A tighter continuous time formulation for the cyclic scheduling of a mixed plant |
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| Authors: | Yves Pochet François Warichet |
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| Affiliation: | 1. CORE and IAG, Université Catholique de Louvain, Belgium;2. CORE and INMA, Université Catholique de Louvain, Belgium;1. Rio de Janeiro State University (UERJ), Rua São Francisco Xavier, 524, Instituto de Química, Rio de Janeiro, RJ, CEP 20550-900, Brazil;2. Petróleo Brasileiro S.A. (PETROBRAS), Avenida Horácio Macedo, 950, Cidade Universitária, Rio de Janeiro, RJ, CEP 21949-900, Brazil;3. Federal University of Rio de Janeiro (UFRJ), Avenida Athos da Silveira Ramos, 149, Bloco E, Cidade Universitária, Rio de Janeiro, CEP 21945-970, Brazil;1. ANCAP, Montevideo, Uruguay;2. Universidade Federal de Santa Catarina, Florianópolis, Brazil;3. Universidad Católica del Uruguay, Montevideo, Uruguay;1. Industrial Engineering Department, Sharif University of Technology, Tehran, Iran;2. Grupo de Sistemas de Optimización Aplicada, Instituto Tecnológico de Informática, Ciudad Politécnica de la Innovación, Edifico 8G, Acc. B, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain;1. Department of Computer Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran;2. Department of Computer Engineering, Arak Branch, Islamic Azad University, Arak, Iran;3. Department of Computer Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran |
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| Abstract: | In this paper, based on the cyclic scheduling formulation of Schilling and Pantelides Schilling, G., & Pantelides, C. (1999). Optimal periodic scheduling of multipurpose plants. Computers& Chemical Engineering, 23, 635–655], we propose a continuous time mixed integer linear programming (MILP) formulation for the cyclic scheduling of a mixed plant, i.e. a plant composed of batch and continuous tasks. The cycle duration is a variable of the model and the objective is to maximize productivity. By using strengthening techniques and the analysis of small polytopes related to the problem formulation, we strengthen the initial formulation by tightening some initial constraints and by adding valid inequalities. We show that this strengthened formulation is able to solve moderate size problems quicker than the initial one. However, for real size cases, it remains difficult to obtain the optimal solution of the scheduling problem quickly. Therefore, we introduce MILP-based heuristic methods in order to solve these larger instances, and show that they can provide good feasible solutions quickly. |
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