A Location Allocation Model for a Territorial Design Problem with Dense Demand

The authors present in this work a proposal that allows establishing the relationships between the facilities location problem and the client allocation within a dense demand environment in territorial design. This proposal can be seen as a basic methodology to give support to the decision making. The use of this application lets one know the production facilities location, warehouses or distribution centers in a geographical space division. On the other hand, solving the client's dense demand for goods or services, means finding the location of facilities in a populated geographic territory, where the population has a demand for services in a constant basis. Finding the location is obtaining the decimal geographical coordinates in longitude, latitude where the facility is located, such that the product or service transport costs the least. The implications and practical benefits of the results from this work allow an organization to be able to design an efficient logistics plan in benefit of its supply chain. The problem the authors present is a territorial design and optimization one due to the fact that the required territorial partition demands the creation of compact zones where the minimum distance between the geographical objects is implicitly optimized. This problem belongs to the NP-hard class, where the use of a metaheuristic to attain approximated solutions becomes a necessity, Variable Neighborhood Search was chosen because it achieves good solutions for this kind of problems. Once the territory has been partitioned into k zones where the centroid of each zone is the distribution center, as a first step the authors proceed to apply the dense demand with continuous functions and this is the main original contribution of this paper: Finding the location of facilities inside a territory where the population has a dense demand for services. The location obtained means having available the decimal geographic coordinates in longitude and latitude from the location point in such a way that the products or services transfer has a minimum cost. Finally the Weber function is minimized, which weights are a function that represents the population's demand in every territory, multiplied by the Euclidean distance between the potential location points and demand points.