J Math Model Algor (2007) 6:135–149 DOI 10.1007/s10852-006-9053-2 Solving Large-scale Profit Maximization Capacitated Lot-size Problems by Heuristic Methods Kjetil K. Haugen · Asmund Olstad · Bård I. Pettersen Received: 18 October 2004 / Accepted: 30 November 2005 / Published online: 20 September 2006 © Springer Science + Business Media B.V. 2006 Abstract This paper introduces a simple heuristic for a quadratic programming sub- problem within a Lagrangean relaxation heuristic for a dynamic pricing and lot- size problem. This simple heuristic is demonstrated to work well on both ‘standard problem instances’ from the CLSP-literature, as well as on very large-scale cases. Additionally, we introduce price constraints within the framework of dynamic pricing, discuss their relevance in a real world market modelling, and demonstrate their applicability within this algorithmic framework. Mathematics Subject Classifications (2000) 90B05 · 90C20 · 90C10. Key words Lagrangean relaxation heuristic · capacitated lot-size scheduling problem · price constraints · profit maximization. 1 Introduction This paper discuss a generalized version of the classical Capacitated Lot-Size Scheduling Problem (CLSP). The generalization, which we name PCLSP [8], in- volves adding dynamic pricing variables to the CLSP problem within a monopolistic market setting. K. K. Haugen (B ) · A. Olstad · B. I. Pettersen Molde University College, Box 2110, 6402 Molde, Norway e-mail: Kjetil.Haugen@himolde.no A. Olstad e-mail: Asmund.Olstad@himolde.no B. I. Pettersen e-mail: Bard.I.Pettersen@himolde.no