This paper examines a mathematical programming method of accounting for capacity costs for the deterministic, multi-item, single operation lot sizing problem. With the capacity constraints of CLSP removed with Lagrangian relaxation, the problem decomposes into a set of uncapacitated single product lot sizing problems which are solved with dynamic programming. The Lagrangian dual costs are updated by subgradient optimization. Feasible solutions (production plans within the capacity limitations) are constructed with a heuristic smoothing procedure. The dual-cost heuristic gave solutions which were better on average than the other algorithms tested (and was faster than some comparable algorithms).