Task force deployment for big events

The basic modelling idea is the following: The location of a task force unit can be specified by its grid rectangle. For each feasible location of a task force unit, it can then be specified in advance which grid rectangles can be accessed within a predefined response time from that location being able to take into account constructional barriers, for instance. Mathematically, a binary parameter dpqrs equal to one indicates that grid rectangle (r, s) can be reached from location (p,q) within a certain amount of response time and a value zero indicates that (r, s) cannot be reached from (p,q). Fig. 3 illustrates this idea. Note that for the applicability of the models, it does not matter whether the response time is defined to be the time of the moment of detection of the incident or the time from the moment the alarm call reaches emergency personnel. Depending on the event area, the access area may be very compact (if, for instance, the event area is a meadow, the access area might be a square) or not (if, for instance, the event area is in the inner city, the access area might be along the street network). Both situations can be represented by parameters dpqrs without problems. More mathematical formulas, diagrams and several maps are included in the article, for more information on the visual material please consult the article.

Interview, report and litreture survey, mathematical models

Minimum number of required task force

In Germany no legal requirements exist that are valid all over Germany and that define in detail how to organize big events with respect to task forces in order to guarantee safety and help. Many decision makerssimply use experience instead of systematic procedures. Local authority districts may or may not have guidelines for such cases. The city of Dresden, for instance, which is the location of the practical case described in this article, has one (see Landeshauptstadt Dresden, 2004). It is based on a handbook for task forces where a non-scientific method to calculate the size of the task force is presented. Often, the task forces themselves have defined a set of rules which are applied.

They collected data through interviews and official reports.

What is the minimum number of task force units and where should these units be located such that the event area can be covered in the sense that any place in the area can be reached within a predefined response time?Given the number of available task force units. Where should these units be located such that the event area is covered best in the sense that a maximum area can be reached within a predefined response time?Given the number of available task force units. Where should these units be located such that the event area is covered best in the sense that the response time needed to reach any place in the area is minimal?

Although, besides the relocation problem, all these problems are theoretically hard to optimize, computational studies revealed that instances of practical relevance can be solved optimally in short time using standard software.

In the case of big events, task force units must be located nearby the event area to ensure safety and help. In this paper, first it was revealed how the number of required task force units is usually determined in Germany. It is realized that very rough estimates are used. Where to locate these task force units best is mainly done by experience of the decision maker. Herewith it was developed mathematical models to give a better decision support in such situations. Basically, three problems were discussed: (1) How many task force units are needed and where to locate them, (2) given a limited number of task force units, where should they be located to cover the event area best to ensure help in a predefined response time, and (3) given a limited number of task force units, where should they be located to cover the event area with a shortest possible response time until help. In addition we discussed the problem of relocating task force units. Although, besides the relocation problem, all these problems are theoretically hard to optimize, computational studies revealed that instances of practical relevance can be solved optimally in short time using standard software. Eventually, we have shown that our approach provides decision support for a real-world case from the city of Dresden where 50000 people gathered together.

The aim of this simulation is to understand with the help of the mathematical programming the number of task force that is needed and  where to locate them in case of a big event.