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中文摘要：
研究了存在需求单向替代的两产品动态批量决策的最优预测时阈问题.构建了包含替代成本、生产转换成本和库存成本在内的成本最小化模型,分析得出在只存在3类再生点（Ⅰ类、Ⅱ类和Ⅲ类）情形下的再生点单调性特征.同时,设计出了多项式时间的前向动态规划算法.运用数值试验分析了最优预测时阈与生产转换成本、替代成本、需求特征（需求增长性和需求波动性等）之间的相互关系,并比较分析了存在替代和不存在替代情形下最优预测时阈的相对大小,发现需求替代将显著增加预测时阈的长度.
英文摘要：
This paper analyzes the dynamic lot-size problem and forecast horizon for the two downward substitution products.By developing a polynomial-time forward dynamic programming algorithm,we compute the optimal decision of production and substitution quantities for a T-period problem to minimize the changeover cost,holding cost and substitution cost.We obtain the minimal last regeneration points monotonicity properties for an optimal solution,this enables us to establish a highly efficient forward algorithm to evaluate the minimal forecast horizon and the corresponding decision horizon.Finally,we use a computational experiment to compare the minimal forecast horizons between with and without substitution of two products and conclude that the substitution increases the minimal forecast horizon.
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