# Dynamic Job and Conveyor-Based Transport Joint Scheduling in Flexible Manufacturing Systems
###### Abstract
In order to address this complexity, we propose a heuristic named Sched-T, which falls under the _stochastic local search_ (SLS) approach [13]. SLS encompasses well-known algorithms such as simulated annealing and tabu search. A primary challenge is evaluating potential moves when exploring the solution space. A slight change in the scheduling sequence has a cascading effect on the remaining tasks, as the sequence depends on transfer times, which, in turn, depend on the execution sequence. While existing solutions rely on an approximate evaluation of each move (e.g., the computation of the critical path), we adopted a randomized approach, accurately assessing a few random neighbors. Given Sched-T's ability to quickly compute complex schedules, especially in the case of dynamic job arrivals, we employed the \"total rescheduling\" strategy [14]. This strategy considers newly arrived jobs alongside those not yet scheduled, resulting in a new schedule that integrates with the current one. This approach is versatile, accommodating events beyond job arrivals, such as scheduled machine maintenance [15]. Here, we evaluate Sched-T on a set of instances publicly available without transfer times [16]. In such cases, our heuristic achieves results comparable to those of the previously proposed versions. Subsequently, we analyze instances generated from a production line where the transfer times are available. Although the problem can be modeled using mixed linear integer programming (MILP) approaches, standard MILP solvers fail to find a solution in a reasonable time. Consequently, Sched-T emerges as the only viable approach. Our results demonstrate that when applying the schedule found by Sched-T to a real-world production line, the predicted makespan closely aligns with the actual outcome. Conversely, using a schedule derived without considering the transport system, as seen in the literature, results in a makespan that is up to 30% larger than that achieved using Sched-T's schedule. In our approach, we consider dynamic arrivals and compare the total rescheduling strategy using clairvoyant scheduling, i.e., a scheduling type whereby future job arrivals are known in advance, and show that the total rescheduling strategy produces close-to-optimal scheduling. This article builds upon the findings presented in [17] in several ways. Specifically, we delve into the scenario of dynamic arrivals, where the schedule must be recalculated,which is in contrast to the static case examined in [17], where all jobs were available at the onset of the scheduling period. This necessitated a redesign of the scheduler to manage partially processed, waiting, and newly arrived jobs. Consequently, this updated definition encompasses the static case as a special instance, thus representing a generalization of the problem. Furthermore, we present a clear system model and problem formulation, along with an expanded comparison of our heuristics. This comparison includes additional instances, additional performance metrics, such as the running time of our scheduler, and diverse layouts for real-world experiments. In summary, the contributions of our work are the following. We provide a heuristic for the JSS problem that takes into account the transport system based on a conveyor belt and no buffers at the stations. We consider a dynamic scenario where jobs continuously arrive while we managed the partially processed jobs and the newly arrived jobs, making for a total rescheduling strategy. We tested our solution in a real-world production line to show that if transport times are not considered, the scheduler produces results that may contain large errors. In summary, the contributions of our work are as follows:  
* We propose a heuristic for the Job Shop Scheduling (JSS) problem that incorporates a transport system based on a conveyor belt and no buffers at the stations. * We address a dynamic scenario where jobs continuously arrive while we effectively manage partially processed jobs and newly arrived jobs by adopting a total rescheduling strategy.