# Dynamic Job and Conveyor-Based Transport Joint Scheduling in Flexible Manufacturing Systems
## 4 Exploring the Solution Space
### Detailed Solution
Given the schedule returned by Sched-T, we ran the jobs on the production line and recorded the makespan. The results are shown in Table 3, columns **Experim.-I**, and **Actual**. Sched-T is able to predict the actual makespan obtained from a real-world production line with an error smaller than 5%. Additionally, in this case, there is no specific job characteristic that might influence the small variability for the different instances. Then, in column **Experim.-II**, we consider what happens if the scheduler does not take into account the transport system, as most of the schedulers in the literature do. In this case, they would produce a schedule that is not optimal. In particular, we run Sched-T by setting all the transport times to zero and we obtain a schedule that is fed to our production line. We record the makespan obtained in this case and compare the error obtained with the one computed in columns **Experim.-I**. If the scheduler does not include the transport times, the resulting schedule contains an error of up to 23%, which is 18% greater than the one obtained by the schedule considering the transport times. Thus, the makespan obtained using the real system by considering the transport time improves the makespan by up to 14% with respect to the one found without considering the transport time. Table 4 shows the results obtained by applying Sched-T to a different plant configuration depicted in Figure 7. This new configuration consists of a modified version of our real-world case study: we added a bay and a machine of the same type on the opposite side of each existing one to implement production redundancy. We built this new configuration by exploiting Tecnotaxic Plant Simulation, a commercial state-of-the-practice discrete event simulation tool. The simulation allows for testing our proposed algorithm on a different scenario, enabling the calculation of simulated production times (e.g., makespan) and demonstrating that Sched-T can also be applied to different plant configurations. We executed the same test using Table 3, generating new instances of the same size. The results show that when considering transport time, Sched-T allows for reducing the error of the estimated makespan, keeping it within 5% and lowering it by 17% when not considering transport time. Figure 7: The modified layout of the production line used to test another scenario. We added a bay and a machine of the same type on the opposite side of each existing one. To sum up, our proposed solution allows us to estimate the makespan within a reasonable time frame with high precision. By correctly estimating the transfer times time, we are able to build a more precise schedule. ### Multiple Arrivals

The results discussed above focused on the efficiency of the solution at each single job arrival. In this section, we evaluate how the schedule changes as new jobs arrive. We consider the same set of instances without the transport system (Section 5.2) and with the transport system (Section 5.3). We remove \(p\)% of the jobs, compute the initial makespan without these jobs, and uniformly spread the arrival of the removed jobs at random between zero and the initial makespan. For each arrival, we update the schedule and the makespan. In order to evaluate the quality of the final makespan obtained in this way, we consider an _ideal_ scheduler that knows all the jobs (the initial ones and the future ones, with their arrival times) in advance and computes a single optimize schedule; we call this scheduler _clairvoyant_. Figure 8 shows the difference (in percentage) between the final makespan obtained after updating the initial makespan at every job arrival and the makespan obtained with the clairvoyant scheduler for different percentages of dynamic jobs (jobs removed from the instances). In both cases (with and without the transport system), updating the schedule at every arrival provides a solution that is comparable to an ideal scheduler that has all the information in advance.