Rounding Off to Powers of Two in Continuous Relaxations of Capacitated Lot Sizing Problems

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Abstract
In the capacitated version of the Divide and Conquer algorithm for lot sizing in multi-stage production/inventory problems, feasibility is often lost when the reorder intervals are rounded off to powers of two. We propose a new algorithm for rounding off the reorder intervals which always produces a feasible policy. We have shown that the relative increase in cost that occurs when the intervals are rounded off using this algorithm cannot exceed 44%, and that for systems with a single capacity machine (including the ELSP), the cost increase cannot exceed 6%. Computational experience with industrial data sets indicates that the algorithm performs very well.