A Lagrangean decomposition optimization approach for long-term planning, scheduling and control

Abstract

A decomposition strategy to address the simultaneous solution of large-scale planning, scheduling and control problems (PSC) is proposed in this work. Long-term 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 non-linear 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.