A hybrid Benders approach for coordinated capacitated lot-sizing of multiple product families with set-up times
研究了多产品族在能力受限下的批量问题，通过Benders分解与进化算法结合，改进了上下界，缩小了对偶间隙。
We examine a coordinated capacitated lot-sizing problem for multiple product families, where demand is deterministic and time-varying. The problem considers set-up and holding costs, where capacity constraints limit the number of individual item and family set-up times and the amount of production in each period. Using a strong reformulation and relaxing the demand constraints, we improve both the upper and lower bounds using a combination of Benders decomposition and an evolutionary algorithm, followed by subgradient optimisation. Through computational experiments, we show that our method consistently achieves better bounds, reducing the duality gap compared to other single-family methods studied in the literature.