I will try my best to concisely explain my query, but may struggle with terminology and core mathematical logic as I do not come from a formal mathematics background.
I have a rudimentary knowledge of linear programming, specifically from its appearance as a function in excel.
For business optimization reasons, I need to make a model which can instruct me on an optimal set of steps to take, such that there are multiple discrete progressions in time (T1...Tn), where the values of decision variables, and the available modifications to those values at each step of T are contingent upon the values that were decided in the previous step of T.
As far as I know, linear optimization can take a single set of variables and set their values all at once such that a given variable is maximized or minimized. However I'm not sure if/how this would work if the model had to determine a chain of values for a decision variable where each subsequent one was contingent upon the previous value, and leading towards an ultimate, optimal result.
My intuition tells me it might have something to do with a series of nested LP models, where I start at the end and then work backwards, but I'm not sure.
Specifically what I'm looking for in answers: 1. To further my research, I'd like to know if what I described actually has a documented term/name associated with it, or whether it is simply a form of linear programming requiring a more complex model than I have thought of. 2. If the latter, any hints in terms of how I could build such a model would be appreciated. 3. Additionally, (although perhaps slightly off topic), a recommendation as to which programming language, method or tool I could use to build such a model would be greatly appreciated. My preference is the excel (or google sheets) linear optimization tool, but as I mentioned, I'm not sure if it's the right fit, or even the kind of processing power that would be required for a model with this many calculations.
** In case my theoretical explanation was insufficiently clear, more tangibly, one can think of it as an LP to maximize board game play efficiency, where the model has to calculate the series of optimal moves to get to the end in the shortest time, where the value of movement each turn will be affected by previous values.