Good ways to select best decision among N decisions, each with a profit/loss distribution? [closed]

I'm working on a problem where an asset owner (e.g., owner of a factory, power plant, etc.) can take a number of possible decisions (say 10). Each of those 10 decisions entails certain actions, but the profitability of those decisions is not known in advance (because of uncertainty in a number of the underlying variables). Empirical distributions of the unknown variables can be derived, and the profit/loss distributions can be computed for each of the 10 possible decisions.

What would be some of the standard ways of deciding which decision was best? Each profit/loss distribution has its own mean, standard deviation, percent of the curve which is negative, worst case scenario, best case scenario, etc. Is there a good standard way to make this comparison?

• Ah, I should clarify: does the owner take one of these possible ten decisions or does the owner make ten decisions, each with its own set of possible actions? Aug 8, 2020 at 0:44
• The former. The decision space is really continuous, but in the first step of the analyses I've effectively discretized those decisions into, say, 10 different ones. Aug 8, 2020 at 14:47

1 Answer

This looks like a classic real options problem. Essentially, each decision is an option which will be chosen strategically: the owner will chose a vector of actions from all possible actions, $$A\in\mathcal{A}$$, that maximizes expected utility given the distributions of key variables and outcomes.

If the owner is well-capitalized, maximizing the expected value of profit would be sensible. Some owners might not have infinite cash or might be worried about risk; in that case it would make sense to maximize the expected profit minus some penalty times the risk (which could be measured in many ways).

For more on real options, you might benefit from reading the introductions by Haugh and Pindyck. Also, you should consider solving such problems with stochastic optimization. Hannah has some excellent notes on that and a more complete reference would be Birge and Louveaux.

• Thank you for the helpful comment. I wasn't aware of the term "real options problem" and that gives me a good number of resources to look into. The resources you've listed look extremely relevant and helpful. And yes, I've started this problem using what might be called stochastic optimization (I'm sampling from the distribution and each sample gets its own LP solution). There might be better ways of formulating this, in particular putting the distributions directly into a single optimization and solving for it there. The resources you listed should help me think about those possibilities. Aug 8, 2020 at 14:54