The so-called reason by analogy is just gradient descent to approach local optima in optmization. The "by first principle" is just providing an approximate (ideally convex) model and solve it analytically for global optima. The problem is generally very hard (#P hard), both for formulating the problem and solving it. Global optimum of course in theory is better, but the quality of your objective function and constraints could easily offset this advantage. If you can come up with a simple linear programming problem for the battery example - that's great, but most likely you won't due to the prescence of competitor, market and policy constraint.