A note on capacitated lot sizing with setup carry over

The “capacitated lot sizing problem with setup carry over” is based on the well known “capacitated lot sizing problem” and incorporates the possibility of preserving a setup state between successive periods. The approach at hand is to decompose the problem using Lagrangean relaxation. Subproblems are to be solved optimally employing dynamic programming techniques. Subgradient optimization guides the approach to heuristic solutions of the original problem. The present paper shows that this algorithm does not necessarily provide the optimal solution to the subproblems. The algorithm's flaw is corrected such that it allows to solve the subproblems optimally.