A simple, transparent move-up model in NFORS

A simple, transparent move-up model in NFORS

A common feature request from NFORS users is a tool that can inform decision makers of move-up strategies for heavy emergency call volume or unexpected surges in requests for service. Given the large amount of emergency incident data collected using NFORS, this functionality is possible. In this blog post, the methodology for an initial move-up model that leverages historical incident data and Geographic Information System (GIS) technology and provides recommendations that optimize a fire department’s resource coverage is described. The project goal is to produce a model that is simple and transparent enough that users can understand exactly how the model generates its results, but sophisticated enough to provide relevant and actionable information and recommendations.

Why are move-ups necessary?

Before we describe the methodology of the model, it is important to illustrate why temporarily transferring units can be advantageous in an emergency response system. First, let’s consider a basic incident heat map generated using the NFORS data from the Richmond Fire Department.

An incident density heat map.

In the figure above, the red regions indicate an area where incidents are most likely to occur. The blue regions indicate areas where incidents are least likely to occur. One of the ways to evaluate a department’s coverage capability is to determine what fraction of incidents occur within a specified travel time from at least one available emergency response unit. Travel time can vary, but as an example, let’s specify any location that is within an eight-minute travel time from an available emergency response unit. This area is assumed to be “covered” and any location that is more than an eight-minute travel time from an available emergency response unit is assumed to be “uncovered.” Using GIS technology, we can determine every location within a fire department’s jurisdictional boundary that is covered according to this definition. Then an incident density heat map can be plotted over the uncovered regions. The resulting map will provide a useful visualization of fire department coverage holes.

First, let’s consider the maximum coverage case, meaning that every station has an available unit. Note that these analyses are usually done for a specific unit type. This blog post focuses on engines as an example, but the same analyses can be done for other unit types (ALS, Rescue Unit, etc.). The covered area (the cross-hatched region) is computed by taking the union of the eight minute travel time polygons for every station. The result is shown below.

An example of a coverage visualization for Richmond Fire Rescue Department. The cross-hatched regions indicate “covered” locations that are within an 8-minute drive time from at least one station with an available unit. The “uncovered” regions are more than an eight minute drive time from a station, indicated in blue on the incident density heat map. This map represents the best possible coverage, when every station has at least one unit that is available and able to respond. Note, the uncovered region in the middle of the Richmond map is largely over a river.

As noted above, the previous visualization represents the case for which every station has an available unit. This situation is not always the case. When stations do not have an available emergency response unit to send to a call for help, they are excluded from the calculation of the covered area. Some incidents require multiple units, which can leave multiple stations without any emergency response units remaining to respond to new incidents. In this situation, units are deployed from other stations to a call for help or they may be repositioned in the vacant station to be available for another incident that may occur. For example, on April 13, 2017, a large fire broke out in a former tobacco factory in Richmond. The department deployed fire engines from ten different stations to extinguish the fire and rescue any trapped occupants. In a situation like this, the ten fire stations are left unable to send these same fire engines to any subsequent new incidents (since they are already on a call). The resulting emergency response area coverage holes are illustrated below.

A visualization of the coverage holes that would have occurred without unit transfers during the tobacco factory fire of 2017. Ten stations dispatched their fire engines to the factory location. Without the transfer of neighboring emergency response units known as move-ups, this situation would have left busy regions of the city uncovered for a subsequent emergency call for help.

As shown above, some of the stations that sent engines to the tobacco factory fire are in areas of high call volume. However the original heat map shows that some of Richmond’s stations are in regions of relatively low call volume. Therefore, moving units from low call volume stations to high call volume stations during periods of high emergency call volume can help fill coverage holes. It is important to note that Richmond conducted emergency response unit transfers during this fire incident, so the figure above does not show the actual coverage profile during the incident. Nevertheless, this example illustrates why unit transfers can be beneficial, and the goal of our move-up model is to provide a quantitative framework for evaluating and recommending unit transfer strategies.

How the model works

At a high level, the model works by solving two optimization problems:

1. If n units of a specific type (i.e. engine, rescue unit, etc.) are available, which n stations should house the available units to optimize coverage?
2. During times of high call volume, what is the best strategy for transferring less busy or available units from their current locations to these busy stations (areas)?

Determining ideal station locations

The first step in finding the best station locations is to determine what “best” means. Although there are many appropriate figures of merit, the current version of the NFORS model attempts to maximize the fraction of incidents that occur within a specified drive time of at least one available unit. In order to show how this is done, let’s consider a simple example.

Imagine that a fire department consists of five stations. The coverage objective is to maximize the fraction of incidents that are within an eight-minute drivetime from at least one available unit in these stations. Using GIS software, a polygon (isochrone) that indicates every location that is within a eight-minute drivetime from each station can be obtained. If a location is within a station’s isochrone, it is “covered” by that station. To gain an idea of the call volume covered by each station, a random sample of 1,000 historical incident locations is taken. The assumption is that this sample gives insight into where new incidents are likely to occur. An illustration of the simplified example is shown below. Note that when showing a relatively small number of incidents, it is easier to visualize the individual incident locations as shown below. When showing a large number of incidents, a heat map is more useful.

A hypothetical department layout for illustrating the move-up model methodology. Five stations are indicated by the five dots. Surrounding each station is a hypothetical eight-minute drivetime polygon (isochrone). The 12 red “x” markers indicate the locations of past incidents in a random sample. Keep in mind that this is only an illustrative example. The actual model uses a random sample of 1,000 incidents and the drivetime polygons are typically more complicated than the circles shown.

Now, let’s say that only two emergency response units are available. This means that we have to pick the two stations that cover the most incidents. This is known as the maximum coverage problem, and a greedy algorithm is often used for these problems. This process means that we build the list of ideal stations by adding the busiest and then sequentially adding the next station that covers the most incidents that are not covered by a station already on the list. In our example, we can simply count how many incidents are covered by each of the five stations and rank them:

Because Station C covers more incidents than any of the other stations, it is the first “ideal” station added to the list. Now we repeat this process, excluding station C and all of the incidents it covers:

Based on the above figure, the rankings are

Station D covers more incidents that have not already been covered by Station C, so it is added to the list of ideal stations. Therefore, the two “ideal” stations to house the two available units are Station C and Station D. As shown below, this results in an aggregated coverage polygon that contains 9 out of 12 (75%) of the incidents in the sample, which is more than any other set of two stations.

Note that Station B technically covers more incidents in total than Station D. However, the coverage overlap between B and C makes it so that C and D form a better set than B and C (9 out of 12 incidents vs. 8 out of 12 incidents).

Determining the movement strategy

Now that the set of ideal stations has been identified, the next step is to determine the best strategy for moving units from their current locations to the ideal stations during times of high call volume in those areas. Specifically, the model identifies the set of moves that minimizes the total distance traveled for the move-up units. This is a special case of the assignment problem.

In our simplified example, let’s say that the two available units are originally at Stations A and B. This results in two possible movement strategies:

1. Unit A moves to Station C; Unit B moves to Station D (the blue strategy below)
2. Unit A moves to Station D; Unit B moves to Station C (the red strategy below)

These strategies are illustrated below:

A visual illustration of the two movement strategies. Stations C and D have been identified as the ideal stations to house available units. However, the available units are originally at stations A and B. To move the available units to the ideal stations there are two possible strategies. The blue strategy is to move Unit A to Station C and move Unit B to Station D; the red strategy is to move Unit A to Station D and to move Unit B to Station C.

Now a cost must be assigned to each strategy. This assignment can be done via travel time, travel distance, or some other custom heuristic. For simplicity, the cost of a strategy will be estimated by total distance traveled. The distances for each of the potential moves are shown in the table below:

The total distance traveled for the blue strategy is 2+1=3 miles. The total movement for the red strategy is 1+1.4=2.4 miles. As a result, the red strategy would be recommended by the model since it minimizes the total distance traveled. In this example, this result is easy to see because there are only two possible movement strategies. In actual use cases, there are often many different potential strategies so it is more computationally efficient to use a technique known as the Hungarian algorithm to find the optimum strategy. The details of this algorithm are beyond the scope of this blog post, but are explained here.

Limitations

Although the current version of the move-up model can provide insight into the effectiveness of potential move-up strategies, it has several limitations. First of all, it always recommends the strategy that optimizes coverage, even if some of the moves provide small coverage benefits and require units to travel long distances. In future versions of the model, the user will be able to specify additional criteria so that the model will only recommend moves above a certain distance if the coverage benefit is above a certain threshold.

The model also optimizes for single unit coverage, meaning that if a location is within a specified travel time of an available unit, then it is assumed to be covered. In some cases, it may be advantageous to have more than just one unit covering locations with large call volumes. Furthermore, if one station has two available units, and another station has no available units, the model will always recommend moving one of the available units to the station with no available units. While the current methodology does not consider the potential impact of mutual aid, these effects may be added as departments request this feature.

Conclusions

This blog post outlines the methodology of the initial move-up model in NFORS. The goal of this model is to provide insight into the effectiveness of movement strategies using NFORS data. This initial version is relatively simple, but it provides a starting point for future iterations. Our goal is to continually improve the model based on user feedback. If you have any questions or comments, please contact us at hello@i-psdi.org. If your department does not yet participate in NFORS, schedule a demo to see the power of analytics https://www.eventbrite.com/e/nfors-demo-registration-45782334194.