A Real-Case Scheduling of Cutting Stock Operations as a Two-Stage Hybrid Flow Shop Problem with Eligible and Common Machines and Job Position Constraints

In this work, we are interested in pattern scheduling that appears in cutting stock problems as a special case of a two-stage hybrid flow shop problem with unrelated parallel machines at each stage. The problem conceptualization emanates from a real case of the cardboard-cutting industry. Some machine eligibility limitations to process specific sub-jobs are combined with common machines between the two stages with multi-function capabilities. Their availability disjunction while processing sub-jobs issued from different stages must be taken into account. In addition to this first complication-enhancing layer, the problem includes a particular job positional constraint. Precisely, even for the shared machines between stages, a unique position for a job is required in the sequence of jobs for each machine. Moreover, setup times related to pattern changeover and transfer between stages are involved. We propose for this new problem setting a mixed integer-programming model that enriches the integrated cutting stock and scheduling research framework. Its objective is to minimize production costs, including job flow time costs and makepan-related labor costs. The industrial study case is used to generate a pattern dataset after solving a prior bin-packing problem with polygon-shaped items. The experimentations about the scheduling problem show that the proposed model yields satisfactory and promising results.