Real-time admission control in a queue-time loop production system

The typical flow shop production system with queue time constraints consists of a queue-time loop with multiple stages and a limit on queue time between two consecutive stages. This paper proposes a mixed integer linear programming (MILP) model to address the dynamic environment such as job arrivals and machine failures of the production system. We determine the admission control decision at each stage in a queue-time loop and then reschedule the production after the real-time status of job arrivals and machine availability are updated. The combinatorial Benders' cuts (CBC) is used to solve the MILP model which decomposes the variables into integer and continuous parts. In order to reduce the model's size, the phase-step method (PS) is proposed and then is combined with the CBC, called CBC-PS method. Further, the production schedule of a multistage queue-time loop is generated. We find that the CBC-PS method can reduce up to 39.1% of the number of scrap jobs compared to first-in-first-out (FIFO), threshold dispatching (TH), and reaction chains (RC) heuristics.