A lot-sizing problem in deliberated and controlled co-production systems

We consider an uncapacitated lot-sizing problem in co-production systems, which it is possible to produce multiple items simultaneously a single production run. Each product has deterministic demand be satisfied on time. The decision choose co-produce and the amount of throughout predetermined planning horizon. show that with strongly NP-Hard. Then, we develop various Mixed-Integer Linear Programming (MILP) formulations LP relaxations all MILPs are equal. separation algorithm based set valid inequalities, lower bounds dynamic relaxation our constructive heuristic used obtain initial solution for solver, form basis proposed Branch & Cut problem. test models algorithms different data sets provide results.