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Scheduling tasks in production facilities are usually hybrid optimization problems of a large combinatorial nature. They involve solving, in near-real time, the integration of the operation of several batch units of continuous dynamics with the discrete manufacture of items in processing lines. Moreover, one has to deal with uncertainty (process delays, unexpected stops) and the management of shared resources (energy, water, etc.) including decisions made by plant operators: still, some tasks in the scheduling layers are done manually. Manufacturing Execution Systems (MESs) are intended to support plant personnel at this level. However, there is still much work to do in terms of performing automatic scheduling, computed in real time, that guides managers to achieve an optimal operation of such complex cyber-physical systems. This work proposes a closed-loop approach to handle the uncertainty arising when facing the online scheduling of supply lines and parallel batch units. These units often share some resources, so effects due to concurrent resource consumption on the system dynamics are explicitly considered in the presented formulation. The proposed decision support system is tested onsite in a tuna cannery, to handle short-term online scheduling of sterilization processes that deal with limited steam, carts, and operators as shared resources

In this article, we develop a systematic approach for efficient field reconstruction in distributed process systems from a limited number of measurements. The approach generalizes previous methods for sensor placement so as to be able to handle field reconstruction problems in arbitrary spatial domains where complex nonlinear phenomena take place. Pattern formation in fluid dynamics or diffusion-reaction systems are examples exhibiting complex nonlinear distributed behaviors, especially when taking place in arbitrary 2D or 3D domains. Our approach exploits the dissipative nature of the diffusion-convection process and the underlying algebraic structure of the finite element method to efficiently construct field representations in terms of globally defined basis functions and to optimally select the placement of sensors. The results will be illustrated on a fluid dynamic process: the Rayleigh−Bénard problem