Assembly flow shop scheduling problem considering machine eligibility restrictions and auxiliary resource constraints

This paper investigates a two-stage production system consists of a fabrication stage followed by an assembly stage. There are some unrelated parallel machines in the first stage to process the parts and then, the parts are assembled into the final product at an assembly workstation. To close the problem to real-world condition, machine eligibility, sequence-dependent setup times, and different release times are considered for the received parts. In addition, most of the researchers deal with machines as the only resource in conducting the scheduling problems. However, other additional resources such as specialised labours, tools, and industrial robots are usually not only required for processing jobs but also are often restricted to use. First, the problem is described and a new mixed-integer linear programming model is proposed that can solve the problem in small-sized scales. Since this problem is well known as a strong NP-hard problem, a new heuristic algorithm is proposed based on the basic idea of Johnson's rule. Moreover, two proper lower bounds are introduced as references to evaluate the performance of the proposed heuristic algorithm. Numerical experiments show high quality of the final solutions provided by the proposed algorithm and also indicate effectiveness of two developed lower bounds.