KEYWORDS: Risk analysis, decision support systems, hurricane damage, highways, inventory, network analysis, impact analysis.

ABSTRACT

After a hurricane hits the Tidewater region of Virginia the road systems may be in complete disorder leaving communities stranded. The aim of the current effort is to aid the Virginia Department of Transportation (VDOT) in assessing the risks, costs and benefits associated with retrofitting equipment, managing spares and reserves, and priority setting for recovery efforts.

The first objective in this project is to develop a tool that aids VDOT in evaluating retrofitting options for the damageable equipment based on cost and potential damage. A second objective is to develop a process to enable VDOT to evaluate spares management systems based upon cost and time to recovery. Lastly, the third objective is the evaluation of alternative schedules for the recovery of intersections after a hurricane. The recovery plan is based on the location and types of critical facilities across the road networks.

The final results of this project are methodology and software that help VDOT choose among policies in order to balance cost, recovery time, and potential damages. These spreadsheets are maintained at the University of Virginia and accessible on the Internet at www.virginia.edu/~risk, so that VDOT has constant access to them into the future.

INTRODUCTION

The effort is in three parts: retrofitting alternatives, spares and reserves and priority setting. Management

of hurricane recovery addresses five categories of hurricanes, which are defined in Table 1.

Figure 1 is a map of the Suffolk District. The hurricane recovery plan is currently applied to the Suffolk District of Virginia but can be adapted to the rest of the state.

Improving hurricane recovery of vulnerable highways will have an impact on the way Virginia copes with other natural disasters, e.g. floods, ice storms, snow removal and other events that cause regional damage to the roadways. In addition, the results for the long-term recovery of signs, lights and signals, but may also apply to the clearing of debris and placement of emergency equipment on the roadways after a storm.

RETROFITTING ALTERNATIVES

One way to improve the resilience of the Suffolk District's highway infrastructure to a hurricane is by retrofitting (strengthening) damageable equipment. Retrofitting for signs, lights, and signals involves making larger support structures, using stronger materials, having deeper foundations or simply adding more fasteners to the structures. Figure 2 shows a shoulder-mounted sign, a highway sign that could be retrofitted.

The result of this portion of the project is an analysis tool for evaluating different retrofitting options, or alternatives. Using this tool, VDOT may find that these preparatory actions will save money in the long run and mitigate the adverse effects of a hurricane.

Scope of Analysis

The equipment on interstates, US highways, and state highways in the Suffolk District and their approximate amounts are shown in Table 2. These approximations were obtained through personal communication with the VDOT personnel Vince Roney, Jerry Pauley, Travis Bridewell, and Jack Meredith.

Definition for the amount of Retrofitting

To analyze retrofitting alternatives, the team defined retrofitting in terms of the degree by which a structure is strengthened. The measure of equipment strength used was ultimate wind velocity. The ultimate wind velocity of a piece of equipment is the maximum wind speed below which the structure will not fail (VDOT 1997b). Three levels of retrofitting were considered: increasing the ultimate wind velocity by 10, 20, and 40 miles per hour (mph). So for example, cantilever sign structures can normally withstand a maximum wind speed of 117 mph. If they are retrofitted to a 10-mph higher ultimate wind velocity, then they can withstand a maximum wind speed of 127 mph. Therefore, VDOT can consider different retrofitting alternatives that specify the level of retrofitting applied to each equipment type.

Hurricane Damage Model

To model equipment damage by hurricane winds, the probabilities of different wind speeds occurring in a hurricane were modeled using a normal density function. Since five categories of hurricanes exist, each category was represented by a different function. Figure 3 shows these functions. The amount of existing and strengthened equipment damaged in hurricanes could then be found using the density functions and the ultimate wind velocities of equipment.

Tradeoff Analysis

If VDOT invests more in retrofitting, the amount of equipment damage in a hurricane would be less. However, VDOT would have less to spend on other projects. The developed tool provides two ways of viewing tradeoffs about whether and to what degree that they should retrofit: 1) graph of retrofitting cost versus percentage of installed equipment damaged and 2) graph of retrofitting cost versus replacement cost for damaged equipment.

Figure 4 shows the tradeoff graph of the first type for two pole span signs. The different curves represent the tradeoffs for the different categories of hurricanes. It was assumed that if VDOT chooses to retrofit, they would replace existing equipment with retrofitted ones when the existing equipment wears out. From personal communication with Vince Roney at VDOT, it was estimated that cantilever and two pole sign structures last 30 years while the other types of equipment last 15 years. The retrofitting cost in the graph is the additional annual cost of replacing worn-out equipment with retrofitted equipment instead of with non-retrofitted ones. The costs to retrofit the different equipment types were estimated using a methodology suggested by Vince Roney (AASHTO 1994). Such graphs were also generated for other types of equipment.

It was shown that tradeoffs for the same retrofitting level are different when different hurricane categories are considered. For example, if VDOT were only concerned with preparing for a category V hurricane, they would not retrofit shoulder-mounted signs because the cost of replacing damaged shoulder-mounted signs is actually greater with retrofitting for that hurricane category.

The choice of retrofitting alternative depends on what tradeoffs VDOT and the citizens of Virginia are willing to make. With these graphs, VDOT will be able to reach a retrofitting decision that balances costs, benefits, and risks according to the public interest.

SPARES AND RESERVES

VDOT's sign production facilities currently may not have the capacity to handle the regional demand produced by hurricane damage. The development of an inventory system for hurricane recovery equipment will allow VDOT to restore transportation systems to a functional state in a more timely manner by having the spares and reserves on hand needed to restore the equipment almost immediately. To aid VDOT in deciding on a level of inventory, the effort has developed software that allows VDOT to evaluate different levels of inventory based upon the investment needed, cost of recovery, and time to recovery.

Framework

Equipment that VDOT may store is in the following categories: ground signs, overhead signs, sign poles, overhead sign poles, signals, and roadway lighting. A further breakdown of these categories into the components that make up the equipment (e.g. signal heads, cabinets, etc.) is also possible.

An automated worksheet was created to enable entry of raw data including cost of equipment, time to install, time to manufacture, balance on hand, etc. VDOT enters the different spares inventory policies that they are considering as the percentage of the equipment that is currently installed on the roadways.

Pre-Hurricane Cost

The first calculation made is the pre-hurricane investment that VDOT would make. This investment involves the purchase price of the equipment needed bring the current level of inventory up to that of the proposed level of the alternatives as well as storage costs. To combine the fixed capital costs of purchasing the equipment and the yearly cost of storing the equipment, the capital cost was annualized. It is assumed that VDOT would incur a percentage of the cost of spares each year as well as the annual facility cost to store the equipment.

Post-Hurricane Cost

The post-hurricane cost of recovery, the cost to purchase the equipment from vendors and contractors that were not accounted for by the spares and reserves, is then calculated. Since both the level of spares as well as the severity of storm that hits affect the amount of replacement equipment needed for recovery, a separatepost-hurricane cost is calculated for each alternative and hurricane scenario. The post-hurricane cost is affected by higher equipment costs that are charged by contractors following a hurricane due to heightened demand. The pre-hurricane annual investment is then graphed against the post-hurricane cost of recovery. A sample of tradeoff between investment and post-hurricane cost for various levels of spares is shown in Figure 5.

Each curve in the graph represents a different hurricane category, and each horizontal line represents a different inventory alternative. Other such figures are available to evaluate levels of spares for various types of equipment.

Time to Recovery

The assessment of time to recovery involves the time to manufacture and deliver the equipment as well as the time it takes to install the equipment. Having spares on hand could greatly reduce the time it takes to replace the damaged equipment by reducing manufacture and delivery time and allowing some equipment to be replaced almost immediately. A separate time to recovery was calculated for each inventory alternative and hurricane scenario. A graphical representation of the tradeoff analysis between the investment made and the time to recovery is provided as an output to the user through the workbook and is similar to the tradeoff analysis between investment and post-hurricane cost shown in Figure 3.

In an automated workbook, the user chooses policies for evaluation, updates raw data and assumptions, and examines the costs and benefits of each policy. The tool captures the realities of VDOT's equipment
procurement, storage, and installation processes as well as the impact of different hurricane scenarios on the depletion of spares.

PRIORITY SETTING ALTERNATIVES

The goal of priority setting is to reduce the time of recovering damaged highways, signs, lights and signals in the Suffolk District and to find the road intersections that connect the most critical facilities the most efficiently. A critical facility is any facility that is essential to the well being of the community.

The priority of intersections is based on connecting the most critical facilities the quickest. The first step is to define and identify critical facilities. The critical facilities are in six main categories: emergency, school, evacuation shelters, shopping, government, and military. These facilities were located on a map and assigned to an intersection that provided access to the facility (ADC 1998). Figure 6 shows a graph of the breakdown of type and number of critical facilities in the Suffolk District. A total of 821 critical facilities were identified across the Suffolk District.

City/county boundaries are used to break the Suffolk District into eleven large sections. If a hurricane only hits a portion of the Suffolk District, then only recovery plans for those sections will be used. Within each city/county, zip codes are used to further break down the sections. Natural boundaries, such as lakes and rivers delineate many of the zip codes making them straightforward to recognize.

Each section is treated as an individual network starting on the lowest level of the hierarchy with zipcodes. To connect critical facilities, intersections must be restored in an order such that intersections adjacent to each other are connected before those that are not adjacent. A method was developed to weigh intersections according to the recovery status of the intersections near to them.

Intersections are recovered according to their total score, which is based on connectivity and the proximity of critical facilities. The total score is comprised of the base score and the connectivity score. The base score consists of the number of critical facilities connected to that intersection multiplied by integer weights assigned to the facility types. Critical facilities more important to the community than others have higher weights. The weights of the facilities can be changed by VDOT. The equation for the base score calculation is:
 

The problem with the base score is the issue of connectivity. Connectivity is a measure of how well the network of roads is interconnected. This affects the Flow of traffic in the area, because people cannot get from one place to another in an unconnected network. An example of high connectivity would be to start the repair in one place, completely repair that area, and then expand to neighboring areas until the repair is complete. Conversely, low connectivity would result from a "jumpy" repair - restoring many different areas without connecting them. Connectivity is the second objective in producing an optimal recovery plan, with the location of critical facilities being the first. Figure 7 shows connectivity for four different recovery paths, along with the theoretical best and worst case.

Figure 7. Connectivity Graph, including best and worst case
scenarios and four actual paths.

Each intersection is also assigned a status.  The intersection can either be damaged, 0, or repaired, 1.  As an intersection is restored the status is changed to a 1, for repaired.  When an intersection is restored its score is multiplied by a connectivity factor,l (0 £ l £ 1), and added to the score of intersections connected to it to give them more importance.  As the factor approaches one, more weight is put on connectivity.  If the factor is zero, connectivity is not factored into the priority setting.  The multiplication of a factor gives more importance to those intersections next to each other, helping to gain connectivity of the entire network.  The order in which intersections are repaired is determined one at a time since the connectivity scores change with every repaired intersection.  The equation for the connectivity score is stated below:

The equations described above are first applied to order the intersections within the individual zip codes.  After the zip codes are complete the methodology is applied to all of the zip codes within each city/county.  Finally the methodology can be applied to order the cities/counties.

The results of the priority setting section of the capstone project are spreadsheets that enable VDOT to generate an order in which intersections should be recovered after a hurricane or other natural disaster with the regional damage.  The weighting of critical facilities and connectivity can change the order.  Also the intersections that are affected by the storm can change.

Comparison of Priority Setting Tools

Two post-hurricane recovery plans were compared.  The first plan, described above, is a hierarchical plan where the Suffolk District is broken into sections and the second plan does not break the Suffolk District into sections.  The formulas and data were the same for both post-hurricane recovery plans.  In the non-hierarchical plan the order of recovery was determined for all the intersections in the Suffolk District at once, rather than by zip codes and then by cities/counties.

Each of the post-hurricane recovery plans has good and bad features.  The pros of the post-hurricane recovery plan presented in this report were time and adaptability.  Determining the order of priority for a list of approximately 212 intersections took more effort than determining the order of intersections within a zip code.  The non-hierarchical plan was not adaptable to small-scale recoveries.  If damage occurred the entire Suffolk District would have to be ordered, rather than just one section.

CONCLUSIONS

Three tools were developed to aid in the recovery of highway signs, lights and signals after a hurricane and have been placed on the Internet for VDOT to access.  A tool was developed that allows VDOT to compare different retrofitting alternatives of their choice.  Tradeoffs between investment in spares and damage reduction are different under different hurricane categories.  A similar tool was also developed that allows VDOT to assess different inventory alternatives on the basis of cost and time to recovery.  The purpose of this tool is to aid VDOT in deciding how much inventory is appropriate and feasible to store to prepare for a hurricane.  Two related priority-setting methods were developed.  Both methods allow VDOT to configure the tools to their policies and needs.  The priority setting tool is useful after a hurricane to determine which intersections should be repaired first.  The three tools capture the details of VDOT operations as well as hurricane effects and essentially transform the raw data into useful information for decision-making.

REFERENCES

American Association of State Highway and Transportation Officials. 1994. Standard Specifications for Structural Supports for Highway Signs, Luminaries and Traffic Signals. AASHTO, Washington, D.C.

ADC. 1998. Street Map Book of Tidewater Virginia, 19th Edition. Alexandria, VA.

FHWA Virginia Division. 1997. "Proceedings."  In Proceedings of the 1997 Post Hurricane Highway Recovery Workshop (Virginia Beach, VA, April 8-10). FHWA, VDOT, VDES, VTTTC, Richmond, VA, 1-2, 109-110.

Virginia Department of Transportation. 1997. Transportation Emergency Operations Center Hurricane Checklist. VDOT, Richmond, VA.

Virginia Department of Transportation. 1997. Hurricane Damage Assessment for Major Structures in Hampton Roads. VDOT, Richmond, VA.

Virginia Department of Transportation. 1997. Emergency Operations Plan. Vol. 7. VDOT, Richmond, VA.

Virginia Department of Transportation VDOT (1998).  Purchasing and Inventory Management Report. VDOT, Suffolk, VA.

BIOGRAPHIES

Heather Chua is a fourth-year Systems Engineering major from Baltimore, MD, concentrating in computer information systems and management systems.  Ms. Chua has accepted a position with American Management Systems and will begin work in July.

Richard Moutoux is a fourth-year Systems Engineering major from Vienna, VA, concentrating in computer information systems.  Mr. Moutoux lives on the only orchard in Fairfax County and is a member of the wrestling team at UVA.  Next semester Mr. Moutoux will return to the System's Engineering department at UVA to begin work on a Master's degree.

Rebecca Selig is a fourth-year Systems Engineering major from Ocean City, MD, concentrating in management information systems (MIS).  Ms. Selig has accepted a position with PricewaterhouseCoopers as a consultant and will begin training in August.

Joshua Tsang is a fourth-year Systems Engineering major.  After graduation, Mr. Tsang will pursue a Master's degree in Systems Engineering from the University of Virginia.  His interests lie in environmental studies and mathematical modeling.  He plans to work this summer with Professor Brian Smith on a traffic-forecasting project.