Multicriteria analysis and visualization of location-allocation problems

In a location-allocation problem (LAP), an optimal number of facilities has to be placed in an area of interest in order to satisfy the customer demand. The optimization objective can be, e.g., to minimize costs or to maximize profit and the situation can be characterized by various constraints. The total location area may also be divided into regions which have each their special characteristics. There are often several plausible scenarios for an LAP representing, for example, different budgets limitations, cost functions, or estimates for market growth. In this Thesis, the emphasis is on retail location-allocation problems and it is illustrated with a case study in retailing. When dealing with a large number of location-allocation solutions for various scenarios, it is necessary to examine which option is the best one according to specified criteria. The first objective of this Thesis is therefore to define decision criteria for retail applications. The proposed criteria include several monetary, facility related, and customer related attributes. Besides the facility locations and customer flows, location-allocation solutions are characterized by various derived properties, for example market share, distance to competitors, and the amount of unassigned demand. These derived properties also include the chosen decision criteria. When the total location area is composed of regions, these properties can be expressed for each region and thus have a spatial distribution. In decision support, it is often important to be able to visualize the solutions and their derived properties: finding suitable visualization techniques is also the second main objective of this Thesis. The visualization of geographic properties can be assisted by geographic information systems (GIS). However, existing tools of GIS software are not sufficient for the visualization of dozens of multi-dimensional location-allocation solutions. This problem can be circumvented either by concentrating on the statistical properties of the solution set instead of examining and comparing the options one by one, or by trying to classify the solutions into groups whose properties can then be more easily compared. The methods of cluster analysis and subgroup discovery could prove useful in grouping the solutions. Also, principal component analysis can be used to reduce the dimensions of the problem and to facilitate visualization.