tag:blogger.com,1999:blog-8781383461061929571.post3696058543734600280..comments2024-03-14T09:08:19.035-04:00Comments on OR in an OB World: Peeking Inside the Black BoxPaul A. Rubinhttp://www.blogger.com/profile/05801891157261357482noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-8781383461061929571.post-81470826197326907812011-05-30T10:54:01.740-04:002011-05-30T10:54:01.740-04:00Fair question. For LPs, I think the answer is no. ...Fair question. For LPs, I think the answer is no. There are more and less efficient ways to model some LPs, and at times it may be useful to understand the impact of degeneracy or density, but it's hard to completely screw the pooch with an LP. LP users sometimes get confused about how to find alternate optima (or find out whether alternate optima exist), but you can answer that in terms of solver output without getting into algorithmic requirements.<br /><br />For MILPs, I'm a bit more ambivalent. (Convexity issues for MINLPs are covered by the post.) Understanding how branch-and-cut works (particularly the bounding part) may help with choices about whether to use a "big M" formulation rather than decomposition, how large to make M, whether to use "indicator constraints" or do the equivalent yourself (back to "big M", but with you rather than the solver picking M), etc. The nice thing about LPs and MILPs, though, is that you automatically get convexity; so, other than maybe thinking a pure LP solver can do a MILP, it's hard to pick the wrong tool for the job.<br /><br />Poor scaling can lead to incorrect results in an LP or MILP, as can subtle modeling issues (too subtle to call them user errors). I don't know whether to classify this as a case where you need to understand something about LP/MILP algorithms, or whether to say it's a generic modeling issue that the user should understand without regard to the solver.Paul A. Rubinhttps://www.blogger.com/profile/05801891157261357482noreply@blogger.comtag:blogger.com,1999:blog-8781383461061929571.post-42295770572284688252011-05-30T08:56:39.268-04:002011-05-30T08:56:39.268-04:00You seem to suggest that understanding the solver ...You seem to suggest that understanding the solver algorithm is important independent of problem type. For LP and MIP, I don't think you need to know the solver innards. Your example makes sense for NLP, but do you have a similar example for LP and MIP?Irvhttps://www.blogger.com/profile/13988868264505680907noreply@blogger.com