A mathematical programming approach for cyclic production and cleaning scheduling of multistage continuous plants Alessandro Alle a , Lazaros G. Papageorgiou b, *, Jose M. Pinto a,c a Department of Chemical Engineering, University of Sao Paulo, Av. Prof. Luciano Gualberto t. 3 n. 380, Sao Paulo, SP 05508-900 Brazil b Centre for Process Systems Engineering, Department of Chemical Engineering, UCL (University College London), Torrington Place, London WC1E 7JE, UK c Othmer Department of Chemical and Biological Sciences and Engineering, Polytechnic University, Brooklyn, NY 11201, USA Abstract The objective of this paper is to address the cyclic scheduling of cleaning and production operations in multiproduct multistage plants with performance decay. A mixed-integer nonlinear programming (MINLP) model based on continuous time representation is proposed that can simultaneously optimize the production and cleaning scheduling. The resulting mathematical model has a linear objective function to be maximized over a convex solution space thus allowing globally optimal solutions to be obtained with an outer approximation algorithm. Case studies demonstrate the applicability of the model and its potential benefits in comparison with a hierarchical procedure for the production and cleaning scheduling problem. # 2003 Elsevier Ltd. All rights reserved. Keywords: Cyclic production and cleaning scheduling; MINLP; Multistage continuous plants 1. Introduction This paper addresses the problem of cyclic scheduling of multiproduct multistage continuous plants (one unit per stage) with performance decay. Performance decay is a serious problem in many chemical processes and has several causes such as catalyst deactivation, fouling etc. As performance decreases, processing units require cleaning to restore productivity to their initial level. There is a trade-off between running the unit at low yield that represents continuous production at the expense of lower efficiency, or stopping it to clean that represents restoring the original efficiency at the expense of production time. The decision of stopping a unit for maintenance interferes with the whole production sche- dule. Therefore, it is important to consider both production and cleaning scheduling decisions simulta- neously. Several analytical methods for determining the opti- mal cleaning schedules for equipment items have been proposed in the literature (Epstein, 1979; Casado, 1990; Sheikh, Zubari, Haq, & Budair, 1996). The main draw- back of these approaches is that they are restricted to a single equipment item. Early works like Dedopoulos and Shah (1995) and Sanmartı ´, Espun ˜ a, and Puigjaner (1997) were dedicated to multipurpose batch plants and considered simulta- neously preventive maintenance and production plan- ning using the STN representation (Kondili, Pantelides, & Sargent, 1993). Dedopoulos and Shah (1995) con- sidered that the number of maintenance tasks that has to be carried out is pre-determined whereas Sanmartı ´, Espun ˜ a, and Puigjaner (1997) allowed this number to vary. Muller-Steinhagen (1998) proposed an integrated approach for developing alternative fouling mitigation strategies based on both experimental and modeling works. Jain and Grossmann (1998) studied the scheduling of single stage plants with parallel units whose perfor- mance decreases with time and therefore shutdown for maintenance after regular intervals is required. A mixed- integer nonlinear programming (MINLP) model was presented using the process information regarding the exponential decay in performance with time to find a cyclic schedule for feed processing. * Corresponding author. E-mail address: l.papageorgiou@ucl.ac.uk (L.G. Papageorgiou). Computers and Chemical Engineering 28 (2004) 3  /15 www.elsevier.com/locate/compchemeng 0098-1354/03/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0098-1354(03)00171-6