. Similar method has been used in Haimes [2004] to compare the impact from within the 12-sectors and within the full sectors. The direct requirement matrix is obtained from the 1997 EIO data set and the direct supply matrix is acquired through Equation . 29
  30. 30. Paper: Two Interdependence Models Ping Chen, 5/24/2010 Input to sectors Exogenous demand (e) Intermediate Total Industry Infrastructures Ouput (O) Non-Infrastructures output (X) Output from sectors e' 1 2 3 n 1 X11 X12 O 1' X13 X1n e 1' X1 (1) Infrastructures 2 X21 X22 O2' X23 X2n e2' X2 (1) Intermediate input (I') I 1' I 2' 3 X31 X32 Value Added n Xn1 Xn2 GDP (z) z' z 1' z 2' Total Industry input (X T ) X 1(1) X 2(1) Input to Industry New Final Demand (e) Intermediate Total Input Infrastructure Non-infrastructure Final Output Output from Industry Output (O') Output (X) 1 2 3 n (c) ' (1) 1 X11 X12 O1 X13 X1n c1 X1 Infrastructure ' (1) 2 X21 X22 O2 X23 X2n c2 X2 ' ' Intermediate Input (I') I1 I2 (1) 3 X31 X32 X3 Non- New Added infrastructure (1) n Xn1 Xn2 GDP' Xn Value (z) Added Value v v1 v2 (v) (1) (1) Total Industry Input (XT) X1 X2 Table 6 Infrastructure Only Economic Input-Output Model The direct requirement matrix A for the infrastructure only economic input-output model is obtained by column normalizing the industry-by-industry input output table (Table 6) using the total industry input (XT); the direct supply matrix B for the infrastructure only economic input-output model is obtained by row normalizing the industry-by-industry input output table (Table 6) using the total industry input (X). The direct requirement matrix measured by inoperability (A*) and the direct supply matrix measured by  inoperability (B*) are obtained by using Equation and with the exception that x is the as-planned productivity only for these infrastructure sectors. Similar method has been used in Haimes [2004] to compare the impact from within the 12-sectors and within the full sectors. The total impact, both supply-drivensupply-constrained and demand-driven impact, measured by inoperability is computed. Figures 2 through 5 show the impact on these selected sectors when the petroleum refinery industry, the power generation and supply 30
  31. 31. Paper: Two Interdependence Models Ping Chen, 5/24/2010 industry, the truck transportation industry and the water supply industry each has a 10% loss of production (inoperability). The results of supply drivensupply constrained and demand-driven impact within these selected infrastructure sectors are presented in two tables: Table 7 and Table 8. Affected Demand Sectors (Resulted Production Loss (%)) PowerSupply WaterSupply PetroRefineAirTrans RailTrans WaterTransTruckTransTelecom InformSci Monetary,etc Hotels,etc Food, etc PowerSupply 10.00% 0.17% 0.12% 0.05% 0.01% 0.01% 0.02% 0.04% 0.04% 0.01% 0.17% 0.14% WaterSupply 0.00% 10.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 0.00% PetroRefine 0.11% 0.09% 10.78% 0.85% 0.20% 0.15% 0.46% 0.00% 0.02% 0.01% 0.01% 0.02% AirTrans 0.01% 0.01% 0.03% 10.02% 0.01% 0.02% 0.04% 0.01% 0.12% 0.05% 0.02% 0.03% Supply RailTrans 0.27% 0.01% 0.02% 0.02% 10.03% 0.01% 0.10% 0.00% 0.00% 0.00% 0.01% 0.02% Sectors (Intial WaterTrans 0.03% 0.00% 0.02% 0.01% 0.01% 10.01% 0.02% 0.00% 0.00% 0.00% 0.00% 0.00% Supply TruckTrans 0.05% 0.03% 0.04% 0.03% 0.04% 0.02% 11.41% 0.01% 0.02% 0.00% 0.02% 0.10% Reduction: Telecom 0.01% 0.13% 0.01% 0.21% 0.01% 0.03% 0.16% 11.92% 0.37% 0.06% 0.11% 0.06% 10%) InformSci 0.00% 0.00% 0.00% 0.01% 0.00% 0.00% 0.01% 0.00% 10.02% 0.00% 0.01% 0.00% Monetary,etc 0.10% 0.07% 0.09% 0.09% 0.08% 0.08% 0.09% 0.09% 0.09% 10.38% 0.12% 0.07% Hotels,etc 0.01% 0.01% 0.02% 0.01% 0.01% 0.01% 0.01% 0.01% 0.07% 0.04% 10.01% 0.02% Food, etc 0.08% 0.01% 0.03% 0.55% 0.01% 0.06% 0.02% 0.01% 0.12% 0.12% 0.04% 10.07% Table 7 Summary of Total Impact from 10% Supply Reduction in the Supply Sectors Demand Sectors (Initial Demand Reduction: 10%) PowerSupply WaterSupply PetroRefineAirTrans RailTrans WaterTransTruckTransTelecom InformSci Monetary,etcHotels,etc Food, etc PowerSupply 10.00% 0.00% 0.09% 0.03% 0.00% 0.00% 0.02% 0.05% 0.00% 0.01% 0.06% 0.23% WaterSupply 0.04% 10.00% 0.00% 0.01% 0.00% 0.00% 0.01% 0.08% 0.00% 0.02% 0.06% 0.10% PetroRefine 0.15% 0.00% 10.78% 0.65% 0.05% 0.02% 0.50% 0.01% 0.00% 0.02% 0.00% 0.04% Affected AirTrans 0.02% 0.00% 0.04% 10.02% 0.00% 0.00% 0.06% 0.03% 0.01% 0.14% 0.01% 0.10% Supply RailTrans 1.51% 0.00% 0.09% 0.05% 10.03% 0.00% 0.44% 0.02% 0.00% 0.01% 0.01% 0.17% Sectors WaterTrans 0.25% 0.00% 0.11% 0.07% 0.01% 10.01% 0.14% 0.00% 0.00% 0.00% 0.00% 0.02% (Resulted TruckTrans 0.06% 0.00% 0.04% 0.02% 0.01% 0.00% 11.41% 0.02% 0.00% 0.01% 0.01% 0.20% Production Telecom 0.01% 0.00% 0.01% 0.09% 0.00% 0.00% 0.10% 11.92% 0.02% 0.07% 0.03% 0.07% Loss (%)) InformSci 0.05% 0.00% 0.01% 0.11% 0.00% 0.00% 0.11% 0.08% 10.02% 0.06% 0.03% 0.07% Monetary,etc 0.06% 0.00% 0.04% 0.03% 0.01% 0.01% 0.05% 0.07% 0.00% 10.38% 0.02% 0.07% Hotels,etc 0.02% 0.00% 0.04% 0.02% 0.01% 0.00% 0.02% 0.02% 0.01% 0.20% 10.01% 0.07% Food, etc 0.05% 0.00% 0.01% 0.19% 0.00% 0.00% 0.01% 0.01% 0.00% 0.12% 0.01% 10.07% Table 8 Summary of Total Impact from 10% Demand Reduction in the Demand Sectors Figure 2 illustrates that the loss of 10% productivity of refined petroleum would bring a higher shock in the air transportation sectors as well as truck transportation sector (0.5-0.6%), because both of them consume a large portion of the supplied gasoline in market. The lack of enough gasoline would undoubtedly bring a significant impact to these two industries. This is because according to the Ghosh model, the sectors which consume the most part of the output from one sector would be affected significantly by the stable output of that sector. By comparison, the decrease of 10% demand in the petroleum sector will not cause too much impact on other sectors; the maximum shock appears in the power generation sector, whose production will be affected by around 0.1%. shows that the shock caused by a reduction of demand on electricity by 10% would bring a large blow to the railway companies (over 0.25%) as the rail transportation sector provides a large portion of its services to the transportation of fuels to the power 31
  32. 32. Paper: Two Interdependence Models Ping Chen, 5/24/2010 generation sector and it will lose this productivity if the power plants reduce their production level. Meanwhile, the disruption in the supply of electricity will unavoidably bring disturbances in the food services and drinking place by around 0.2% as these places have a higher reliance on electricity supply. Besides this, the petroleum refinery plants, hotel industries and telecommunication services will see a reduction in their productivities from 0.05% to around 0.1% when they lose 10% of their electricity supply. Figure 4 shows that the disruption of the supply of truck transportation sector’s service by 10% would cause the food service sector to be the one that is affected the most (0.15-0.2%). However, the lost production demand in the truck sector will cause a loss of sale in the Petroleum Refinery sector by 0.45%. Impacts Comparison of 10% Petroleum Refineray Perturbation (Supply Driven vs. Demand Driven : Infrastructure Sectors) 0.90% 0.80% Supply Driven Impact 0.70% Demand Driven Impact 0.60% Inoperability 0.50% 0.40% 0.30% 0.20% 0.10% 0.00% ns s ns i ns m y ly tc c Sc c an pl et et pp co ,e ra ra ra up rm y, ls , r kT T ilT rT le Su od ar rS fo er te Te Ai uc Ra et Fo er In at Ho we on Tr at W Po W M Dependent Infrastructure Sectors Figure 2 Supply vs. Demand Driven Impact: Petroleum Refinery Industry 32
  33. 33. Paper: Two Interdependence Models Ping Chen, 5/24/2010 Impacts Comparison of 10% Power Supply Perturbation (Supply Driven vs. Demand Driven : Infrastructure Sectors) 1.60% 1.40% Supply Driven Impact 1.20% Demand Driven Impact Inoperability 1.00% 0.80% 0.60% 0.40% 0.20% 0.00% e ns s ns ns i m ly tc c Sc c an in et et pp co ,e ra ra ra ef rm y, ls, r kT T lT le rT Su od R ar fo er te i Te tro Ai uc Ra et Fo er In at Ho Pe on Tr at W W M Dependent Infrastructure Sectors Figure 3 Supply vs. Demand Driven Impact: Power Generation Impacts Comparison of 10% Truck Transportation Perturbation (Supply Driven vs. Demand Driven : Infrastructure Sectors) 0.60% Supply Driven Impact 0.50% Demand Driven Impact 0.40% Inoperability 0.30% 0.20% 0.10% 0.00% e ns ns i s m y tc ly c Sc c an in pl et et pp co ,e ra ra ef up rm ls, y, Tr ilT le rT Su od R ar rS fo te er Te tro Ai Ra et Fo er In at Ho we Pe on at W Po W M Dependent Infrastructure Sectors Figure 4 Supply vs. Demand Driven Impact: Truck Transportation Here, in the supply-constrained example, each experiment treats the assumed disrupted sector as a primary supply sector for the production in the demand sectors. That is, if the demand sector loses their supply from the primary supply sector, even if they have stores or uninterrupted supply from other sectors, that part of production won’t be implemented. For example, Figure 3 assumes that power generation is the primary input to the production of the petroleum refinery sector and therefore assumes that a10% reduction in the electricity supply will cause the corresponding 0.1% reduction in the petroleum refinery sector. Similarly, when the Leontief model was tested, it was assumed that the 33
  34. 34. Paper: Two Interdependence Models Ping Chen, 5/24/2010 power plant is the initially affected demand sector with its demand curtailed by 10%. Therefore, all the sectors that supply the power sector will reduce their production correspondingly, and the rail transportation sector would reduce their production by around 0.25%, which means that the electricity sector is one of the largest clients of rail transportation services and the loss of demand from this sector causes a reduction of production by 0.25% in the railway sector. 34
  35. 35. Paper: Two Interdependence Models Ping Chen, 5/24/2010 7. Typical Supply Sector and Typical Demand Sectors Section 3 presented two methods to classify supply and demand sectors based on how much that sector purchases versus how much it sells, or the amount of suppliers versus the amount of consumers. Both of them measure the direct supply and demand connections of these sectors. However, as the interdependence model suggests, both direct and indirect connections exist among these sectors; it could become a partial conclusion to identify the major role of one sector by counting only the direct connections. In this section, we will discuss other ways of classifying these sectors based on the overall impact that could be produced through their direct and indirect connections. The results from the Leontief and Ghosh models could be very different as shown in Figures 2 through 4. For instance, the initial disturbance on any sector as a demand sector and as a supply sector could bring dramatically different impacts on other sectors. Moreover, the comparison between the results of the Leontief and Ghosh models indicates that some sectors behave more like “supply” sectors while others behave more like “demand” sectors. The following is a simple methodology that can separate the sectors as a typical demand sector or a typical supply sector by using the result from the Leontief and Ghosh model and counting both direct and indirect dependencies. It can be done by acquiring and comparing the total impact that the initially disturbed sector has as a demand sector by collecting the output from the Leontief model, and as a supply sector by collecting the output from the Ghosh model. If the total impact as a demand sector is higher than the impact as a supply sector, that sector is said to behave more like a typical “demand” sector; otherwise, it behaves like a typical “supply” sector. By applying this criterion, we can perform a diagnosis on the critical infrastructure sectors that have been identified. For example, from Figure 2, we see that, overall, the impact that the petroleum sector has on other sectors as a supply sector would be muchis higher than it has as a demand sector (Figure 2),, which implies that it functions more like a supply sector rather than a demand sector. 35
  36. 36. Paper: Two Interdependence Models Ping Chen, 5/24/2010 Tables 7 and 8 compare the output (total impact) from the Leontief model and the Ghosh model for each infrastructure sector which is assumed to be interrupted. Table 9 shows the overall impact by assuming the initially lost economic value from each affected sector is $1 Million, the total economic loss it could bring to the entire economy system is listed and the classification is made based on the comparison of the output from the two models. Each sector indicated in the “Sector Name” column is assumed to be the initially disturbed sector. Depending on the types of chain disruption generated, two kinds of total impact are listed in column (1) and column (2). Column (1) assumes that the initially disturbed sector brings a demand-driven chain disruption, that is, the demand from that sector decreases and the total impact among the entire economy system is computed; column (2) assumes the initially disturbed sector brings a supply-drivensupply- constrained chain disruption, that is, the supply from that sector decreases and the total impact is computed. Table 10 shows the overall impact by assuming the production in each infrastructure sector is reduced by 10% because of unstated reasons, the total inoperability level over the whole system is listed and the classification is made. The Leontief Input-Output matrix and the Ghosh matrix utilized here are derived from the original full matrix with 511 sectors in total. Therefore, the impact is a summation over these 511 sectors as well. Still, 485 sectors classification are conducted over 483 sectors. with classification. 36

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