Optimal Resource Allocation Model to Prevent, Prepare, and Respond to Multiple Disruptions, with Application to the Deepwater Horizon Oil Spill and Hurricane Katrina

Industrial and Manufacturing Systems Industrial and Manufacturing Systems Engineering Publications Engineering

1-28-2021

Cameron A. MacKenzie Iowa State University, [email protected]

Amro Al Kazimi Iowa State University

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Abstract Determining how to allocate resources in order to prevent and prepare for disruptions is a challenging task for homeland security officials. Disruptions ear uncertain events with uncertain consequences. Resources that could be used to prepare for unlikely disruptions may be better used for other priorities. This chapter presents an optimization model to help homeland security officials determine howo t allocate resources to prevent and prepare for multiple disruptions and how to allocate resources to respond to and recover from a disruption. In the resource allocation model, prevention reduces the probability of a disruption, and preparation and response both reduce the consequences of a disruption. The model is applied to the US Gulf Coast region and considers a Deepwater Horizon‐type oil spill and a hurricane similar to Hurricane Katrina.

Keywords resource allocation, oil spill, hurricane mitigation, emergency response

Disciplines Operational Research | Risk Analysis | Systems Engineering

Comments This is a manuscript of a chapter published as MacKenzie, Cameron A., and Amro Al Kazimi. "Optimal Resource Allocation Model to Prevent, Prepare, and Respond to Multiple Disruptions, with Application to the Deepwater Horizon Oil Spill and Hurricane Katrina." In S. Chatterjee, R.T. Brigantic, and A.M. Waterworth, eds., Applied Risk Analysis for Guiding Homeland Security Policy. New York: John Wiley & Sons (2021): 381-403. DOI: 10.1002/9781119287490.ch15. Posted with permission.

This book chapter is available at Iowa State University Digital Repository: https://lib.dr.iastate.edu/imse_pubs/261 Optimal Resource Allocation Model to Prevent, Prepare, and Respond to Multiple Disruptions, with Application to the Deepwater Horizon Oil Spill and Hurricane Katrina

Cameron A. MacKenzie and Amro Al-Kazimi Industrial and Manufacturing Systems Engineering Department, Iowa State University

Abstract: Determining how to allocate resources in order to prevent and prepare for disruptions is a challenging task for homeland security officials. Disruptions are uncertain events with uncertain consequences. Resources that could be used to prepare for unlikely disruptions may be better used for other priorities. This chapter presents an optimization model to help homeland security officials determine how to allocate resources to prevent and prepare for multiple disruptions and how to allocate resources to respond to and recover from a disruption. In the resource allocation model, prevention reduces the probability of a disruption, and preparation and response both reduce the consequences of a disruption. The model is applied to the U.S. Gulf Coast region and considers a Deepwater Horizon-type oil spill and a hurricane similar to Hurricane Katrina.

Keywords: resource allocation, oil spill, hurricane, mitigation, emergency response

1.1 Introduction

Disruptions, including man-induced accidents, terrorist attacks, and natural disasters, are becoming more costly and occurring more frequently. Globally, the cost of natural disasters has risen from about $50 billion per year in the 1980s to an annual average of $200 billion in the 2010s (Associated Press, 2014). From 2011 to 2013, the U.S. federal government spent approximately $136 billion in disaster relief (Weiss and Weidman, 2013). The Gulf of Mexico has been especially vulnerable to significant disruptions, such Hurricanes Katrina and Rita in 2005 and the Deepwater Horizon oil spill in 2010, which resulted in several fatalities, physical destruction, environmental damage, and business losses ranging from $40 billion to more than $100 billion.

Al Kazimi and Mackenzie (2016) review the literature on the economic consequences of disruptions. The largest disruptions—such as an earthquake with a magnitude of 8 or more, Hurricane Katrina, and the September 11 terrorist attacks—led to economic losses that exceeded $100 billion. The Great Hanshin Earthquake in Japan in 1995 may have induced $144 billion in losses (Okuyama, 2009), and the 2011 Japanese earthquake and tsunami resulted in $84 billion in production losses in March and April (MacKenzie et al., 2012c). The United States suffered about $3 billion in lost wages due to Hurricane Sandy in 2012 (Park et al., 2014c), and the 2011 Joplin Tornado in Missouri was estimated to cost $6 billion (Richardson et al., 2014). Some potential but yet unrealized terrorist attacks, such as a dirty bomb or a shoulder-borne missile fired against an airplane, could lead to widespread panic, leading to losses in the tens or even hundreds of billions of dollars (Gordon et al., 2007, Park et al., 2014b). Disruptions that disable key infrastructure systems such as waterway ports (Rose and Wei, 2013, MacKenzie et al., 2012a) or the electric grid (Anderson et al., 2007) can induce economic losses of approximately $10 billion.

The occurrence of these disruptions raises questions about how much should the United States prepare to mitigate these disruptions. The U.S. federal government spent almost 16 times more on disaster relief than disaster preparedness from 1985 to 2004 (Healy and Malhotra, 2009), but determining how best to spend money on disaster preparedness is challenging. Disruptions are uncertain, and knowing the time and geographical location of these disruptive events is impossible. There are many competing priorities for resources, and money spent preparing for disruptions cannot be spent on other important items, whether the money is from a federal, state, or local government’s budget or from the private sector.

Studies on resources used to prepare for disruptions generally conclude that the benefits of preparing for natural disasters exceed the costs (Rose et al., 2007, Garrett and Sobel, 2003, Healy and Malhotra, 2009). For example, levee improvements in New Orleans would have cost about $3-6 billion and saved New Orleans from the $120 billion in losses due to Hurricane Katrina (Godschalk et al., 2009). This chapter extends backward-looking benefit-cost analysis undertaken by these studies into a forward-looking model to help a decision maker determine how much to spend in preparing for a disruption while accounting for uncertainty in the disruption and competing priorities for other resources.

Numerous operations research models recommend how resources should be allocated to prepare and respond to disruptive events (McLay, 2015, Altay and Green III, 2006, Banerjee and Gillespie, 1994). Disaster management models recommend the best way to allocate discrete resources (Chelst and Barlach, 1981, McLay and Mayorga, 2013), determine which vulnerable locations to protect (Church et al., 2004, Morton, 2011, Smith et al., 2013, Willis, 2007, Alderson et al., 2013), and schedule and organize emergency logistics (Campbell et al., 2008, Caunhye et al., 2012). Other models focus on protecting against specific disruptions such as earthquakes (Dodo et al., 2007, Dodo et al., 2005, Ermoliev et al., 2000, Gearhart et al., 2014) or hurricanes (Legg et al., 2013). Game theoretic models recommend allocations to protect against strategic actors such as terrorists (Bakir, 2011, Bier, 2007, Hausken, 2008, Major, 2002). Some game theoretic model trade off between preparing for terrorist attacks and preparing for natural disasters (Zhuang and Bier, 2007, Shan and Zhuang, 2013) and studying organizational cooperation for disaster relief (Coles and Zhuang, 2011).

This chapter makes several unique contributions to the literature on operations research models for homeland security. First, it develops a general model of allocating resources that can be applied to any type of disruption. Second, the model accounts for uncertainty in the disruption and incorporates alternatives for what else could be done with resources if they are not used for disruptions. Third, the model is applied to two disruptions: an oil spill in the Gulf of Mexico and a hurricane in one of the five U.S. Gulf States. Unfortunately, the Gulf States experienced both of these disruptive events in the early 2000s. The likelihood of the hurricane is large enough that a decision maker should allocate a significant portion of the budget to preparing for a hurricane like Katrina. However, the chance of a large oil spill similar to that of Deepwater Horizon is relatively small. Unless the budget is really large, a decision maker should not spend money on preventing or preparing for an oil spill.

The rest of the chapter is as follows. Section 1.2 presents the model: the initial model that includes the probability of a disruption and an extension to account for uncertain parameters. Section 1.3 applies the resource allocation models to a severe oil spill and a severe hurricane. The data for the oil spill is derived from previous studies by MacKenzie et al. (2012b) and MacKenzie et al. (2016) who present an optimal resource allocation model to respond to and recover from an oil spill. Concluding remarks appear in Section 1.4.

1.2 Model Development

1.2.1 Resource Allocation Model Disruptive events can lead to fatalities, injuries, economic losses, and environmental damage. Although this multi-objective problem could be modeled via a multi-attribute utility function, the resource allocation model in this chapter simplifies the consequences to a single objective: total production losses in the economy. The Interoperability Input-Output Model (IIM) is an economic model that translates direct losses in individual industries due to a disruption to total production losses in the entire economy (Santos and Haimes, 2004, Santos, 2006). The IIM has been used to estimate economic losses from the September 11 attacks (Santos, 2006), the 2003 electric blackout in the Northeast United States (Anderson et al., 2007), and Hurricane Katrina (Crowther et al., 2007). Crowther et al. (2007) and MacKenzie et al. (2016) incorporate the IIM into the objective function to help make better resource allocation decisions. 2

The resource allocation model considers two possible disruptive events. Disruption 푗, where 푗 = 1,2, directly impacts 푚푗 industries, where 푚푗 ≤ 푛 and 푛 is the total number of industries in the economy. The ∗ direct impacts for industry 푖 due to disruption 푗 is represented by 푐푖,푗 which is a proportion of total ∗ production in that industry. A vector 퐜푗 of length 푚푗 accounts for all of these direct impacts. The total ⊺ (푛×푚푗) ∗ production losses due to disruption 푗 are calculated via the IIM: 퐱 퐁 퐜푗 where 퐱 is a vector of (푛×푚푗) length 푛 representing the normal production of each industry in the economy and 퐁 is a 푛 × 푚푗 matrix that translates the direct impacts in the 푚푗 industries to total impacts across the 푛 industries in the economy. The matrix 퐁(푛×푚푗) is derived from the square matrix of order , 퐁 = (퐈 − 퐀∗)−1, by selecting ∗ only the columns in 퐁 that correspond to the 푚푗 directly impacted industries. The matrix 퐀 is the normalized interdependency matrix in the IIM.

Unlike many resource allocation models in which the decision variables are discrete, the decision variables in this optimization model are continuous variables to represent items like money, time, or labor. A decision maker allocates resources in order to minimize the expected production losses from the disruptions. Prior to the disruption, the decision maker allocates 푧푝,푗 which goes to prevent and prepare for disruption 푗. If no resources are allocated prior to a disruption, the probability of disruption 푗 is 푝̂푗. Allocating 푧푝,푗 prior to the disruption may help to prevent the disruption by reducing 푝̂푗 to 푝푗 where 푝푗 ≤ 푝̂푗. The parameter 푘푝,푗 describes the effectiveness of allocating resources to reduce the probability of disruption 푗 (prevention).

Preparedness reduces the consequences if a disruption occurs. If the disruption occurs, the decision maker also allocates resources to respond to and recover from the disruption. The decision maker can choose to allocate resources to assist a single industry, and 푧푖,푗 represents the resources allocated to help industry 푖 recover from disruption 푗. The decision maker also determines 푧0,푗, which are resources that help all industries recover from disruption 푗. Resources that can benefit all industries could include activities for debris removal, cleaning up after the disruption, and ensuring that critical systems such as electric power, telecommunications, and utilities are operating.

∗ The direct impacts to industry 푖 from disruption 푗, 푐푖,푗, are a function of the pre-disruption allocation 푧푝,푗, resources for all industries 푧0,푗, and resources targeted to that specific industry 푧푖,푗. If no resources are ∗ allocated, the direct impacts to industry 푖 is 푐푖̂ ,푗, and allocating resources to 푧푝,푗, 푧0,푗, or 푧푖,푗 reduces the ∗ ∗ ∗ direct impacts to 푐푖,푗 where 푐푖,푗 ≤ 푐푖̂ ,푗. The parameter 푘푞,푗 describes the effectiveness of allocating pre- disruption resources to reduce the direct impacts (preparedness), 푘0,푗 describes the effectiveness of allocating resources after the disruption to benefit all industries, and 푘푖,푗 describes the effectiveness of allocating resources after the disruption to benefit industry 푖. The total amount of resources that can be allocated is given by 푍 (a budget constraint).

If neither disruption occurs, resources that would have to gone to responding to and recovering from a disruption can be used for other priorities. If this is a public sector allocation, those resources could be used for other government programs or returned to the taxpayers. The function 푔(푧푝,1 + 푧푝,2, 푍) describes the economic benefit if no disruption occurs and those response and recovery resources are used for other priorities. The function 푔(푧푝,1 + 푧푝,2, 푍) is strictly decreasing in 푧푝,1 + 푧푝,2, strictly increasing in 푍, and non-negative for 푧푝,1 + 푧푝,2 ≤ 푍. If 푧푝,1 + 푧푝,2 = 푍 (i.e., all the resources are spent on pre-disruption allocation), no resources are available to increase regional production if no disruption occurs and 푔(푍, 푍) = 0. Since the decision maker wishes to minimize expected production losses if a disruption

3 occurs and maximize the production gain if no disruption occurs, minimizing the objective function requires inserting a negative sign before the expected gain in production (1 − 푝1 − 푝2)푔(푧푝,1 + 푧푝,2, 푍).

The model assumes that the disruptions are rare events, and no more than one disruption will occur. The decision maker chooses these decision variables in order to:

⊺ (푛×푚1) ∗ ⊺ (푛×푚1) ∗ minimize 푝1퐱 퐁 퐜1 + 푝2퐱 퐁 퐜2 − (1 − 푝1 − 푝2)푔(푧푝,1 + 푧푝,2, 푍) (1-1) subject to 푝푗 = 푝̂푗 exp(−푘푝,푗푧푝,푗) 푗 = 1,2 (1-2) ∗ ∗ 푐푖,푗 = 푐푖̂ ,푗 exp(−푘푞,푗푧푝,푗 − 푘0,푗푧0,푗 − 푘푖,푗푧푖,푗) 푖 = 1, … , 푚푗, 푗 = 1,2 (1-3) 푚푗 푧푝,1 + 푧푝,2 + 푧0,푗 + ∑푖=1 푧푖,푗 ≤ 푍 푗 = 1,2 (1-4) 푧푝,푗, 푧0,푗, 푧푖,푗 ≥ 0 푖 = 1, … , 푚푗, 푗 = 1,2 (1-5)

The model assumes that the probability and consequences of the disruption are reduced via an exponential function. This assumption echoes other studies in the risk management literature (Bier and Abhichandani, 2002, Dillon et al., 2005, Guikema and Paté-Cornell, 2002, MacKenzie et al., 2016) because a decreasing ∗ exponential function has marginally decreasing returns. The first dollar invested to reduce 푝̂푗 or 푐푖̂ ,푗 produces more benefit than the second dollar allocated. Other possible allocation functions could be linear, quadratic, or logarithmic (MacKenzie and Zobel, 2016). The risk could also be inversely proportional to the amount of resources.

1.2.2 Extension to Uncertain Parameters

As will be discussed in the application section, the optimization model requires estimating several parameters. Estimating these parameters poses challenges, and considerable uncertainty exists with these parameters. The optimization model in 1.2.1 is extended to account for parameter uncertainty by assuming the model parameters have known probability distributions. The decision maker continues to desire to minimize expected production losses.

Since the objective function remains expected production losses in the uncertain model, the model only ∗ requires the expected values of the parameters 푝̂푗, 퐱, 퐁, and 푐푖̂ ,푗, not the full probability distributions. It is necessary to have the full probability distribution for the effectiveness parameters 푘푝,푗, 푘푞,푗, 푘0,푗, and 푘푖,푗 if these parameters are uncertain. The application section will present results for the optimization model when the effectiveness parameters are uncertain.

1.3 Application: Deepwater Horizon and Hurricane Katrina

The resource allocation model is applied to the U.S. Gulf Coast and two disruptions: a large oil spill such as the Deepwater Horizon oil spill (푗 = 1) and a severe hurricane such as Hurricane Katrina (푗 = 2). The Deepwater Horizon oil spill occurred on April 20, 2010 when an explosion on the Deepwater Horizon oil rig in the Gulf of Mexico led to 5 million barrels of crude oil pouring into the Gulf of Mexico. Eleven employees were killed by the explosion, and 16 other people were injured. BP, who operated the oil rig, initially budgeted a total of $37 billion for expenses related to the spill (Fahey and Kahn, 2012).

Hurricane Katrina made landfall in Louisiana and Mississippi as a Category 3 hurricane on August 29, 2005 and resulted in the costliest and one of the most deadly hurricanes in U.S. history. The levees in New Orleans collapsed resulting in massive flooding and thousands of homes that needed to be evacuated. Between 1,245 and 1,836 people died from Katrina (Beven et al., 2008, Brunkard et al., 2008), with the vast majority of fatalities occurring in New Orleans. Estimates for the business losses from

Hurricane Katrina range between $74-149 billion (Hallegatte, 2011, Hallegatte, 2008), and the federal government spent between $75 and 110 billion in recovery and reconstruction.

This section applies these two major disruptions to the resource allocation model to determine how money should be allocated to prevent and prepare for these two types of disruptions and how money should be allocated if one of the disruptions occurs in the Gulf Coast. Parameters for this study are estimated from journal articles, media stories, and government databases. Results are presented using these initial estimations. Sensitivity analysis on the consequences parameters is explored, and the model is extended to account for uncertain effectiveness parameters.

1.3.1 Parameter Estimation

The model accounts for economic losses in the five Gulf States: Texas, Louisiana, Mississippi, Alabama, and Florida. As explained in 1.2.1, the decision maker wishes to minimize the expected economic losses from the disruptions. This assumption ignores the casualties and environmental damage (which a decision maker would also want to minimize) except to the extent that these other factors influence the economic production in the region.

The IIM is populated with data from the U.S. Bureau of Economic Analysis (2010, 2010a, 2010b). The model aggregates the five Gulf States into a single economy with 푛 = 63 industries and the vector 퐱 and the matrix 퐁 are both populated with this data from the year 2009. The decision maker is a hypothetical decision maker with a limited budget but who controls resources across the 5 states. In reality, decisions are made at a federal level, state and local levels, and in private industry.

The opportunity cost function 푔(푧푝,1 + 푧푝,2, 푍) is linear with respect to 푍 − 푧푝,1 − 푧푝,2 so that each dollar spent for prevention and preparedness reduces economic output by the same amount. Zandi (2008) estimates that the multiplier effects from increasing government spending or reducing taxes range from 0.3 to 1.7, depending on the government program. The model assumes the decision maker will choose alternatives that lead to larger economic gain, and 푔(푧푝,1 + 푧푝,2, 푍) = 1.5(푍 − 푧푝,1 − 푧푝,2) for 0 ≤ 푧푝,1 + 푧푝,2 ≤ 푍. For every dollar not spent on the oil spill or hurricane, the region increases its economic production by $1.50.

1.3.1.1 Oil Spill Parameters

MacKenzie et al. (2012b, 2016) provide parameter estimations for the Deepwater Horizon oil spill, and the numbers from those papers are used in this chapter. The Deepwater Horizon oil spill directly impacted 푚1 = 5 industries: (1) fishing and forestry because fewer people ate seafood from the Gulf, (2) real estate because housing prices dropped, (3) amusements and (4) accommodations because fewer people traveled to the Gulf States, and (5) oil and gas due to a moratorium on off-shore drilling. Table 1-1 depicts the ∗ initial direct impacts 푐푖̂ ,1 and the effectiveness parameters 푘푖,푗 for each of these five industries.

Table 1-1. Input parameters for oil spill.

∗ 풊 Industry 풄̂풊,ퟏ 풌풊,ퟏ (per $1 million) 1 Fishing and forestry 0.0084 0.074 2 Real estate 0.047 0 3 Amusements 0.21 0.0038 4 Accommodations 0.16 0.0027 5 Oil and gas 0.079 0.0057

푝̂1 = 0.045 −4 Prevention 푘푝,1 = 2.8 × 10 −4 Preparedness 푘푞,1 = 1.6 × 10 −5 All industries simultaneously 푘0,1 = 1.0 × 10

Since MacKenzie et al. (2012b, 2016) only consider response and recovery from an oil spill, it is necessary to estimate the parameters for prevention and preparedness, specifically 푝̂1, 푘푝,1, and 푘푞,1. Forty oil spills occurred in the Gulf of Mexico from 2006 to 2010, and 푝1̂ = 0.045 is the annual probability of a large oil spill of more than 10,000 barrels of oil (U.S. Bureau of Ocean Energy Management, 2011, 2012). Since 5 million barrels is much larger than 10,000, this estimate of 푝1̂ likely overestimates the likelihood of an oil spill on the scale of a Deepwater Horizon oil spill.

The number of oil spills has decreased by about 1,000 over the past 30 years (Etkin, 2004), and about $150 million is spent annually to prevent oil spills. These two data points enable an estimate for 푘푝,1, the effectiveness of preventing an oil spill, depicted in Table 1-1. Estimating the effectiveness of preparation (which reduces the consequences) is derived from Healy and Malhotra (2009), who calculate that investing $6.7 million in preparedness reduces damages by almost $50 million. According to Rose et al. (2007), FEMA mitigation grants have benefit-cost ratios ranging from 1.5 to 5.1. Healy and Malhotra (2009) also conclude that preparedness is 15 times more effective than response, and 푘0,1 = 푘푞,1⁄15 in the model.

1.3.1.2 Hurricane Parameters

Hurricane Katrina directly impacted more industries than the Deepwater Horizon oil spill, and the resource allocation model assumes that a hurricane directly impacts 푚2 = 32 industries. Since this chapter represents the first appearance of applying a hurricane to this resource allocation model, this section describes in detail the sources of information and data used to estimate parameters for the hurricane. Table 1-2 depicts parameters for the 32 industries. Tourism was adversely impacted by Katrina, which includes industries 푖 = 1,2,3,4 in the model. According to Louisiana’s Board of Tourism, Louisiana’s revenue from tourism was $1.1 billion in 2004, $860 million in 2005, and $643 million in 2006 (LSU Division of Economic Development, 2011). The drop in tourism revenue in 2005 and 2006 ∗ can be attributed to Katrina, which is used to calculate 푐푖̂ ,2 for retail, amusements, accommodations, and food services (restaurants). The effectiveness parameter 푘푖,2 for these industries follows the argument as in MacKenzie et al. (2012b, 2016), which relies on a study by Oxford Economics (2010) estimating that tourism marketing creates a 15:1 return on investment.

Table 1-2. Input parameters for hurricane.

∗ 풊 Industry 풄̂풊,ퟐ 풌풊,ퟐ (per $1 million) 1 Retail trade 0.0047 0.015 2 Amusements 0.031 0.026 3 Accommodations 0.017 0.026 4 Food services 0.017 0.0090 5 Farms 0.029 0.0012 6 Fishing and forestry 0.029 0.0052 7 Construction 0.029 0.00017 8 Wood products 0.029 0.0028 9 Nonmetallic minerals 0.029 0.0021 6

10 Primary metals 0.029 0.0014 11 Fabricated metals 0.029 0.00083 12 Machinery 0.029 0.00089 13 Computer and electronics 0.029 0.00064 14 Electrical equipment 0.029 0.0039 15 Motor vehicles 0.029 0.00099 16 Furniture 0.029 0.0041 17 Miscellaneous manufacturing 0.029 0.0024 18 Food and beverage 0.029 0.00048 19 Textile 0.029 0.0099 20 Apparel 0.029 0.021 21 Paper 0.029 0.0015 22 Printing 0.029 0.0043 23 Chemical products 0.029 0.00033 24 Plastics and rubber products 0.029 0.0018 25 Wholesale trade 0.029 0.00021 26 Utilities 0.0027 0.016 27 Water transportation (ports) 0.015 0.0039 28 Education 0.024 0.012 29 Oil and gas 0.040 0.00038 30 Petroleum products 0.052 0.00038 31 Federal government 0.026 0.0017 32 State government 0.036 0.00063 푝̂2 = 0.56 Prevention 푘푝,2 = 0 −4 Preparedness 푘푞,2 = 1.6 × 10 −5 All industries simultaneously 푘0,2 = 1.0 × 10

Industries for 푖 = 5,6, … , 25 represent the private sector that Katrina directly impacted by damaging their buildings, factories, and offices used for production (Hallegatte, 2008). Holtz-Eakin (2005) states that of the $20 to 40 billion in reconstruction costs, one-third went to energy and one-third went to housing. Presumably, the final third (approximately $10 billion) went to the private sector. The Economics and Statistics Adminsitration (2005) estimates that industry infrastructure damages from Katrina were between $16 and 32 billion. Based on these government statements, the model proportionally divides $28 ∗ billion in damages among these 21 private sector industries in order to calculate 푐푖̂ ,2 = 0.029 for each of these industries. The effectiveness parameters are estimated based on job recovery in New Orleans after Katrina. 204,700 jobs in New Orleans were due to Katrina, and one year after Katrina, New Orleans was gaining 3,700 jobs per month. Since approximately $20 billion was spent on repairing infrastructure, 푘푖,2 for these private sector industries reflects the job gain as a measure of the benefits from spending that $20 billion.

Crowther et al. (2007) estimate that Louisiana lost 17 percent of its electric power from September through November, Mississippi lost 3.9 percent of its power, and Alabama lost 1.1 percent of its power. ∗ This data is used to calculate 푐26̂ ,2 = 0.0027 for the utilities industry (푖 = 26). The effectiveness parameter for the utilities industry is derived from $231 million being spent on electric utilities after Katrina (Burton and Hicks, 2005), and utilities were fully restored in about 3 months.

The Gulf States are home to many important seaports, many of which were severely disabled by Katrina. Immediately after Katrina, the ports were operating at about 40 percent capacity (Crowther et al., 2007). 7

By January 2006, ports were operating at 70 percent capability, and it cost $350 million to relocate companies while ports were closed (Grenzeback et al., 2008). It cost $30 million to get the Port of Mobile 95 percent functional, and it cost $250 million to repair the Port of New Orleans. Tt took approximately five months to increase ports’ functionality from 40 to 70 percent at a total cost of 350 + 30 + 250 = ∗ $730 million—which is used to estimate 푐27̂ ,2 and 푘27,2 for the ports (푖 = 27).

Crowther et al. (2007) estimate that $650 million was lost in the education sector due to Katrina and ∗ 푐28̂ ,2 = 0.024 for the education industry, 푖 = 28. The University of Tulane spent $291 million to reopen in 3 to 4 months after the hurricane, which provides an estimate for 푘28,2. The oil and gas industry, 푖 = 29, and the petroleum industry, 푖3 = 30, lost about 37 percent over 50 days and 82 percent over 3 months (Crowther et al., 2007). Between $6-10 billion was spent to restore these industries, and 10 percent of the oil was still offline as of June 19, 2006.

Hallegatte (2008) calculates that the government’s lost production to Katrina was $17 billion, which this application divides proportionally between the federal government 푖 = 31 and the state government 푖 = 32. The federal government spent about $5.05 billion in repairing government facilities (Walker, 2006), and this application assumes that these facilities were repaired in one year in order to estimate 푘31,2 and 푘32,2.

Twenty-five hurricanes of category 2 or more struck at least one of the Gulf States between 1970 and 2014 (Hurricane Research Division, 2015), and the probability of a hurricane is estimated as 푝̂2 = 0.56 per year. Similar to the oil spill model, none of the other 24 hurricanes caused as much damage as Katrina. Since the consequences attempt to replicate the damage caused by Katrina, this probability overestimates the likelihood of a hurricane as damaging as Katrina. Since it is impossible to reduce the probability of a hurricane, 푘푝,2 = 0. The same values for 푘푞,2 and 푘0,2 are used as in the oil spill disruption since these numbers are based on a comprehensive cost-benefit analysis of preparedness and response money (Healy and Malhotra, 2009).

1.3.2 Base Case Results

The resource allocation model is solved for budgets ranging from 푍 = $0 to $50 billion. Matlab’s fmincon function is used to solve the nonconvex optimization problem. Table 1-3 depicts the optimal allocation for each industry for several budgets. The results reveal several interesting trade-offs between allocating resources for one versus the other disruption and between pre- and post-disruption allocation. As Figure 1-1 shows, if the budget is $20 billion or less, a decision maker should allocate the vast majority of the budget to prepare for a hurricane, 푧푝,2, and not spend any money in preventing or preparing for an oil spill, 푧푝,1 = 0. A severe hurricane is twelve times more likely than a large oil spill, and a decision maker should focus most of the efforts on preparing for a hurricane. As the budget increases from $30 billion to $50 billion, the decision maker should allocate less money to prepare for a hurricane. If the budget is this large, the decision maker can focus on helping individual industries recover more quickly if a hurricane occurs. Money that is not spent preparing for a hurricane can increase regional production if no hurricane occurs. It is never optimal to spend any money to help all industries recover simultaneously for a hurricane (푧0,2 = 0) because it is more effective to spend money preparing for a hurricane and targeting individual industries for recovery.

Table 1-3. Optimal allocation for different budgets (millions of dollars).

Budget Disruption Industry 5,000 10,000 20,000 30,000 40,000 50,000

Pre-disruption 0 0 0 0 504 1,072 All industries 0 0 1,889 13,564 25,049 36,477 Fishing 0 0 46 46 46 46 Oil spill Real estate 0 0 0 0 0 0 Amusements 0 147 1,209 1,209 1,210 1,210 Accommodations 5 232 1,752 1,752 1,752 1,751 Oil and gas 198 303 1,011 1,011 1,011 1,011 Pre-disruption 4,797 9,319 14,092 12,417 10,428 8,433 All industries 0 0 0 0 0 0 Retail trade 46 72 135 175 196 217 Amusements 28 43 79 102 114 126 Accommodations 31 46 82 105 117 129 Food services 92 134 237 304 339 373 Farms 0 0 0 271 546 809 Fishing and forestry 0 0 0 2 63 122 Construction 0 0 0 1,311 3,165 4,935 Wood products 0 0 0 155 269 377 Nonmetallic minerals 0 0 0 128 276 418 Primary metals 0 0 0 324 556 778 Fabricated metals 0 0 0 405 784 1,147 Machinery 0 0 0 314 667 1,005 Computer, electronics 0 0 0 153 650 1,124 Electrical equipment 0 0 0 57 139 218 Motor vehicles 0 0 0 422 742 1,048 Hurricane Furniture 0 0 0 77 154 228 Misc. manufacturing 0 0 0 68 197 321 Food and beverage 0 0 0 675 1,328 1,952 Textile 0 0 0 29 61 92 Apparel 0 0 0 0 14 28 Paper 0 0 0 239 446 644 Printing 0 0 0 73 146 216 Chemical products 0 0 0 1,120 2,073 2,983 Plastics and rubber 0 0 0 220 393 558 Wholesale trade 0 0 0 0 1,067 2,540 Utilities 0 0 36 74 94 112 Water transportation 0 0 0 108 188 265 Education 6 37 114 164 190 215 Oil and gas 0 0 0 521 1,620 2,670 Petroleum products 0 0 2,445 4,550 5,649 6,698 Federal government 0 0 378 1,706 2,400 3,062 State government 0 350 2,402 3,730 4,424 5,086

Figure 1-1. Optimal allocation to spend prior to a disruption.

Since the probability of an oil spill is initially 0.045, preventing and preparing for an oil spill does not reduce the probability or consequences enough to justify allocating resources if the budget is small. It is better to spend the money on preparing for a hurricane or using the money to benefit regional production via 푔(푧푝,1 + 푧푝,2, 푍). If the budget is $35 billion or more, the decision maker should allocate between $500 million and $1 billion to preventing and preparing for an oil spill. If an oil spill occurs, the decision maker should spend most of the remaining budget on helping all industries recover, 푧0,1, if the budget is more than $20 billion. Stopping the spill and cleaning up the oil more quickly will limit the economic consequences.

Figure 1-2 depicts the production losses if an oil spill or a hurricane occurs. If no money is available for any mitigation activities, the production losses from an oil spill are $49 billion, and the losses from a hurricane are $113 billion. As the budget increases, the losses from the hurricane decrease rapidly since such a large portion of the budget goes to preparing for a hurricane. If the budget is $15 billion, the losses from the hurricane are $13 billion. This large decrease in losses from the hurricane is at the expense of reducing losses from the oil spill, and the production losses from an oil spill diminish gradually ($24 billion with a $15 billion budget). Since the hurricane is more probable than the oil spill, the region is more likely to suffer losses from the hurricane than from the oil spill. As the budget increases from $25 billion to $50 billion, the losses from the hurricane remain relatively constant at approximately $850 million, but the losses from the oil spill should be reduced even further to $1.24 billion with a $50 billion budget. The losses from the hurricane remain relatively constant due to the exponential function and the decreasing marginal benefit. If the budget is $40-50 billion, the losses from the oil spill decrease more rapidly because a lot more money should be spent to benefit response and recovery from the spill.

Figure 1-2. Production losses for each disruption.

1.3.3 Sensitivity Analysis on Economic Impacts

Parameters for this model are derived from historical disruptions based on government reports, journal articles, and media stories, and the model and parameter estimation relies on several assumptions. As discussed previously, the Deepwater Horizon oil spill and Hurricane Katrina are two of the costliest events of their types in U.S. history. If an oil spill or hurricane occurs again in the Gulf of Mexico, it is more likely that production losses will be less than those generated by the model. Nevertheless, the model may underestimate the production losses that occurred due to Katrina. The model calculates that the losses from Katrina with no budget were $113 billion. Other estimates of the economic consequences from Katrina approach $149 billion.

Sensitivity analysis on the direct impacts from these disruptions is conducted to analyze the effect the ∗ consequences should have in determining how to allocate money prior to a disruption. Each 푐푖̂ ,푗 is varied ∗ between 0 percent and 200 percent of its original value (as depicted in Tables 1-1 and 1-2). Each 푐푖̂ ,푗 in a disruption varies by the same percentage. The budget is $30 billion.

Figure 1-3 depicts the optimal pre-disruption allocation 푧푝,1 and 푧푝,2 for each disruption and a function of the initial direct impacts. Not surprisingly, as the initial impacts increase for each disruption, the decision maker should allocate more money to prevent and prepare for the disruption. The pre-disruption allocation ranges between $200 million and $1.6 billion for the oil spill and between $2 billion and $16 billion for the hurricane. Since the Deepwater Horizon oil spill and Hurricane Katrina represent the most extreme disruptions, a decision maker may believe the most likely economic impacts from an oil spill and a hurricane are 50 percent of the base case. To prepare for this more likely circumstance, the decision maker should continue not to spend anything on preparing for an oil spill and spend approximately $7 billion to prepare for a hurricane, compared to $12.4 billion on hurricane preparedness with the original values. It may be wasteful spending to prepare for an extremely severe hurricane.

Figure 1-3. Pre-disruption allocations for (a) the oil spill and (b) the hurricane as initial impacts vary (millions of dollars).

The most interesting insight from the sensitivity analysis is the effect of one disruption’s consequences on the optimal allocation for the other disruption. The economic impacts of the oil spill have relatively little effect on how much should be spent to prepare for a hurricane. As the oil spill’s consequences increase, the amount allocated to prepare for a hurricane should decrease slightly. However, the potential economic impacts of the hurricane have a large effect on how much the decision maker should spend to prevent and prepare for an oil spill. As the economic consequences increase for the hurricane, the decision maker should reduce the amount spent on the oil spill to be able to spend more preparing for the hurricane. For example, if the economic consequences of the oil spill are 150 percent of the base case, the decision maker should spend about $200 million (if the hurricane’s impacts will be very severe) to $1.4 billion (if the hurricane will not have any impact). Such an analysis can help a decision maker understand how to optimally trade off between preparing for one disruption versus another and how spending money to prepare for one disruption should impact how much he or she spends for another disruption.

1.3.4 Model with Uncertain Effectiveness

Despite the best efforts to estimate the effectiveness of allocating resources, there is uncertainty around the effectiveness parameters 푘푝,푗, 푘푞,푗, 푘0,푗, and 푘푖,푗. This section extends the resource allocation model to account for uncertain effectiveness and considers that five parameters are uncertain. Since preventing a hurricane is impossible, 푘푝,2 remains 0. The five parameters that are uncertain this extension are 푘푝,1, 푘푞,1, and 푘0,1 (for the oil spill) and 푘푞,2 and 푘0,2 (for the hurricane). Each parameter can be one of the following seven values: 10-7, 10-6, 10-5, 10-4, 10-3, 10-2, and 10-1, and each value is equally likely. The five uncertain parameters are assumed be independent of each other.

As discussed in the previous section, other parameters such as the initial consequences or the probability of a disruption may also be uncertain. However, since the decision maker is minimizing expected production losses, the optimization model does not need to include distributions for these parameters if the expected values of these parameters can be estimated. The model with uncertain effectiveness is solved twice: (1) assuming the initial expected impacts follow the same values from Tables 1-X and 1-X, and (2) assuming the initial expected impacts are half as large as in the base-case model.

Matlab’s patternsearch function is used to calculate the optimal allocation with the probability distributions for the effectiveness parameters. Table 1-4 displays the optimal allocation for the model with effectiveness uncertainty if the initial expected impacts remain the same as in the base case. The decision maker should allocate less money to prepare for the hurricane than in the model with deterministic parameters because preparing for a hurricane may be less effective and the effectiveness of helping individual industries does not change. The decision maker should allocate a little bit of money to prevent and prepare for an oil spill because this pre-disruption may be really effective in reducing the probability of the oil spill.

Table 1-4. Optimal allocation for model with effectiveness uncertainty with base-case initial impacts (millions of dollars).

Budget Disruption Industry 5,000 10,000 20,000 30,000 40,000 50,000 Pre-disruption 54 57 122 182 232 280 Oil spill All industries 141 242 6,273 17,551 29,033 40,724 Individual industries 574 910 3,521 4,157 4,628 4,912 Pre-disruption 4,232 8,792 10,084 8,110 6,107 4,085 Hurricane All industries 512 1,152 3,514 3,944 3,985 3,985 Individual industries 203 0 6,280 17,765 29,676 41,651

Table 1-5 depicts the optimal allocation for the model with effectiveness uncertainty if the initial impacts are half as large as in the base case. If the budget is $40 billion or more, the decision maker should allocate a combined $1 billion prior to either disruption. This suggests that if the expected initial impacts are on the order of $20-50 billion, if the response and recovery efforts will be effective, and if significant uncertainty exists over the effectiveness of the pre-disruption allocation, then the decision maker should spend very little to prepare for the disruptions. It is better to allow the response and recovery allocation to reduce the consequences. If no disruption occurs, the money can be used for other priorities.

Table 1-5. Optimal allocation for model with effectiveness uncertainty with 50 percent of initial impacts (millions of dollars).

Budget Disruption Industry 5,000 10,000 20,000 30,000 40,000 50,000 Pre-disruption 42 45 122 186 238 289 Oil spill All industries 178 1,687 11,219 22,604 34,185 44,210 Individual industries 537 2,441 3,817 4,384 4,775 5,501 Pre-disruption 4,243 5,827 4,842 2,827 802 0 Hurricane All industries 512 2,304 3,848 3,985 3,985 4,004 Individual industries 203 1,824 11,188 23,002 34,975 45,707

1.4 Conclusions

This chapter has presented a resource allocation model to prevent, prepare, and respond to disruptive events. The model considers two potential disruptions, and the decision maker desires to minimize the expected production losses as calculated with the economic model, the IIM. The model is applied to the Deepwater Horizon oil spill and Hurricane Katrina. Results from the application recommend that the decision maker should allocate billions of dollars to prepare for a hurricane but should not allocate money to prevent or prepare for an oil spill. A hurricane is more likely and more costly than an oil spill. If the consequences from a hurricane are less severe than Katrina or if a lot of uncertainty exists about the 13 effectiveness of preparing for a hurricane, the decision maker should not allocate less money for the hurricane.

The economic cost of the Deepwater Horizon oil spill has been estimated between $10 and $30 billion (Aldy, 2011, Park et al., 2014a). This cost corresponds well with the resource allocation model which estimates the oil spill’s production losses to be $28 billion if the budget is $12 billion. BP spent about $12 billion to stop the spill. Production losses from the hurricane are $112 billion according to the resource allocation model if no money is spent. This is similar to other studies on the economic impact from Katrina (Park, 2008, Hallegatte, 2008, Holtz-Eakin, 2005). However, losses from the hurricane are only $13 billion if the budget is $15 billion. Such a large decrease seems to overestimate the effectiveness of allocating resources for a hurricane as damaging as Hurricane Katrina. However, if only a few billion dollars had been spent prior to Katrina to reinforce the levees in New Orleans, the city would have likely been spared considerable damage.

Limitations of using this model include the difficulty of estimating parameters for the model. Historical disruptions can be used, but estimating parameters from these disruptions is challenging. Sensitivity analysis and incorporating uncertainty can help address these challenges, but a decision maker may be hesitant to rely on a model due to the assumptions. The model only considers production losses, and future extensions can include consideration of other consequences such as casualties and environmental damage. The model assumes a risk-neutral decision maker who minimizes expected production losses. A risk-averse decision maker might be appropriate for these high-consequence, low-probability events. Finally, when a disruption occurs, resources may not be able to be allocated and deployed immediately, and developing a dynamic model as in MacKenzie et al. (2016) represents another useful extension.

Despite the assumptions in the model and these limitations, the resource allocation model represents a useful operations research tool for homeland security professionals. The model helps the decision maker to consider (1) the benefits of allocating resources for one disruption versus another disruption; (2) the benefits of allocating resources prior to a disruption versus after a disruption; and (3) the benefits of allocating resources for disruption preparedness versus using those resources on other priorities. The chapter builds on the prior benefit-cost analysis of prior mitigation grants for disaster preparedness and relief to create a practical prescriptive model for determining how resources should be allocated for future disruptions.

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