# Using Spatial Multi Criteria Analysis for simultaneously locating various facilities?

Is it possible to use SMCA (Spatial Multi Criteria Analysis) for determining simultaneously where to locate various facilities?

Suppose, for example, I'm planing to build a new city and everything has already been determined, with the exception of the hospital locations. If I needed to build a single hospital, it would be easy to use Spatial Multi Criteria Analysis to determine where it should be placed. Nevertheless, how can the problem of determining the locations of possibly many hospitals be approached?

I googled every possible keyword to find similar problems, but no success so far. My current guess is that I should break the problem in two, first creating a model with SMCA to assign a cost to each choice of hospital location and then creating a single utility function combining the costs of any combination of choice locations. Then I could use gradient descent (or other non-linear optimization procedure) to find the combination of locations which maximizes my utility function.

I hope this makes sense! I'm new to Operations Research and I just got the opportunity to receive "free consulting" for my company, but for that I need to submit a project until Friday and my boss believes this is a problem we could tackle.

• Welcome to OR.SE! There is a large body of literature on facility location, which might help you. However, that literature has its own set of methodologies (usually using integer programming, not nonlinear programming), which doesn't necessarily include SMCA. – LarrySnyder610 Sep 4 '19 at 20:57

Although it seems to be late to answer this question (as you need to submit a project until Friday), the following papers can be helpful in determining a solution approach to the multi-facility decision-making framework:

In the paper1, the authors applied mixed integer goal programming in determining the facility location, route and flow of different varieties of recyclable waste paper in the multi-item, multi-echelon and multi-facility decision-making framework.

While surveying the MCDM methods in facility location problems the paper2, stated that: "There are many decision-making problems whose information is spatial (geographical). In many real-world problems, the decision-maker likes to pursue more than one target or consider more than one factor or measure. Such a desire transforms the decision-making problem to a multi-objective decision making (MODM) problem or a multi-attribute decision making (MADM) problem. These groups of problems all come together in one category, named multi-criteria decision making (MCDM) problems."

Also, (based on my own experience for master thesis), there are some of the MADM methods which can be used to rank the alternatives based on their closeness to the most desired option for the DMs and also their remoteness from least desired answer. Examples of these type of methods are TOPSIS and ELECTRE.

[1] Pati, Rupesh Kumar, Prem Vrat, and Pradeep Kumar. "A goal programming model for paper recycling system." Omega 36.3 (2008): 405-417.

[2] Farahani, Reza Zanjirani, Maryam SteadieSeifi, and Nasrin Asgari. "Multiple criteria facility location problems: A survey." Applied Mathematical Modelling 34.7 (2010): 1689-1709.

• Just a small note: The goal of OR.SE is to build a body of good Q&A for anyone to use in the future. It's not (only) here to help people get immediate help with projects. What I mean is, even though the OP needed an answer for a certain deadline, your answer is not late or irrelevant just because it misses that deadline. – LarrySnyder610 Sep 6 '19 at 12:41