Rounding Off to Powers of Two in Continuous Relaxations of Capacitated Lot Sizing Problems
针对多阶段生产/库存问题中分治算法因舍入再订货间隔到2的幂次而丢失可行性的问题，提出新算法保证可行，并证明成本增加不超过44%（单机系统不超过6%），工业数据验证效果良好。
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.