Optimization models for a lot sizing and scheduling problem on parallel production lines that share scarce resources

The purpose of this paper is to propose mathematical models represent a lot sizing and scheduling problem on multiple production lines that share scarce resources investigate the computational performance proposed models. main feature differentiates from others in literature decision which organize should be taken considering availability necessary resources. optimization criterion minimization costs incurred process (inventory, backlogging, organization lines, sequence-dependent setup costs). Nine mixed integer are given and, also, results an extensive study carried out using set instances literature. indicates efficient formulation, able provide high quality solutions for large sized instances, can obtained classical model by making binary variables explicit, facility location reformulation as well single commodity flow constraints eliminate subsequences. Moreover, results, it also clear consideration makes significantly more difficult than traditional one.