Dear or-exchange community, I have what might seem like a trivial question to the most of you, but it puzzles me and I cannot figure it the answer out with complete certainty. I am dealing with 2-stage stochastic programming and I solve programs that have focused on the expected cost so far. Now, I am planning to focus a bit on the minimax side of things. Let's assume that I have a 2-stage SP problem, where in my 1st stage I have to make an investment decision for equipment and for its capacity between two options. In the second stage the operation of this equipment is set to meet some demand. What is uncertain is the cost of operation for each equipment, which I assume consists of three discrete scenarios with known probabilities for each. Therefore, in total, I can create nine combinations of scenarios with their probabilities. It's clear, therefore, to me how to formulate the expected cost problem. For the minimax problem, now, do I have to consider all scenarios again and minimize the worst case or would it suffice to directly take the scenario that gives me the highest cost for both pieces of equipment and solve directly for that? Of course in this case I will not know how to operate it in the other scenarios, but I will know my worst-case outcome, which is what I am interested in. Is this the notion behind minimax problems? Or should I still consider all scenarios, multiply each with their probability and then minimize the worst outcome with probability-weighted scenarios? Does all this make any sense? Any feedback will be appreciated. Regards, George M.
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gmavrom |