Discrete Optimization Fuzzy chance constrained linear programming model for optimizing the scrap charge in steel production Aiying Rong a, * ,1 , Risto Lahdelma b a Technical University of Denmark, Department of Manufacturing Engineering and Management, Building 425, 2800 Kgs, Lyngby (Copenhagen), Denmark b University of Turku, Department of Information Technology, Joukahaisenkatu 3-5, FIN-20520 Turku, Finland Received 10 February 2006; accepted 1 February 2007 Available online 20 March 2007 Abstract Optimizing the charge in secondary steel production is challenging because the chemical composition of the scrap is highly uncertain. The uncertainty can cause a considerable risk of the scrap mix failing to satisfy the composition requirements for the final product. In this paper, we represent the uncertainty based on fuzzy set theory and constrain the failure risk based on a possibility measure. Consequently, the scrap charge optimization problem is modeled as a fuzzy chance constrained linear programming problem. Since the constraints of the model mainly address the specification of the product, the crisp equivalent of the fuzzy constraints should be less relaxed than that purely based on the concept of soft constraints. Based on the appli- cation context we adopt a strengthened version of soft constraints to interpret fuzzy constraints and form a crisp model with consistent and compact constraints for solution. Simulation results based on realistic data show that the failure risk can be managed by proper combination of aspiration levels and confidence factors for defining fuzzy numbers. There is a tradeoff between failure risk and material cost. The presented approach applies also for other scrap-based production processes. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Fuzzy sets; Linear programming; Chance constraint; Scrap charge optimization; Steel production 1. Introduction A general trend during the past decades is that scrap-based steelmaking has increased its share, reaching around 40% of global crude steel produc- tion in 2001 (Rautaruukki, 2001). Steel is also the world’s most important recycled material. Use of the steel scrap as a raw material for steelmaking results in saving 600 million tonnes of iron ore and 200 million tonnes of coke each year (EURO- FER, 2001). With the growing concern on environ- mental issues, the popularity of using scrap could further increase because scrap-based steelmaking emits significantly less CO 2 as compared with inte- grated steelmaking using metallurgical coke as reductant for iron-making. Undoubtedly, the use of the scrap offers the opportunity to produce high quality products most economically. 0377-2217/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2007.02.017 * Corresponding author. Tel.: +45 45254768; fax: +45 45256005. E-mail addresses: aiying.rong@gmail.com, ar@ipl.dtu.dk (A. Rong). 1 The research was done when the first author was employed by Universtity of Turku. Available online at www.sciencedirect.com European Journal of Operational Research 186 (2008) 953–964 www.elsevier.com/locate/ejor