THE QUALITY-CONSTRAINED SCHEDULING PROBLEM IN PLASTICS COMPOUNDING Abdunnaser Younes,* Ali Elkamel, Michelle Leung, Costas Tzoganakis and Ali Lohi Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada Interest is increasing in plastic compounding plants that offer tailor-made resins. Such plants produce a wide range of products in small quantities and with frequent changeovers. The underlying scheduling problem has been extensively researched; however, the concept of incorporating qualities of the finished product in the problem of plastics compounding has not been considered. We express product qualities as an additional problem constraint so that the production schedule ensures product quality. The additional constraint makes this mixed integer nonlinear program (MINLP) problem more difficult to solve. Several case studies are solved to illustrate the utility of the proposed approach. Experiments demonstrated that qualities of the finished product can be ensured a priori if the appropriate relations are developed and inte- grated in the optimisation model. As well, this paper provides insight into the economic aspects of the scheduling problem under consideration. Experiments showed that none of the cost components (operation, raw material, inventory, penalty or utilities) can alone play the role of the optimisation criterion. Keywords: scheduling, plastics compounding, quality constraints, opportunity cost INTRODUCTION P roduction scheduling is a common problem that occurs in multi-product manufacturing facilities where a wide range of products are produced in small quantities, resulting in frequent changeovers. Customarily, the scheduling of batch and semi-continues pro- cesses is treated from either a multi-product or multi-purpose perspective (Elkamel, 1993). In multi-product plants, the pro- cessing units are arranged a priori and the products undergo the same sequence of operations. In multipurpose plants, the plant is configurable and hence different products can undergo different operation sequences. Several formulation and solution procedures have been pro- posed for the scheduling of batch and semi-continuous processes. We will not attempt to review the vast literature; we only cite a few mathematical programming approaches. The MILP formu- lation presented by Sahinidis and Grossmann (1991) leads to tighter linear programming relaxation. However, the formulation is restricted to special cases only. Tsirnkis and Reklaitis (1993a, b) presented a search strategy to partition the problem domain. The- oretically, the strategy leads to exact solutions when the fineness of the partitions approaches zero. However, since the number of partitions increases as well, the computation time becomes pro- hibitively large with very fine partitions. Kondili et al. (1993) presented a general framework tackling scheduling problems in multi-product or multi-purpose batch chemical plants. They pro- posed different schemes to improve the performance of the branch and bound technique in MILP. Tsirnkis et al., (1993) proposed an efficient two-level decomposition strategy for the MILP problem in multi-purpose batch chemical plants with resource constraints. In this paper, we are concerned with a plastics compounding plant that offers tailor-made resins. This kind of scheduling prob- lem has already been studied in the past. Schulz et al. (1998) presented two different mathematical formulations, a continuous time representation model and a fixed-grid model, to schedule a multi-product polymer batch plant. The polymerisation process that they had studied was a combination of serial and parallel processes. Wang et al. (2000) solved a similar problem using an augmented genetic algorithm. Castro et al. (2002) addressed ∗ Author to whom correspondence may be addressed. E-mail address: ayounes@uwaterloo.ca Can. J. Chem. Eng. 9999:1–15, 2012 © 2012 Canadian Society for Chemical Engineering DOI 10.1002/cjce.21739 Published online in Wiley Online Library (wileyonlinelibrary.com). | VOLUME 9999, 2012 | | THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING | 1 |