Facility Design and Planning

Comprehensive Facility Location Models

Comprehensive facility location models are useful in the formulation of location and allocation concepts, whose principal goal is a determination of the appropriate location for a facility. These models are useful where an organization intends to exercise cost efficiency. Also, quadratic area models may be employed at the micro and macro levels to work out a suitable location for a facility, particularly those facilities that show significant flow as well as interaction (Zanjirani 34). In this paper, some of the models will be considered and a detailed discussion of their application will be provided. For the models that are to be discussed, sufficient heuristic, as well as optimal solution approaches, are also provided.

Set Covering Model

One of the models used in the location of facilities is the Set Covering Model. This model is applicable where the planner wants to ensure that those who need the services of a particular facility have access to at least one such facility. An example that thoroughly illustrates this point is that of a fire station or emergency facilities, colleges, libraries or state institutions which need to be located in a strategic location so that it can comfortably serve the target population. Where the facility is within range, it can be assumed that the user is well covered (Zanjirani 35). The solution to this model can be arrived at by use of general purpose branches as well as bounds. However, this approach is tedious, particularly when the problem to be addressed is colossal. For this reason, there exists a greedy model that has been used to provide a practical solution efficiently. This model is based on the assumption that c j ≥0, j = 1, 2. . . . n.

Uncapacitated Location-Allocation Model

The second type of model that has been found to facilitate facility location appropriately is the Uncapacitated Location-Allocation Model. This model considers a number of factors such as a number of facilities, the population that will make use of the facilities, the cost that will be incurred while transporting a single unit from a facility to the user. Also, the model considers fixed costs, particularly commissioning and operating expenses, the units desired as well as the quantity of units moved from facilities to users. The solution to this model is based on a general purpose approach that is common in many operations research literature. The solution involves establishing root nodes which are then solved by the use of simplex algorithms. A y variable is selected, which is then assigned a practical value. Then two additional subproblems evaluated and a decision will have to be made on the approach to solve them based on two additional tests.

Multiple Warehouse Model

Perhaps a more rigorous model that is useful where there exist real challenges and related constraints. This model applies to problems where there are various products with a known capacity where the need for these commodities as well as the location of those who need them is usually known. For this reason, such goods are sent to the consumers through several warehouses. The restriction, in this case, is that not more than one of these warehouses can be used to serve users in a given region. The purpose of such restriction is to ensure efficiency. Factors such as upper or lower bounds in the context of the capacity of the warehouses, where they can be located, the cost of transportation as well as related fixed costs are all known. The key challenge, in this case, would be finding out the precise location at which the warehouses can be installed. The solution to this model is provided through the use of multiple programming tools. However, due to the existence of binary variables, those minor challenges can be addressed.

Factor Rating Model

Many planners make use of the factor rating model in selecting appropriate locations for various facilities. The use of this model requires a planner to establish the critical factors that influence the location of a facility. The factors are then rated based on their importance. Where factor scores highly on the rating scale, that factor is considered as the prominent and guiding principle. The planner then assigns each of the potential locations according to the observed merits. The rating for each site is then calculated by finding the product of each location and essential factors in this place. The sum of all the goods is worked out for all the factors involved and the location showing a prominent score is the best place. For instance, if a new facility is to be located in India's Delhi, the best location is decided by comparing the factor rating of each location. The best location is that which has the highest factor score.

Load Distance Model

A model that has received wide applicability, particularly in the location of healthcare facilities in India is the load distance model. This model evaluates location on the basis of proximity. The model's objective is a selection of locations that substantially minimize the total weight of loads that are moved to and from a facility. The length between points is assessed based on a coordinate grid. The alternative calls for the use of time instead of distance. A firm that intends to establish a location for its new facility, particularly one that will minimize costs associated with distance, will select a point that will generate acceptable costs even where large loads are to be moved to and from the facility. To arrive at the maximum load and distance relation, distance measurements are used and are multiplied by relevant loads that are likely to be moved from and to the facility. Such loads can be articulated regarding tones for each week. For instance, if this facility is to be used to serve various tracts in a city such as Delhi, coordinate systems such as the one below would be a right approach as centers of the tracts.

Locations of consideration would be (5.5, 4.5) or (7, 2). In this case, the population serves as loads and is used to work out the best location on the basis of rectilinear lengths. The approach to such a problem based on the load distance model would be to calculate load distance scores for each point using the model shown below:

DAB = |XA - XB| + |YA - YB|

Based on this model, the sums of the score for the point (5.5, 4.5) is 239 while the score for the point (7, 2) is 168. From these two values, it can be seen that the best location for this facility would be the point (5.5, 4.5). This model is simpler than the rest but is only applicable to challenges that have very few variables that impact decision-making processes.

Works Cited

7, Farahani R. Facility Location: Concepts, Models, Algorithms and Case Studies. Dordrecht [The Netherlands: Physica-Verlag, 2009. 34-42. Print.