Thought experiments, facility location problems, big box retail

I often play around with a thought experiment in which I imagine a big box store such as a Meijer store, but with the merchandise rearranged according to an attraction/repulsion schema in which complementary goods mutually attract and competing goods mutually repel (mathematically a very difficult problem, hence a thought experiment, rather than something more ambitious like a simulation). The Meijer store contains books, which includes cookbooks. So I imagine a cookbook sold by Meijer as having x and y (and z) coordinates within the store. The cookbook contains some number of recipes. I think of each of these recipes as having x,y,z coordinates, even though the recipes are virtual rather than physical objects. The recipes are “attracted” to the cookbook in which they reside, but they are also “attracted” to the ingredients they call for (in grocery) and the kitchen equipment they call for (in cookware, appliances, etc.). The prepared recipes (in the initial state anyway) are, like the written recipes, virtual objects which nevertheless can be assigned locations for the purposes of modeling. These objects in turn would attract to tableware, which would in turn attract to tables (but also to cupboards…and dishwashers…each object has a life cycle!) So dishwashers “attract” dishes and “repel” other dishwashers. Plates attract spoons but repel other plates. Repulsion between like objects serves to distribute them more evenly. The TV sitcom Last Man on Earth explored the idea of someone living a seemingly comfortable lifestyle for some period of time on the merchandise in an abandoned big box store, in a post-apocalyptic setting. In a non-post-apocalyptic setting (hopefully with reasonably functional supply chains) an “efficient” arrangement of things and virtual things, and ultimately people, in the interior space of a big box store (or perhaps even better, a mall) could I imagine house (and support much of the economic activity of) a few hundred people, in some comfort.

Originally appeared as a comment on Reddit.