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I recently asked this question about formulating a max flow diagram for hospital patients. I am now considering a secondary objective which is to maximize the effetiveness of the scheduled treatment. I know that if a single-objective minimum cost network flow IPs has integral parameters, then its LP relaxations has the integrality property.

Would dichotomic search for biobjective LP relaxation guarantee finding a subset of the IP's nondominated frontier? Would it guarantee finding the entire nondominated frontier?

Note: I do realize there are other ways to solve this, but I am specifically looking to answer these two questions, if anyone can help here.

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    $\begingroup$ +1 But the reason why you have a close vote right now is probably because you're asking multiple questions in one post. I think you should ask separate questions if you have multiple questions. $\endgroup$
    – Nike Dattani
    Jan 14, 2022 at 0:12
  • $\begingroup$ Sorry, I'm no expert in the topic of your question, I just came across the question in the review queue because someone had voted to close it! $\endgroup$
    – Nike Dattani
    Jan 14, 2022 at 1:56

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The first thing that comes to mind, is, to try to model the process in something like (timed?) colored Petri nets. Then, perhaps do some process mining and network partitioning and shortest path tree computations. As long as the search converges to a local minimum, it would be locally non-dominated. So, if you add a dimension for every position in the space, it would be globally non-dominated. For finding the entire frontier, we simply solve the problem in a projected surface space. You should probably think of some separate quality statistic and search heuristic for the entire non-dominated solution space as well.

Also, consider using one of the well-known process mining and modeling packages. Those should be able to do most of the things I've mentioned out of the box, and many more.

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    $\begingroup$ Well, you did ask multiple questions. But sure. I will think about it, and update my answer. $\endgroup$
    – Discrete lizard
    Jan 14, 2022 at 5:36
  • $\begingroup$ Can you delete this? The system won't let me delete the post. $\endgroup$
    – Devita J
    Jan 17, 2022 at 22:21
  • $\begingroup$ Why do you want to delete it? We want to keep question and answer pairs, so that we do not only help you, but to help others in the future as well. If you want to delete it, you can flag it for the moderators, but they will likely refuse your request, as there has already been a partially useful answer. $\endgroup$
    – Discrete lizard
    Jan 18, 2022 at 8:53
  • $\begingroup$ Because the person who proposed this questions doesn't want me to post it publicly. $\endgroup$
    – Devita J
    Jan 18, 2022 at 11:21
  • $\begingroup$ @DevitaJ Can you provide more information about the reason for this removal request? Also, please make ticket to the CM team to remove this information. or.stackexchange.com/contact $\endgroup$
    – Discrete lizard
    Jan 18, 2022 at 14:21

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