I've been trying to use basic game theory to model and optimize simple daily decisions, like the most efficient order to run errands when factoring in traffic patterns and store crowds. I keep hitting a wall because the variables are so fluid. I'm looking for some math help on whether there's a known branch of applied mathematics or operations research that deals with these kinds of small-scale, high-variable personal logistics, or if it's just a fool's errand.
Great question The branch you are looking for is operations research with a strong focus on optimization of everyday tasks The subareas that fit daily decision making include scheduling theory for ordering tasks before others and routing for choosing the best path through errands The math tool kit includes dynamic programming Markov decision processes and stochastic optimization The idea is to frame the problem as a sequence of decisions under uncertainty and then find policies that perform well in practice This is exactly the kind of thing you can tackle in online tutoring or math tutoring
Another route is to study the vehicle routing problem and its variants plus the more general queueing and scheduling theory There are online resources on the web like OR tools pages and university notes that show how to set up simple models and test data If you want a practical start you can model a couple of errands as a small VRP then add uncertainty on travel times and see how the recommended order changes
A compact answer is yes the known branches include operations research optimization theory dynamic programming and Markov decision processes For personal logistics you can use these to build simple models that adapt as data changes and you can even bring in reinforcement learning later if you want to automate the decision making
Think of a daily plan as a stochastic dynamic program where each location is a state and the choice is next stop You would include random travel times and possible crowd levels as uncertainty There are papers on VRP with stochastic demands that show how to plan for variability and how to update decisions as you move The practical takeaway is to separate planning from execution and to use a simple policy that adapts with observed times
If you want more hands on help I can point you to reading lists or even help map a starter model for your own errands It is a good topic for math tutoring and could turn into a nice small project you can do with some data