# Fire Service Level Can Be Selected By Evaluating Public, Private Costs

Fire Service Level Can Be Selected By Evaluating Public, Private Costs

In determining the amount of fire protection a municipality should provide, there is an important trade-off between the public costs of a fire department and the private costs of fire insurance.

This article illustrates a use of mathematical methods which sets a lower bound on the amount of fire services which a city should provide. This is done by finding the point at which the sum of the public and private costs are minimized.

Municipal decision-makers face the difficult task of determining the amount of funds to be allocated for fire department services. This decision affects both the insurance class of the city and the total cost of fire protection. Total fire protection cost is the sum of the tax dollars spent for fire department services (public expenditures) and fire insurance premiums paid by residents and businesses (private expenditures). This article describes a recent project to measure these costs in Boulder, Colo.

Since fire insurance rates are a function of the fire protection level defined by the Insurance Services Office or a similar organization, cities having higher-rated fire protection receive lower insurance rates. This relationship provides a trade-off between money spent on fire services and money spent on fire insurance.

The municipality that spends more money on fire services, thereby raising the quality of the fire department, will have to spend less on fire insurance premiums. The total cost of fire protection is the sum of fire service and insurance costs, as demonstrated in the accompanying graph.

The lowest point on the total cost curve is the least cost class for a municipality. In moving from class 10 to the minimum cost class, the savings in insurance costs are greater than the additional cost of the fire services needed to achieve the least cost class. Any movement beyond the least cost class might be partially justified in terms of life hazard, as the cost of the additional services needed for the higher grade exceed the insurance savings from the move.

Fire service costs

The first component needed for finding the least cost class is the mix and the associated cost for fire department services needed to achieve each insurance class. The insurance class for a city is determined through the application of a grading schedule by the Insurance Services Office. The set of services provided by a municipality is evaluated and a class is assigned.

Since it is possible that many different sets of fire services could satisfy the requirements for any given insurance class, it is desirable to determine the least cost set of services which would qualify for each class. The schedule defines five areas to be rated: (1) water supply, (2) fire department, (3) fire service communications, (4) fire safety control, and (5) miscellaneous additional deficiencies. Fire services in each area are graded on the basis of the percentage a given city is deficient with respect to the standard. These percentages are converted to points and a city’s insurance class is determined by the total number of deficiency points.

A mathematical technique called zero-one integer linear programming can be used to identify the least cost set of fire services for any specified number of deficiency points. This approach includes both expense items, such as fire marshals, and capital items, such as fire apparatus. The capital and expense items are the decision variables for the model, and together they form a set of actual or possible fire services. The municipality must decide which of these services to purchase.

Deficiency points

For each fire service item, an equivalent annual cost must be calculated, and the number of deficiency points avoided by its implementation must be determined.

This information-gathering task may be undertaken in a two-phase approach. Using a current rating of the city, the first phase is an examination of all present fire services to determine their value in deficiency points and their cost. The second phase is to examine the grading to determine what fire services could be added to eliminate deficiencies that currently exist.

For example, consider the fire safety control section of the grading schedule. This section involves inspection of facilities. The number of deficiency points is primarily a function of the number of fire marshals and inspectors. In Boulder, where the methodology was tested, there were three fire marshals. The fire safety control section was graded with 211 deficiency points. In phase one, the fire marshal was asked to simulate a grading under configurations of two, one and no fire marshals. This yielded the following results:

The deficiency point value of the first fire marshal is the difference between 566 points with no fire marshals and 486 with one fire marshal (80 deficiency points). Values for the second and third fire marshals can be calculated in a similar manner. In the second phase, the grading was simulated with up to six additional fire marshals and inspectors and the deficiency point value of each was calculated. The maximum number that could be effectively used was nine. Diminishing returns were such that more than nine eliminated no deficiency points.

Selection for least cost

All other fire services were graded to find the deficiency point value for each actual and potential fire service element. The two-phase approach yielded a set of fire services that included all present services and all possible additions that would have any impact on a city’s grading.

With this information, it is possible to select the least cost set of services for a specified number of deficiency points using the mathematical model.

The model was run on an IBM 360 model 67 computer. The results were the least cost mix of capital and expense items (fire services) at selected deficiency point levels, and the total cost for the mix at that point.

Since an insurance class is 500 deficiency points wide, a decision needs to be made as to the permitted number of deficiency points to achieve any class. This may be necessary because of subjectivity in grading. On the basis of a subjective judgment, it was decided that an optimistic solution would be one that was one-fourth of the way into the insurance class, and a pessimistic solution would be one that was three-fourths of the way into the class. The results from the application of the model in Boulder are presented in table A (page 28).

Insurance costs

The second component of the total costs depicted in the graph are insurance costs for all of a city’s residents and businesses under each of the insurance classes. The survey of premiums was segmented into three groups:

1. One and two-family dwellings.
2. Apartments.

A random sample of buildings was taken from each of the three groups. Insurance premiums for these buildings were then determined under the rate schedules for each of the 10 insurance classes. This provided the basis for inferences about the insurance costs for all buildings in the city.

No attempt was made to separate the insured from the uninsured buildings. A change in the level of fire services changes the risk position of the owner who chooses to self-insure. A basic assumption is that the expected fire loss for a self-insured building will change in the same dollar amounts as the fire insurance premiums on insured buildings.

Fire insurance premiums change with fire loss experience, and the basis for class difference is due to fire loss differences for the building under a set level of fire protection. It is, therefore, not an unreasonable assumption to equate premium changes to potential fire loss changes. This assumption provides the basis for treating every item in the sample as if it were an insured building and costing every item in the population as if it were insured.

It was possible to obtain building and contents replacement costs for oneand-two-family dwellings and apartments through the use of assessor records and a replacement cost estimator developed for the insurance industry. The sample of businesses needed to be interrogated to estimate replacement costs for the contents of buildings.

The premiums were calculated by using the ISO advisory schedules. These schedules are standards used by all member insurance companies unless they specifically apply to the insurance commission for an exception. To simplify the presentation, only the differences in insurance costs between class 1 and all other classes are presented. Also, for a better understanding of the costs of residences versus businesses, the Boulder insurance costs for residences will be presented separately and then combined with businesses.

Two total cost curves were developed for Boulder. The first included only insurance costs for residences. The second curve included both residences and businesses.

Minimum cost level

Considering only residential insurance costs, Boulder should be a class 6 to minimize the total fire protection costs. With the addition of business insurance costs, the minimum cost class is also class 6.

It is interesting to note that the minimum cost point is not sensitive to variations in the cost of fire services represented by the optimistic and pessimistic values for fire service cost. Total cost calculations were also made using upper and lower confidence limits for the insurance cost estimates. These calculations indicated that the minimum cost point was not sensitive to sampling error.

The mathematical model provided the least cost set of fire services to obtain a class 6 rating. Any fire services beyond the base mix specified for class 6 must be partially justified in terms of life hazard. These additional services will cost more than they will save in insurance premiums for the community.

In addition to the determination of the least cost quantity and mix of fire services for Boulder, a number of alternatives were explored by telling the model certain services must be provided because of existing political realities perceived by the city. Using this methodology, it is possible to determine the least cost class and mix of services with assumed minimum configurations of services.

Six configurations

The alternatives for Boulder were narrowed to six possible configurations. These six configurations were a result of combining political reality with least cost mixes of fire services.

The primary configuration for Boulder at the time of the study was five fire companies and three fire marshals. The first alternative for Boulder was to reduce fire services to the least cost level and mix of fire services. The results of this alternative are summarized as follows:

Alternative 1

The fire service costs are public expenditures for municipal fire services. The excess insurance costs are the additional private costs for not having the best possible fire protection (class 1). Total costs are the sum of the public and private costs and represent the amount Boulder citizens and businesses pay for fire protection.

If consideration is given to political realities, this alternative is probably not viable. The remaining five alternatives all assume that the current five fire companies are in their present locations and all fire services are a minimum acceptable configuration for the community. With minimum configuration, the least cost class shifts from six to four. The results are summarized as follows:

Alternative 2

More fire marshals

This shift is the result of a change in the fire service cost curve. This curve becomes flat rather than decreasing because the five fire companies were held in the solution even when they were not needed to meet the deficiency point constant. Upgrading from the class 4 rating of alternative 2 to class 3 can be accomplished with the addition of three fire marshals. The results are summarized as alternative 3.

Alternative 3

A fire protection problem often recognized in Boulder has been the lack of a fire station in South Boulder to provide better service to citizens there. The two remaining alternatives propose configurations to deal with this problem.

The fourth alternative is to maintain the present five fire companies, but relocate one of the two pumper companies at the central station to South Boulder. As the specific location of fire companies has little effect on the grading, the results would be the same as alternative 2 except for an increase of \$10,000 in fire service cost, representing the annual cost of the additional station.

The fifth alternative is to provide more protection for South Boulder by adding a sixth fire company. This would result in an additional annual cost of approximately \$160,000. The results are as follows:

Alternative 5

The addition of the sixth company would not increase the class from class 4 to class 3. The sixth company avoids only 132 deficiency points, which are not sufficient to achieve a class 3 rating.

The sixth alternative is to add a sixth company and sufficient fire services to achieve a class 3 rating. This could be accomplished with the addition of two fire marshals. The results are:

Alternative 6

Simulating the structure for different configurations allows the municipal decision-maker to evaluate the alternatives and make rational policy decisions.

Problems encountered

A number of problems were encountered in the application of the methodology. Two main problems encountered in this research were:

1. Many grading schedule provisions allow subjective judgments on the part of the grading engineer. This may result in gradings for the same condition varying from municipality to municipality or gradings that vary over time in the same place when no changes have occurred in a specific item. This subjectivity makes it difficult for municipalities to predict the effects of upgrading or downgrading fire protection.
2. Although it may be impossible to remove all the subjectivity from the grading schedule, clearer and more definitive statements on the standards could reduce uncertainty in the application of the schedule. The ISO response to this criticism has been that their grading engineers use additional information in their application of the schedule but the additional information is usually not available to municipalities.

TABLE A Fire Service Costs by Class

However, ISO plans to publish a commentary on the grading schedule. This commentary will provide the philosophy behind the need for the grading item, the basis for its specific value, and information on how to estimate the item’s grade.

3. Deficiency point values have not kept pace with developments in fire service planning. The deficiency points avoided by optimally locating stations are almost nonexistent. Considerable research effort has gone into solutions to the problems of allocation, redeployment, and dispatching. If in fact these problems are as important as researchers indicate, then the grading schedule should give deficiency point weight to these items.

TABLE B

Estimated Increases in Insurance Costs

Above Class 1 for Boulder, Colo.

The problems mentioned would indicate that the piecemeal approach to revision of the grading schedule may not be yielding a document that is balanced and up to date. The only solution is a systems approach to the development of a grading schedule that considers the area to be graded, the points per item, the cost per point, and tin size of the municipality. This study is necessary, for there is no economic incentive for municipalities to find better ways of doing things that do not meet the requirements of the grading schedule.

However, ISO has repeatedly warned that the grading schedule is not to be interpreted as the ultimate authority in the planning and design of municipal fire defenses. The application of techniques in this study indicates that this is a warning that should be respected.

Boulder results unique

It is important for other municipalities to recognize that the results derived from the Boulder data base cannot be generalized to their communities. ISO has indicated that due to the quality of Boulder’s excellent gravity water system, the city could attain a class 6 rating with few fire department services. This situation, however, is unique to Boulder and represents a rare occurrence.

The methodology presented can, however, be applied to any municipality. It must be recognized that the level and mix of services resulting from the model are only optimal with respect to the grading schedule and to the accuracy of cost estimates for fire service projects.

If this schedule places incorrect deficiency point values on individual grading items or cost estimates are unrealistic, then the quantity and mix derived from its application may not be the best for the community.