A Lagrangean Decomposition Optimization Approach for LongTerm Planning, Scheduling and Control Abstract   A decomposition strategy to address the simultaneous solution of largescale planning, scheduling and control problems (PSC) is proposed in this work. Longterm PSC problems are hard to solve because of the large number of both discrete and continuous decision variables embedded in such optimization formulations. Improved optimal decisions can be realized by taking into account natural interactions present in PSC problems. This is the main justification for a simultaneous solution approach of such optimization problems, although this consideration strongly increases the computational solution of PSC problems. In this work, the integrated PSC problem is reformulated using Lagrangean Decomposition, resulting a model decomposed into planning and scheduling (PS) and control (C) subproblems. In the case study, the proposed solution strategy was applied to a multiproduct CSTR represented by the model of Hicks and Ray, which presents strong nonlinear behaviour, over planning horizons of three, four, eight, twelve, and sixteen periods lasting one week each. Moreover, the PSC model incorporates a nonlinear model predictive control (NMPC) scheme in order to realize dynamic transitions which are as smooth as possible. The results were compared, in terms of the optimal profit and the CPU time consumed, against those produced by the direct solution of the problem (without using a decomposition strategy) for the specific case of three planning periods, showing a significant reduction in the computational effort.

An Optimal Control Approach to Scheduling and Production in a Process using Decaying Catalysts Abstract   This article presents a novel approach to optimise scheduling and production planning to meet seasonal demand in an industrial process using decaying catalysts, based on its formulation as a multistage mixedinteger optimal control problem (MSMIOCP). Unlike existing methodologies, the MSMIOCP formulation allows to solve this problem as a standard nonlinear optimisation problem without combinatorial optimisation methods, which can be advantageous in providing reliable, robust and efficient solutions. Using this formulation, four case studies of this problem, differing in reaction or deactivation kinetics, are investigated. Two different solution implementations are used, each having their own relative advantages. The first implementation demonstrates a bangbang behaviour for the linear scheduling controls, consistent with a theoretical analysis, but faces integration problems and does not always produce high quality solutions. The second implementation, while not demonstrating the bangbang property, always produces high quality solutions and shows the advantages of the MSMIOCP formulation over existing methodologies.