Computers & Operations Research 32 (2005) 537–555 www.elsevier.com/locate/dsw A Lagrangean-based heuristic for multi-plant, multi-item, multi-period capacitated lot-sizing problems with inter-plant transfers Murali Sambasivan * , Salleh Yahya Graduate School of Management, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia Abstract This paper addresses scheduling of lot sizes in a multi-plant, multi-item, multi-period, capacitated envi- ronment with inter-plant transfers. A real-world problem in a company manufacturing steel rolled products provided motivation to this research. A Lagrangean-based approach, embedded with a lot shifting–splitting– merging routine, has been used for solving the multi-plant, capacitated lot-sizing problem. A “good” solution procedure developed by Sambasivan (Ph.D. Dissertation, University of Alabama, Tuscaloosa, 1994) has been used for solving the relaxed problem. About 120 randomly generated instances of the problem have been solved and it has been found that Lagrangean-based approach works quite “eciently” for this problem. ? 2003 Elsevier Ltd. All rights reserved. Keywords: Capacitated lot sizing; Lagrangean-based heuristic; Multi-plant production planning 1. Introduction Capacitated production lot-sizing problems pose challenges to solve owing to its combinatorial nature. Aras [1] has shown that the multi-item, capacitated lot-sizing problem with setup costs are NP-Hard. Many researchers have attempted to solve single plant, multi-item, capacitated lot-sizing problems to “very close to optimality” [2–6]. But they were not quite successful in solving large-scale problems because they could not predict the number of cutting planes that need to be generated, or the number of iterations that are required in a branch and bound approach. One group of researchers worked towards developing heuristics to solve large-scale problems [7–10]. A promising heuristic to solve large-scale problems based on Lagrangean approach was developed by Trigerio et al. [11]. This approach has gained prominence to solve capacitated lot-sizing problems. The Lagrangean relaxation * Corresponding author. Fax: +603-89434019. E-mail addresses: murali@econ.upm.edu.my, sambasivan@hotmail.com (M. Sambasivan). 0305-0548/$-see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.cor.2003.08.002