ORIGINAL ARTICLE A new algorithmic approach for capacitated lot-sizing problem in flow shops with sequence-dependent setups M. Mohammadi & S. A. Torabi & S. M. T. Fatemi Ghomi & B. Karimi Received: 9 February 2009 / Accepted: 12 October 2009 / Published online: 8 November 2009 # Springer-Verlag London Limited 2009 Abstract In this paper, we propose a new algorithmic approach to solve the large-sized instances of lot-sizing problem in capacitated pure flow shops with sequence- dependent setups within a reasonable computation time. Two solution algorithms are provided based on a more simplified version of the problem combining the rolling horizon approach with a specific heuristic. To evaluate the effectiveness of the proposed algorithms, some numerical experiments are conducted, and corresponding results are compared with those of previously developed heuristics by the authors. The comparative results indicate the superiority of the second proposed algorithm in solving the large-sized problem instances. Keywords Capacitated lot-sizing problem . Pure flow shop . Sequence-dependent setups . Rolling horizon 1 Introduction Lot-sizing and scheduling tasks are the main parts of an operative production planning and control system. Lot sizing deals with determining the production amount of each product (i.e., one lot) at each production run often over a finite multiperiod horizon in which a lot indicates the quantity of a given product processed on a machine continuously without interruption after its respective setup. Moreover, scheduling is to determine the produc- tion sequence in which the products are manufactured on a machine [9]. However, because of interrelationship between these problems, simultaneous lot sizing and scheduling is essential especially when sequence- dependent setup costs and times occur [9]. Involving sequence-dependent setups is an important consideration in many practical applications. Because of their prevalence in, and importance to, industry and because of the challenges they present to solution methodologies, lot- sizing and scheduling problems that involve a sequence- dependent setup have attracted attention from many researchers [25]. Lot-sizing and scheduling problems have been an active area of research starting from the seminal paper of Wagner and Whithin [24]. Along with the setup issue, there are various other features to be dealt with when modeling lot- sizing and scheduling problems, among them are the segmentation of the planning horizon, the time dependence of the model parameters, the information degree of the model parameters, the number of products and production stages, the production structure, and the capacity restric- tions [9, 14, 20]. In the literature, lot-sizing and scheduling models are classified into the small and big bucket problems [8]. Small bucket problems split the planning horizon in small time periods so that the number of products to be manufactured at each period is limited. Small bucket problems are more divided into the discrete lot-sizing and scheduling problem (DLSP) and proportional lot-sizing M. Mohammadi : S. M. T. Fatemi Ghomi : B. Karimi Department of Industrial Engineering, Amirkabir University of Technology, 424, Hafez Avenue, 15916-34311 Tehran, Iran S. A. Torabi (*) Department of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran e-mail: satorabi@ut.ac.ir Int J Adv Manuf Technol (2010) 49:201–211 DOI 10.1007/s00170-009-2366-3