You are faced with locating ambulances in a city. You would like to find the loc

Question

You are faced with locating ambulances in a city. You would like to find the locations of a fixed number of ambulance bases. Let P be the number you want to locate. You would like to maximize the number of demands (demands occur on nodes of the network) that can be covered within 5 min of the nearest ambulance. However, you require that the selected sites be such that all demand nodes can be covered by an ambulance within 10 min.

a) Using the notation we have defined for the set covering and maximum covering problems as well as any other notation you require, formulate this problem as an integer linear programming problem. Clearly define any new notation that you use. Clearly state in words what each of the constraints and the objective function is doing.

b) What can you say about the minimum value of P (the number of facilities to be located), which is an input, such that the problem will have a feasible solution?

Explanation / Answer

Location is often considered the most important factor leading to the success of a private- or public-sector organization. Private-sector organizations can profit from a good location, whether a small coffee shop with a local clientele or a multinational network of factories with distribution centers and a worldwide chain of retail outlets. Location can help keep fixed and overhead costs low and accessibility high. Public-sector facilities, such as schools, hospitals, libraries, fire stations, and emergency response services (ERS) centers, can provide high-quality service to the community at a low cost when a good location is chosen.

Given facilities that provide goods and services and a set of demand points that consume them, the goal of location-allocation is to locate the facilities in a way that supplies the demand points most efficiently. As the name suggests, location-allocation is a twofold problem that simultaneously locates facilities and allocates demand points to the facilities.

Initially, it may appear that all location-allocation analyses solve the same problem, but the best location is not the same for all types of facilities. For instance, the best location for an ERS center is different than the best location for a manufacturing plant. The next two examples demonstrate how the goals of location-allocation problems vary according to the type of facility being located.

When someone calls for an ambulance, we trust it will come to their aid almost instantly; the emergency response time depends considerably on the distance between the ambulance and the patient. Typically, the goal for determining the best sites for ERS centers is to make it possible for ambulances to reach the most people within a defined time frame. The specific question may be: Where should three ERS facilities be placed so that the greatest number of people in the community can be reached within four minutes?

The ArcGIS Location-Allocation analysis layer offers seven different problem types to answer specific kinds of questions, including questions like those posed in the two examples above. The seven problem types are the following:

Details and examples of the individual problem types are described in the Location-allocation analysis layer properties section of this document.

The workflow to perform a location-allocation analysis is similar to performing any other analysis in the ArcGIS Network Analyst extension

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