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.