I know it depends on the specific problem instance, but approximately how large of an MIP problem can we write and still be guaranteed that an optimization solver will find a solution? For instance, if we have a mixed integer program with 1,000 variables and 1,000 constraints, can we be guaranteed that no matter what the variables and constraints are, modern optimization software will be able to spit out a solution in a reasonable time frame (defined as 1 month or less on a standard computer)? What about 1 million variables and constraints, or a billion variables and a million constraints, etc.
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graphtheory123
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You might get more feedback here for this one. (don't forget to mention that you xpost). – Kuifje Dec 08 '22 at 14:36
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How do I mention that I xpost? Like I just say it in the question description and then an administrator sorts it out? – graphtheory123 Dec 09 '22 at 18:32
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yes you can mention that you have already posted here, and that you have not received enough attention so trying elsewhere. – Kuifje Dec 10 '22 at 10:14
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This is very problem dependent. There are easy problems and difficult ones. The easy ones allow for larger instances to be solved relatively quickly. – Erwin Kalvelagen Dec 19 '22 at 21:51