production-assembly problem with parallel machines in three steps and in distributed factories

Distributed factories represent a type of manufacturing system in which production is spread outacross multiple geographically dispersed locations. this approach offers several advantages, includingreduced transportation costs, improved responsiveness to customer demand, increased flexibility andenhanced supply chain resilience. the production-assembly flow shop problem with three stages is ascheduling problem focused on optimizing the sequence of jobs to be processed on a set of machines. in thisproblem, the first and third stages involve dedicated parallel machines, meaning that each job is assigned toa specific machine and cannot be processed on any other. the second stage consists of identical parallelmachines, where all machines are functionally equivalent and capable of processing any job. a model ispresented for minimizing total tardiness times. since the problem under investigation is np-hard, solving itexactly is either impossible or highly time-consuming (depending on the processor’s capability) for largeinstances. consequently, the hybrid biogeography-based optimization dominance rules (hbbo) algorithmis proposed to address the problem in larger instances. this algorithm is an enhanced version of thebiogeography-based optimization (bbo) algorithm, incorporating dominance rules. the taguchi methodhas been employed to determine appropriate parameter values. the results obtained from the model andalgorithm demonstrate the algorithm’s acceptable efficiency and the inclusion of dominance rules has furtherimproved the outcomes.