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Scheduling in Production, Supply Chain and Industry 4.0 Systems by Optimal Control: Fundamentals, State-of-the-Art, and Applications

Specific scheduling problems with complex hybrid logical and terminal constraints, non-stationarity in process execution as well as complex interrelations between dynamics in process design, capacity utilization, and machine setups require further investigation and the application of a broad range of methodical approaches. One of these approaches is optimal control. The objectives of this survey are twofold. The first objective is to derive major contributions, application areas, limitations, as well as research and application recommendations for the future regarding optimal control applications to scheduling. The second objective is to explain control engineering models in terms of industrial engineering and production management. In this paper, we provided a survey on the applications of optimal control to scheduling in production, supply chain, and Industry 4.0 systems with a focus on the deterministic maximum principle. Optimal control approaches take a different perspective as mathematical programming methods which represent schedules as trajectories. We consider optimal control models, performance analysis qualitative methods, and computational methods for optimal control. We provide a brief historic overview and clarify major mathematical fundamentals whereby the control engineering terms are brought into correspondence with industrial engineering and management. The survey allowed the group-ing of models with only terminal constraints with application to master production scheduling, models with hybrid terminal-logical constraints with applications to short term job and flow shop scheduling, and hybrid structural-terminal-logical constraints with applications to customized assembly systems such as Industry 4.0. Computational algorithms in state, control, and conjunctive variable spaces are discussed. Finally, we derive major contributions, application areas of different control methods, and their limitations. This paper also delineates research and application recommendations for future research.