We consider a lot sizing problem with setup times where the objective is to minimize the total inventory carrying cost only. The demand is dynamic over time and there is a single resource of limited capacity. We show that the approaches implemented in the literature for more general versions of the problem do not perform well in this case. We examine the Lagrangean relaxation (LR) of demand constraints in a strong reformulation of the problem. We then design it primal heuristic to generate upper bounds and combine it with the LR problem within a subgradient optimization procedure. We also develop it simple branch and bound heuristic to solve the problem. Computational results oil test problems taken from the literature show that our relaxation procedure produces consistently better solutions than the previously developed heuristics in the literature. (c) 2007 Elsevier B.V. All rights reserved.