Service Level Networks When it

Service Level Networks

When it comes to urban planning, there are many issues to address. One of them involves problems with facility location. This is something that is easily overlooked, but that can cause serious issues as development of the project moves along. In order to avoid location difficulties, any person or company planning a facility of any kind in an urban area needs to take the time to carefully look over where the facility will be placed and all of the factors that can surround it (Chan & Kumaraswamy, 1996). How valuable a location is also depends on the facility that is being constructed there (Larson & Odoni, 1997-1999). For example, downtown would not be a good place for a landfill, but it would be perfect for a postal facility.

People often like to be able to walk to things like the post office and the courthouse, as well as local restaurants and attractions. By locating them downtown they become central (and thus more convenient) to a lot of people (Larson & Odoni, 1997-1999). Areas like landfills and recycling centers, however, should be a reasonable distance from homes and other businesses because of odors, noise, and other issues that they may produce. Often, companies that create various business models do not spend the time considering where land really is compared to other businesses and homes (Chan & Kumaraswamy, 1996). They look at the cost of the land, but do not judge the other factors of location well.

Examined here will be three types of problems with facility planning and location issues -- center problems, requirement problems, and median problems. These all must be addressed for a company or individual to have the best chance of finding the right location for a new business. Without clear consideration of these three factors (as opposed to only one or two of them) there is a distinct possibility that the facility will end up located in an area that is inconvenient for the company and for the people who live and work near it, causing problems all around (Chan & Kumaraswamy, 1996). Because of those concerns, it is important to define and address the three problem areas.

Center Problems -- These are also often called minimax problems, and they are more likely to be seen with facilities that handle emergency services, such as police, fire, and ambulance. Facilities like these must be located so that they can serve the maximum number of people within the shortest distance (Larson & Odoni, 1997-1999). In other words, they have to be located in the 'center' of things, so that they can serve more people effectively and efficiently. Putting a fire station on one side of town instead of in the middle, for example, would be indicative of a center problem. For larger towns, there will be more than one fire station -- but they all should still be located as centrally as possible based upon the geographic boundaries of the districts that they serve (Larson & Odoni, 1997-1999).

Requirements Problems -- Problems with requirements come about because there are a prespecified number of facilities that are required to meet certain standards in specific areas (Larson & Odoni, 1997-1999). The locations of these facilities are often decided early on, as well, and it is up to the companies and the town regulators to ensure that the facilities go in where they are supposed to, even if another location appears to be better. This is a more general concern that does not apply only to emergency services (Larson & Odoni, 1997-1999). By locating facilities in places (and quantities) that meet the requirements, specific standards of performance will more easily be met.

Median Problems -- With median problems, it is usually non-emergency services that are at issue. These types of problems are related to the number of facilities that must be located close to one another, so as to provide people who need the services with the right kinds of opportunities (Larson & Odoni, 1997-1999). Generally, these types of facilities are things like town halls, government agencies, and transportation companies like taxis, bus stations, and train stations. People do not want to go to the court house on one side of town, then be required to drive all the way across town to the police station, for example. Having all of the facilities of a specific type in one, centralized location makes a difference in the lives of the people who live in that town, as well as the traffic flow and other urban planning factors (Larson & Odoni, 1997-1999).

There are extensions and variations on the three different kinds of problems, as well as some overlap and mingling within them (Larson & Odoni, 1997-1999). That is very important to realize and take note of, since it can lead to significant applications in the field of urban service. Having said that, a more in-depth discussion of the issue as a whole is warranted at this point. It can be very beneficial for anyone looking to plan a facility in or around any type of urban area, and can also be used in rural areas.

When looking at an in-depth study of facility location problems, network models of metropolitan or urban areas are particular convenient and helpful as resources (Larson & Odoni, 1997-1999). These models will be used throughout this section of the literature review, in order to provide more clarity to the study at hand. Transportation arteries will be represented as links within a particular network (Frank & Frisch, 1971). Where they intersect will be the nodes. Travel, then, takes places in the nodes and along the links of a network, and is restricted to those areas (Larson & Odoni, 1997-1999). It is also assumed that demands for services of any kind will be generated only at a specific number of points, and those will be designated as network nodes (Larson & Odoni, 1997-1999).

Some may feel that this finite number when it comes to places for service will lower the usability and usefulness of the network, but this is really not the case. As many nodes as a person wants can be placed along the networks, allowing realistic and detailed models of a particular areas, the people moving through it, and the things that those people need (Larson & Odoni, 1997-1999). The intensity of demand for service of a particular node will be weighted, so that the true value of it and need for it as represented in society can really be seen. Without this weight, it would appear that all of the nodes were equal (Larson & Odoni, 1997-1999). Both studies and common sense show that this is not the case, and that some nodes (services and/or businesses) are more heavily used and requested than others. These nodes create more traffic, and therefore should be weighted differently (Larson & Odoni, 1997-1999).

From the standpoint of median problems, consider the following:

An undirected network G (N, a) with n nodes, where k is a positive integer (i.e. The number 1 or higher), and specific points on a graph helps to provide the minimum distance between points and the j node. In other words:

Source: Larson & Odoni, 1997-1999 http://web.mit.edu/urban_or_book/www/book/chapter6/6.5.2.html

Complicated, yes, but it is required to really address the median problem issues. It helps to find the k medians and from that the expression of the average travel distance (Larson & Odoni, 1997-1999). There is an assumption made in the above equation that must be noted, however. That assumption indicates that the demands that come about through any given node will then be exclusively served by the facility that is closest to that node (Larson & Odoni, 1997-1999). Of course, real life tells people that this is not necessarily the case. It should work that way, but there are times when it does not. This is the crux of the problem -- things should be convenient for everyone, but they are often not, because of where the facilities are located. Urban planning and facility location concerns are trying to address this, which is why studies of this nature are actually necessary.

Facility planners who get to that point are generally familiar with Hakimi's Theorem, which would indicate that there would be at least one set of k-medians that would be found solely on the G. nodes (Hakimi, 1964). There is much practical significance to the theorem, because it shows that the search for places to locate facilities can be limited to the nodes of G, instead of the infinite number of points that could be seen all along the G. link (Larson & Odoni, 1997-1999). That narrows down the field somewhat, and it's also great news for any person or facility company or organization that is trying to determine where to locate something. They won't be left picking a random point along the G. link, and can, instead, choose one of the already-established nodes as a place in which to locate their facility (Larson & Odoni, 1997-1999).

If the number of facilities that is required works out to be larger than the number of nodes that are available, locating at least one facility per node will mean a travel distance of zero, overall (Larson & Odoni, 1997-1999). In other words, the facilities that are available will be laid out in the best possible pattern and fashion so as to maximize efficiency and convenience for people who use the services (Handler & Mirchandani, 1979). There is obviously no way to put all of the facilities into the same space, and some of them take up more land than others, but there is no reason that urban planning officials, city leaders, and companies that want to build in a particular area cannot work together to meet everyone's needs. Often they want to accomplish this, but they simply are not sure what the best way to go about it would be.

Consider, as an example, a network model of an urbanized area, shown on the following pages and reproduced from Larson & Odoni, 1997-1999 http://web.mit.edu/urban_or_book/www/book/chapter6/6.5.2.html.

All of the nodes (a through H) indicate points at which service demands are being generated. Major roads in the area also intersect at these nodes. A new facility is expected to be located in the area, and the prospective users of that facility will need to travel to it if they want to use the services provided there (Larson & Odoni, 1997-1999). They cannot simply make a phone call or conduct their business online. The demand figures for the services (on a daily basis and in units of 100s) are seen in parentheses next to each node. The numbers next to the links are length of road segments, measured in miles. In order to determine where the facility should be located, the information in the figure can be used to determine the shortest average travel distance (Larson & Odoni, 1997-1999). This is an excellent way to figure out the best location for a facility, and to avoid the problems that often come from poor planning of a facility's location (Lock, 1996). From the information collected based on the figure, it is possible to calculate minimum distance figures, as shown here:

Then, the results would be extrapolated and tabulated:

The same type of figures can also be used for more rural areas, where the nodes would then be towns, instead of points within one town (Larson & Odoni, 1997-1999). This is an important issue for medical and other emergency services, because it is vital that these services are set up to minimize the distance they will have to travel when responding to a call for help. The services will likely need to be located within one of the towns, but calculations will need to be performed to determine which town, just as they would be performed to determine where, within a specific town, something should be located so the travel distance for everyone involved will be minimized as much as possible (Larson & Odoni, 1997-1999).

Consider, as well, that the calculations that allow a person to determine where a facility should be placed based on median issues can also be used to determine where more than one facility should go. That is great for cities that are expanding and looking to add more facilities, and also for urban areas that are revamping and reinventing themselves to the point that they are trying to bring in more business (Mirchandani & Odoni, 1979). It is also good for cities that know they need to adjust their layout, or that see the need for services that are not where they should be for maximum efficiency (Larson & Odoni, 1997-1999). As urban areas grow and spread out, one fire station, police precinct, or medical facility might not be enough (Toregas, Swain, Revelle, & Bergman, 1971). They need more, and determining where to place that facility can literally make the difference between life and death for some people who need those types of services.

Median problems are not the only issue, however. There are also requirements problems that must be addressed. Facilities have to be in certain places to achieve the standards that they must meet in order to be effective (Larson & Odoni, 1997-1999). These standards could have been set by their parent company, or they could have been set by city, state, county, or federal leaders who have imposed specific rules and restrictions on companies in a particular area (Rosenfeld, 1994). When the question of where to place a facility and how to handle things most effectively is asked from a requirements standpoint, the same basic calculations can still be used as a baseline to provide answers (Larson & Odoni, 1997-1999).