Fire Technology, 37, 219–234, 2001 © 2001 Kluwer Academic Publishers. Manufactured in The United States. Manpower Deployment in Emergency Services Richard Church, Department of Geography, University of California at Santa Barbara, Santa Barbara, CA 93106-4060 Paul Sorensen and William Corrigan, ISERA Group, Inc., 135 E. Ortega, Santa Barbara, CA 93101 Abstract. In order to adequately respond to emergencies, it is necessary to maintain a sufficient level of personnel as well as geographic coverage. Planning for geographic and manpower coverage can involve a wide variety of factors, including union restrictions, frequency and spatial distribution of calls, and road network accessibility. The focus of this paper is on manpower deployment across such agencies as police, fire, and EMS. Since the cost of manpower is the single largest cost factor in providing such services, it is also one of the central elements in efficient service provision. This paper discusses some of the differences in manpower planning among the different emergency services. It also presents details associated with several special models that have been developed in police and EMS planning in order to efficiently deploy manpower throughout each week. We conclude with comments on future needs for research and development in deployment planning and operations. Key words: deployment, emergency services, optimization, integer programming 1. Introduction Providing emergency services is expensive. Cities such as Los Angeles spend more than $250 million a year just in the fire department alone. If we add to that the cost of paramedic response and the costs of police (in terms of emergency response issues), it is easy to understand that such services are far from being small items in a city budget. This doesn’t even take into account the emergency transport provided by private ambulance companies in Los Angeles. As an another example, the Toronto Metropolitan Government oversees a public agency that provides ambulance transport and emergency response, which requires posting over 120 ambulances at various locations each day. In Toronto as in many metropolitan areas, ambulance dispatch is coordinated with the dispatch of fire equipment from one of the cities within the Toronto Metropolitan Government. Even though equipment and facility costs can be high, labor costs tend to be the single highest cost element of providing fire, EMS, and police emergency response services. Consequently, manpower planning is one of the central elements in efficient emergency services provision. The focus of this paper is on manpower planning. Even though fire, EMS and police emergency response all require geographical coverage and appropriate levels of staffing, personnel deployment across the three different services do vary. One of our objectives is to discuss both the similarities and differences in manpower deployment in emergency 220 Fire Technology Third Quarter 2001 response services. We will also present details as to how such deployment problems have been modeled, especially in police and EMS. We begin with a short history of labor issues and emergency services. We then discuss deployment planning in general, the complexities of the deployment planning problem, recent deployment planning and operations improvements, and finally examples of new models and promising applications. 2. Historical Issues in Manpower Deployment With the exception of volunteer fire brigades, labor costs have played a major role in the evolution of emergency services such as fire protection. Fire protection first became popular in the US as a service in eastern cities such as Baltimore and Philadelphia. Such services were provided by private insurance companies, each trying to protect the property that they insured. In the event of a fire, several fire companies would respond, but only the fire company representing the homeowner’s insurance company would fight the fire. Even with higher rates of fire, such duplicated services were expensive. Obviously, one consolidated fire department in a city meant an opportunity for reducing duplicated equipment and crews provided by competing fire insurance companies. The major impetus for such consolidations was the potential to reduce costs, especially labor. The provision of fire services soon became the obligation of most moderate to large city governments. To protect themselves in underwriting fire insurance policies, insurance companies took on a role of rating the level of service provision. Because of the cost of manpower, many areas still rely on the use of volunteers for the bulk of their fire fighting force. Just as in the evolution of fire services, labor costs have played a major role in emergency medical response. Historically, EMS was unregulated and pre-hospital care involved just transportation. To keep labor and vehicle costs to a minimum it wasn’t surprising that such services were often provided by funeral homes in many areas. This made sense from a labor perspective, as many funeral homes had employees either on call or available around the clock. Funeral homes could also use their vehicles for transport if they didn’t have a vehicle devoted to ambulance services. The level of care and personnel training was minimal if not nonexistent. Federal regulation in the early 1970s established standards on training requirements for paramedics and emergency medical technicians. Regulation was necessary to improve services, but this was at a substantially increased labor cost. Requirements to provide trained personnel, and the push to meet response time standards (especially in terms of trauma) meant that EMS became a primary activity instead of a secondary income source. In earlier times, the number of police officers either walking a beat or driving a patrol car per thousand people was greater than that of today. Labor pressures have forced many cities to reduce patrol units to one person from two. Even the time devoted to specific tasks has changed dramatically. More time is now spent in responding to problems than performing routine patrols. Over time many cities have kept the growth of police officers to less than historical trends in order to keep costs down. Some cities have even experimented with integrating police and fire departments in order to seek savings on needed personnel
1 2 3. Many companies have begun to rely on security services, special patrols and alarm systems in order to minimize insurance costs and Manpower Deployment in Emergency Services 221 losses from theft. Such private sector ventures provide services that were once part of typical police patrols. It is easy to see that a common trend in all types of emergency services is an attempt to contain costs. Since labor is the highest single cost factor in any one of these services, there is continued pressure in most cities to keep the number of full time emergency services personnel as low as possible. 3. Defining the Manpower Deployment Problem Since labor is the single largest cost factor in providing emergency services, it is logical to ask just what should it take to maintain a certain level of service. This is the essence of the deployment problem. We can define the deployment problem as: • To determine the best combination of staffing and equipment over time and space in order to meet demand. There are two main components of this problem: • Personnel component: To identify the appropriate level of staffing by crew-shifs over hours of the week • Location-allocation component: Locate & allocate the appropriate type of equipment to meet service demands over space and time The deployment problem is associated with identifying just what is needed in terms of equipment and personnel in order to meet some desired set of standards. For example, the standard may be able to respond to 90% of the calls of EMS within 8 minutes. Given this standard for service and given the geographical distribution of the potential demands, it is necessary to solve both a spatial and temporal allocation problem. The first major research project involving emergency deployment is the now famous New York City Rand project which was funded by the federal government during the 1970s [4]. The historical approach is to handle the two problem components as separate issues. For example, in police departments it is common to start with a given manning level or target. As the first step officers are allocated to specific divisions or stations using estimates of workload or some model like the parametric allocation model of Rider [4]. Then, the schedules of individual officers are often determined at each station. Police departments have the flexibility to make changes on a frequent basis, although this is often not done. In fire departments, it is common to locate stations for spatial coverage. The location decisions are usually the result of a long-term planning process. Such models as the location set covering model are typically used [5]. Given station locations, equipment is then allocated in order to provide adequate first and second due response [6]. Simple models like the square-root law have been used to estimate response times in an urban area [7]. Colner and Gilsinn [8] provide one of the first comprehensive location modeling frameworks for fire department deployment analysis. Then, personnel are usually assigned 24 hour shifts to staff equipment to appropriate levels. Changes in equipment allocation and staffing plans are seldom made except when new stations 222 Fire Technology Third Quarter 2001 are added, moved or closed. In operation, equipment may be moved in order to shore up problems in spatial coverage due to some stations responding to active incidents. Workload imbalances across stations can often become a management and labor problem. For EMS services, it is common to estimate demand temporally, by hours of the week [9]. Thus, for each hour of the week there is a desired number of ambulances to be operated. Demand normally fluctuates significantly, from low levels in early morning hours to relatively high levels in afternoon and evening hours. The next task is to identify when certain shifts should start during the week in such a manner that operating vehicles match as closely as possible the demand or need for operating vehicles. Next, spatial deployment plans are generated. Spatial deployment plans specify how various levels of available units in specific hours of the week should be distributed. For example, if 15 ambulances are scheduled for operation in a given hour and six are busy, how should the remaining nine units be scattered across the region in such a manner as to keep response time compliance as high as possible. This operation plan is called a systems status management plan. Finally, individual crews are assigned shifts to cover. Some researchers have developed specialized queuing models which address both demand and spatial allocation in order to estimate both numbers of ambulances needed and posting patterns [10]. A number of location models have been developed to address the static posting problem. These models include such approaches as maximizing expected coverage [11], minimizing the resources needed to provide a level of pre-specified level of reliability [12], optimizing combined services like basic life support and advanced life support in a two-tiered model [13], hypercube queueing [14], and providing accessible trauma care [15]. 4. The complexity of the Deployment Planning Problem Components Depending upon the application, the complexity of the deployment problem may vary. For example, if the problem is to operate one fire station with two pieces of equipment, then both the station location problem and the scheduling problem can be considered relatively simple. We recognize that the station location decision may be a difficult choice due to possible property owners and opposition, but there are usually a small but countable number of location alternatives with which to deal. On the opposite end of the spectrum, planners face problems like developing an ambulance posting plan for 10 ambulances, involving 100 potential sites across a city. The number of alternative plans that are possible is no longer a small easy to enumerate example, but a situation where the number of alternatives equals:
 100! 100 = 10 10! 90! which evaluates as 17,310,309,456,440 possibilities. The point is that the complexity of such a problem can grow exponentially. It is literally impossible to generate and evaluate all 17 trillion solutions. What is needed is a way to identify the best solution without enumerating all possibilities. Manpower Deployment in Emergency Services 223 The same types of complexity examples hold true for the personnel scheduling component of the deployment planning problem. On the simple side of the spectrum is the 24 hour shift patterns used in many fire departments. The constant shift pattern of 24 hours-on and 48 hours-off, yields a simple scheduling solution providing a constant unit manning 24 hours a day, seven days a week. If demand fluctuates widely throughout the week, it may be desirable to schedule crews to vary according to that demand. This is what typically happens with ambulance companies. When shifts are allowed to vary in length of days, duration of working hours, and starting times, the resulting scheduling problem can then become rather complex. Just as the number of distinct alternatives to the posting problem grows with problem size (i.e., number of potential posting points and number of vehicles) the number of potential solutions to the personnel deployment problem grows with increasing number of shift types and starting times. Since both posting/location problems and personnel scheduling problems can be complex, the combined deployment problem can be difficult to solve optimally as well. 5. Making Improvements in Deployment Planning and Execution Because the deployment planning problem is relatively complex, is important to develop good planning models and techniques to aid decision makers and operations personnel. Even though advancements in both planning and execution have been made, such advancements have evolved over time as developments in computers, software, database systems, etc. have made new technological approaches possible. We can easily classify these improvements into two main areas: execution/operation, and planning. For the execution/operations area, a number of developments have helped improved deployment. They are: 1. The capability to track vehicles dynamically using AVL and GPS technology to better monitor system status. 2. Improved Computer Aided Dispatch (CAD) systems that contain map databases, and can aid in helping dispatching closest vehicles, monitoring response coverage, etc. In long-term deployment planning, many areas now employ one or more of the following approaches: 1. Use CAD data • to better assess demand over space and time rather than only keeping track of the number of calls in a given time period • to assess system performance criteria 2. Use GIS for mapping • crime locations, EMS calls, etc. • visualize system during operations • exploratory data and trend analysis 3. Use optimization models • for fire station location • for equipment allocation to stations 224 Fire Technology Third Quarter 2001 Unfortunately, many of these techniques have only recently been adopted. Their value in providing gains in service provision or system efficiency has been substantial in some cases (see for example [16]). In order to make substantial gains in system efficiency, it is important to generate optimal or near optimal solutions for deployment planning and execution problems. This requires capabilities that can: 1. solve each component of the deployment planning problem optimally, 2. handle both components of the deployment planning problem in a coordinated optimizing model, 3. seek solutions which are robust: solutions that can perform well in a variety of situations, 4. model for persistence: generate solutions which are not short-sighted, 5. support integration with CAD data, GIS, and decision support technology, and 6. monitor plans easily and efficiently. The above capabilities are important needs in the emergency services arena. If techniques and software are developed which can provide such capabilities to fire, police, and EMS departments, then it is possible that better solutions to the deployment planning problem can be developed and supported. In fact many of these elements are the subject of current research and development. To demonstrate this, we will give two examples of models developed to solve the personnel scheduling components of the deployment planning problem in the next section. 6. Model Developments in Police Deployment Planning There have been a number of deployment planning models that have been developed in the last decade. Some of these models deal with the manpower component of the deployment problem
17 18. To illustrate the promise that such modeling may have for the emergency services arena, we will provide two examples, one for police and one for EMS. In this section we give details on a police deployment planning model that has been developed for the San Francisco Police Department. In Section 7, we describe a similar type of model that has been developed for the pre-hospital care industry. The following model, called the Police Patrol Scheduling System (PPSS), was produced in order to provide better manpower personnel deployment in terms of workload demand over the hours of the week [19]. The model that was developed is an integer programming problem. It is necessary to define the following notation for the model presentation: i = index for hour, j = index for day, h = hours in shift, d = days in shift, TA = set of start time indices i j that are acceptable, Manpower Deployment in Emergency Services 225 Sij = set of start times that contribute personnel to the coverage of i j given h d , NOij = the number of officers starting the work week at i j, T = the set of selected start times, K = the number of officers on duty at any i j, NA = the number of officers available, NP = the number of patrol groups, Rij = the number of officers required each hour and day,  = a value greater than or equal to one, where higher values reflect a high degree of management concern for large hourly shortages,  = a value that balances the relative importance of total shortage minimization to minimization of maximum hourly shortage, Pij = officers on duty at i j, Uij = shortage of officers at i j, Oij = surplus of officers at i j. We can now define the PPSS model as: Minimize Z =  Uij +   Uij  ij ij 1. Definition of officers on duty at a given time as a function of number starting certain shifts Pij =  NOkl ∀ i j kl∈Sij 2. Definition of shortage and surplus officers scheduled Pij + Uij − Oij = Rij ∀ i j 3. Number of starting times/groups is limited to the number of supervisors Number T ≤ NO 4. Starting times are feasible T ∈ TA 226 Fire Technology Third Quarter 2001 5. Cannot schedule any more patrol officers than available  NOij ≤ NA ij∈T 6. Must schedule at least a minimum number of patrol officers in a given time period Pij ≥ K ∀ i j 7. If anyone is assigned a given starting time, then a minimum number of others must be scheduled as well NOij ≥ M ∀ NOij > 0 and ∀ ij 8. Non-negativity conditions for the decision variables NOij ≥ 0 Oij ≥ 0 ∀ i j ∀ i j Pij ≥ 0 Rij ≥ 0 ∀ i j Uij ≥ 0 ∀ i j ∀ i j This model was developed by Taylor and Huxley [19]. The model was imbedded in a decision support system and utilized a heuristic solution procedure. The information flows that supported the use of this system are given in Figure 1. Notice that the main information source in the PPSS is the CAD (computer aided dispatch) data base. The forecasting step results in the number of officers needed by hour by day. The heuristic “Integheuristic” produces efficient scheduling solutions to the above model given the demand scenario. An expert rule based system helps fine tune the results of the heuristic and helps produce schedules with desired properties. One of the important features of the model is that, when officers are scheduled to begin a shift, a group of officers begins at the same time. This fits the typical operations model where a group starting on a shift meet together and are briefed by a group leader on current situations and needs, as well as giving out assignments. This type of property appears to be the exact opposite of what is desired in EMS deployment. The number of shifts that start at a given time should be limited in number as it is desirable to minimize the disruption in service caused by shift changes occurring in any short period of time. The application of this model to San Francisco yielded very encouraging results. First, the system provided solutions that provided higher levels of officers on the street during periods of high demand. Solutions provided up to 25% more patrol units in times of need, equivalent to adding 200 officers at a cost of $11 million a year. Second, response times improved by an average of 20%. Third, revenues from traffic violations increased by $3 million per year. Consequently, the costs of patrol were effectively lowered with higher revenues and service improved with better temporal deployment. This is a sterling example of the power provided by using a discrete optimization model in deployment planning. Manpower Deployment in Emergency Services 227 Figure 1. Information flows for the Police Patrol Scheduling System. 7. Model Developments in EMS Deployment Planning The second example deals with a model that has been developed for use in EMS services by the authors. Figure 2 gives an example of how demand for unit (vehicle) coverage varies over the hours of a week. The figure shows approximately how many operating units are needed in each hour. A vertical gray bar is given for each of the 168 hours of the week. The height of each bar represents the needed number of active crews during that hour. The basic goal is to schedule shifts in such a manner as to match as closely 228 Fire Technology Third Quarter 2001 Figure 2. Example unit demand graph by hours of the week for an EMS operation. as possible the varying needs over each day of the week. If the number of units that are scheduled in a given hour is more than what is needed in that hour, then utilization drops and average costs increase. If the number of units that are scheduled in a given hour fall below what is needed, then utilization rates are too high resulting, in dropped calls, lower response compliance, and overworked crews. Efficient scheduling will deploy personnel as close as possible to the unit demand curve. Other requirements restrict the number of simultaneous shift-starts and shift-ends, vehicles in operation and the need to minimize costs, the number of personnel or full time equivalents (FTE), or optimize some measure of scheduling close to the unit demand curve. In order to formulate the EMS deployment model it is necessary to introduce the following notation: i = the index for time periods of the week, e.g., 15 minute intervals, k = the index of shift types, e.g., 4 consecutive day 12 hour shift,   1 if a shift of type k with a start time of i is on duty during time aikt = period t   0 otherwise Manpower Deployment in Emergency Services  1 if a shift of type k with a start time of i, starts at time period t 0 otherwise  1 if a shift of type k with a start time of i, ends in time period t = 0 otherwise bikt = cikt 229 mi = the minimum number of crews that should work during time period i, ti = the highest target for crew assignments in time period i, mps = the maximum number of simultaneous shift starts, mpe = the maximum number of simultaneous shift endings, v = the maximum number of available vehicles, E = the maximum limit of full-time-equivalent employees to be used, xik = the number of shifts of type k that start in time period i, nt = the shortfall in the maximum desired staffing target for time period t. Using the above notation we can formulate a version of the EMS deployment planning problem. The model that we present here is based upon the assumption that daily start times for a specific crew shift do not vary. Varying such start times can also be accomplished but requires an extended formulation. The objective formulated below involves minimizing unit shortages as measured against the demand target in each time period. Minimize Z =  nt t 1. Meet the minimum staffing requirements for time period t  aikt xik ≥ mt for each time period t ik∈S 2. Define the shortfall in unit-hours provision from the desired target in time period t  aikt xik + nt ≥ tt for each time period t ik∈S 3. Ensure that no more than a certain number begin a shift in the same time period  bikt xik ≤ mps for each time period t ik∈S 4. Ensure that no more than a given number end a shift in the same time period  ik∈S cikt xik ≤ mpe for each time period t 230 Fire Technology Third Quarter 2001 5. Use no more than a maximum level of vehicle deployment  aikt xik ≤ v for each time period t ik∈S 6. Use no more than a certain limit of FTE of employees (or cost or UHs)  fik xik ≤ E ik∈S 7. Non-negativity of decision variables xik ≥ 0 integer for each i k ∈ S nt ≥ 0 for each time period t The above model is another example of a discrete integer programming problem. Just as in the San Francisco Police Patrol Scheduling System, this model can be solved with general purpose integer-linear programming software. Unfortunately, realistic problem sizes can tax the ability of current off-the-shelf software to the extent that solution times are unacceptably large. This has led to the development of a heuristic solver for the above model. The solver is based upon a TABU search process and involves a technique called strategic oscillation. The solver can solve two related problems: minimizing shifts (or total cost of scheduled shifts) needed to cover all workloads; or minimizing shortfalls to target needs in each hour subject to a constraint on total number of shifts (or total cost of scheduled shifts). The above model and solver has been embedded into a decision support system designed under support provided by the National Science Foundation. This model has now been tested in several major metropolitan areas and has resulted in deployment plans which reduced needed manpower by up to 8–10%, increased compliance, and aided in shift negotiation with employees. As an example, in Kansas City, Missouri and Kansas City, Kansas, the ambulance services authority, the Metropolitan Ambulance Services Trust (MAST), has used this model to study the deployment of EMS shifts. MAST contracts with Emergency Providers Incorporated (EPI), an ambulance company, to provide and manage an EMS staff. EPI in Kansas City developed the schedule depicted as a black line in Figure 3. Figure 3 superimposes their deployment plan (in terms of number of active shifts scheduled in each hour) against the unit demand graph (UDG) depicted in Figure 2. The schedule itself was developed manually. Typically, this is done in a group setting, involving several management personnel and shift supervisors, and requires considerable time and effort. Since it can be a laborious task to superimpose the aggregate levels of unit deployment over a UDG without some link to a computer data base, it is often difficult to assess the quality of a given schedule. For example, in the first hour of the week, i.e., Sunday from 2400–0100, the number of units needed is approximately 16 (top of the grey bar), however, only 10 units are scheduled to be working in that hour (height of the black line), which leaves a deficit of six unit hours uncovered. In the 38th hour of the week (1300–1400 on Monday, represented by the tallest spike on the second hump) Manpower Deployment in Emergency Services 231 Figure 3. Current deployment plan superimposed on the unit demand graph for Kansas City Metropolitan area. about 24 units are desired but 28 are scheduled, a surplus of four unit hours. The possible consequences of the current plan in these two hours are: (1) in the former hour, delays responding to calls and difficulties meeting response time compliance standards and (2) in the latter hour, a low unit hour utilization value or crews with a dearth of work. In applying the Decision Support System for Kansas City, the graphic in Figure 3 was generated for the current deployment plan. From this, MAST officials could see that there were a number of possible time periods in which the deployment plan could be improved. Using the heuristic solver, several possible deployment plans were generated. One of them is depicted in Figure 4. This model-generated plan utilizes over 100 fewer unit hours per week while reducing the maximum number of vehicles in use at any one time from 34 to 27. Essentially, the cost of the model plan involves 200 person hours per week less than the current plan (which is equivalent to using five full time people fewer than the current plan). In addition, the number of units needed in each hour is met in all but a handful of hours by the model-generated plan and there are rarely more than three extra units staffed at any one time. Also, note the longer vertical drops (when moving from left to right on the graph) on the current plan; these are times when numerous shifts end at the same time and when the potential need for crews working overtime in order to answer or complete calls is at its highest. 232 Fire Technology Third Quarter 2001 Figure 4. An example model deployment plan superimposed on the unit demand graph for Kansas City Metropolitan area. Table 1 displays summary statistics in comparing what was the current plan with the plan generated by the optimization model. The current deployment plan provided 588 unit hours of coverage beyond that desired by the proposed deployment levels and the model plan provided less than half that in surplus coverage. However, the current plan had a 243 unit hour deficit compared to only a nine unit hour deficit for the model derived plan. Thus, in order to provide equivalent coverage with respect to the deficit measurement, the current plan would have to add at least six crews each working approximately 40 hours per week. TABLE 1 Summary Statistics Comparing Current Plan and Model Plan Current Deployment Plan Total Mean Std. Dev. Range Model Deployment Plan Deficit Coverage Surplus Coverage Deficit Coverage Surplus Coverage 243 −32 18 −71 588 64 25 110 9 −04 03 −10 248 17 12 57 Manpower Deployment in Emergency Services 233 The benefits of the model include reducing the number of unit hours staffed during each week, avoiding cyclic times of high call volume compared to staffing levels, ensuring a more evenly spread work distribution, the possibility of minimizing mandatory overtime, and worker participation in the deployment process. When the model was first applied it coincided with a request by EPI to add three more units to help improve the current schedule. By using the model, MAST was able to effectively evaluate the EPI plan. Without considering other issues, it was clear that three additional units would not be needed to improve the schedule. In fact, better deployment may yield reductions in needed staff and vehicles. Now, both EPI and MAST have installed the model for use in future planning. 8. Summary The deployment planning problem deals with determining the best times and locations in which to deploy emergency response assets. In order to solve this problem one needs to characterize the demand across space and time, solve an integrated scheduling and location model, negotiate with unions and potential crews, and manage dynamically over time so deployment is adjusted accordingly to changing system status. This planning and operation problem is important to fire, police and EMS services. Inefficient solutions can mean poor performance, wasted money, and lost lives and property. New technologies have been utilized in helping to improve systems status monitoring and readjustment. Digital-based CAD systems have been used to monitor unit availability, GPS technology has been utilized to track spatial distributions of available equipment, and new models have been developed to prescribe equipment repositioning. Advancements have also helped improve advanced planning using CAD data to characterize demand by space and time as well as using GIS to map and analyze demand patterns, response times, and changing demographics. Finally, emphasis has also been placed in designing new models that can be used to optimally deploy assets over time. Examples of such models have been presented in this paper and applications suggest that improvements in both compliance and costs can be made. Emergency services deployment planning is an important problem, involving a labor intensive and expensive service. Even though many improvements in the planning process have been provided by the use of computer aided dispatch systems, status monitoring, Geographical Information Systems, GPS, and simulation and optimization models, there exists a substantial need for deployment models with greater capabilities. These include the development of truly integrated deployment planning models for simultaneous equipment scheduling and posting, better models of demand and travel time estimation, and better spatial simulation models for emergency services. 9. Acknowledgements Some of this work was supported by a National Science Foundation Grant (DMI-9529706 titled “Design and development for a decision support system for emergency services”). This grant was administered as a part of the Small Business Innovative Research Grant Program at NSF. We wish to acknowledge this support and to acknowledge as well the input that we received in this work from many individuals from numerous cities 234 Fire Technology Third Quarter 2001 and ambulance companies throughout the US and Canada. We appreciate the sincere interest and cooperation of Judd Palmer of EPI and Jim Jones from MAST. We would also like to express our appreciation for helpful comments made during the review process. References [1] K. 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