en Optimization Techniques Optimization Techniques پژوهشي Research <div style="text-align: justify;"><em><span style="font-size:12.0pt"><span style="font-family:&quot;Times New Roman&quot;,serif">This paper addresses pattern scheduling within cutting stock problems, treating it as a specialized instance of a two-stage hybrid flow shop (HFS) problem with unrelated parallel machines at each stage. Originating from a real industrial case in the corrugated cardboard-cutting industry (UNIPACK), the problem incorporates machine eligibility restrictions, shared bi-functional machines across stages, and a novel positional constraint that prevents job splitting on shared machines. To address these complexities, we propose a mixed-integer programming (MIP) model that minimizes production costs comprising weighted job flow-time costs and makespan-related labor costs. We complement this with a genetic algorithm (GA) metaheuristic for larger instances. The MIP achieves optimality for instances with up to 20 jobs; for instances with 22&ndash;32 jobs, it returns the best feasible solution found within a 225-second time limit. For all instances where an MIP reference exists (up to 32 jobs), the GA solutions deviate from the MIP reference by an average of 5.2%. For larger instances (up to 200 jobs), the GA produces near-optimal solutions in under 120 seconds, demonstrating strong scalability. Computational experiments on 16 benchmark instances confirm the effectiveness of both approaches and highlight their complementary strengths. </span></span></em></div> Cutting stock, scheduling, hybrid flow shop, eligible machine, shared machine, positional constraint, setup time, mixed-integer programming, genetic algorithm. 121 133 http://ijiepr.iust.ac.ir/browse.php?a_code=A-10-3524-1&slc_lang=en&sid=1 Oumaima Ben REBAH imaoumaima@gmail.com 1800319475328460015353 1800319475328460015353 Yes Department of ManagementGraduate School of Commerce of Sfax, University of Sfax.Sfax, Tunisia. Abdelkarim Elloumi abdelkarim.elloumi@fsegs.usf.tn 1800319475328460015354 1800319475328460015354 No Department of Quantitative MethodsFaculty of Economics and Management, University of Sfax.Sfax, Tunisia. Racem Mellouli racem.mellouli@fsegs.usf.tn 1800319475328460015355 1800319475328460015355 No Department of Quantitative MethodsFaculty of Economics and Management, University of Sfax.Sfax, Tunisia.