Section 7.4 The Big Problem: Optimizing the Placement of Mobile Health Clinics
How can nonprofits take multiple social determinants of health into account in order to create accurate measures of medical need in the communities they serve? How many possibilities do they need to consider when deciding where to place mobile clinics? How might the number of possibilities thus depend on the types of resources available? How could geographical considerations (such as not wanting to have multiple clinic locations too closeWindow() together) be taken into account?
Let’s imagine that a nonprofit such as Open Arms Free Clinic 1 (OAFC) has tasked us with finding the best locations in a community for their mobile clinic. To get an idea of the size of the problem to be solved, we may first want to compute the number of possibilities of where we might place the clinics, under a few different scenarios or assumptions. This motivates the multiplication and division rules for counting, which leads to the idea of permutations and combinations. In the next section, we will consider some more complex scenarios motivating the counting techniques of the addition and subtraction rules.
Next we need to quantify medical need. We will introduce a basic way of combining several variables of interest in a single model called a parametric linear model. In doing so, we will establish a measure of medical need based on social determinants of health, and use it to identify the areas of greatest need.
Perhaps the solution we obtain in the previous step is inadequate because it suggests mobile clinic placements that are clustered too closeWindow()ly together. We will describe how we can account for this by introducing some additional assumptions that will help us ensure that we are spreading out our resources. In the process, we will learn about discrete optimization.
Finally, we will consider one additional variable closeWindow()ly related to poverty, and put everything together. A similar solution to this problem was presented to OAFC in Spring of 2022 by actual students at Beloit College.
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