Mathematical model and simulated annealing algorithm for setup operator constrained flexible job shop scheduling problem

In the vast majority of the published article on flexible job shop scheduling problems (FJSP), machines are the only resources with limited capacities. There are also a sizable number of research articles in FJSP in which workers (machine operators) are constraining resources in addition to machines. In those articles, a worker performs the sequential steps of the production process and must stay with a machine. However, we argue that with the increasing adoption of numerically controlled machines with self-controlling capabilities, operators become machine tenders rather than individuals performing the sequential steps of the production process. Hence, the assumption of machine tenders as constraining resources that can result in the idling of expensive numerical controlled machines cannot be justified. Moreover, the replacement of machine tenders with automation and robotics increasingly becomes standard practice. In contrast, skilled setup operators remain critical and constraining resources since automating their tasks cannot be easily achieved. This paper proposed a mathematical model for a new setup operator constrained flexible job shop scheduling problem (SOC-FJSP) where setup operations are assumed to be anticipatory (detached). Contrary to a machine tender, a setup operator needs to stay with the machine only while performing setup. Once setup is completed, a setup operator becomes free and available to perform setup operations on a different machine. The assumption of a setup being detached from operations allows the overlapping of a setup operation of a job with the setup and processing of its preceding operation, enabling makespan reduction and better utilization of machine tools and setup operators. To solve the proposed mathematical model, we develop a simulated annealing (SA) algorithm. We further expand the model and the algorithm to account for sequence-dependent setup time and workload balancing among the setup operators. Extensive numerical studies were conducted to illustrate the various attributes of the proposed mathematical model and the convergence behavior of the proposed algorithm.