Robust minimum cost flow problem under consistent flow constraints

Abstract The robust minimum cost flow problem under consistent constraints (RobMCF $$\equiv $$ ? ) is a new extension of the (MCF) problem. In RobMCF problem, we consider demand and supply that are subject to uncertainty. For all realizations, however, require value on an arc needs be equal if it included in predetermined set given. objective find feasible flows satisfy requirements while minimizing maximum occurring among realizations. case finite discrete scenarios, derive structural results which point out differences with polynomial time solvable MCF networks integral demands, supplies, capacities. particular, Integral Flow Theorem Dantzig Fulkerson does not hold. this reason, entire paper. We show strongly $$\mathcal {NP}$$ NP -hard acyclic digraphs by reduction from (3, B 2)- Sat Further, demonstrate weakly series-parallel providing Partition . If addition number scenarios constant, propose pseudo-polynomial algorithm based dynamic programming. Finally, present special for can solve time.