Abstract Various commodities including blood, pharmaceutical, and agricultural products are perishable in nature and require special storage conditions, such as controlled temperature. However, expanding the space of cold storage is expensive. Therefore, storage capacity frequently restricts the operational efficiency of enterprises in the perishable product industry. Numerous enterprises have adopted the policies of product substitution and multiple item joint procurement to achieve an efficient inventory management and reduce their operation costs. This paper considers a two-product dynamic lot-sizing problem for perishable inventory under product substitution and limited storage capacity. This study aims to identify the ordering, inventory, and substitution decisions over a planning horizon under the criteria that (i) the inventory holding costs and deterioration rates are age dependent, (ii) a one-direction product substitution and joint ordering of two products are possible, and (iii) the storage capacity has an upper bound that limits the inventory quantities. The contributions of this study are summarized in three points. First, we develop a dynamic programming algorithm by using two structural properties to solve the dynamic lot-sizing problem with perishable inventory and demand substitution under storage capacity constraints. Second, we obtain the forecast horizons for the general problem by using the marginal analysis method and for the case with constant unit ordering costs through establishing the monotonicity of the regeneration points of two products. Third, we determine the effects of storage capacity, product lifetime, joint setup, and inventory costs on the length of the forecast horizon and the total costs by using a detailed test bed of instances. The major findings are also discussed in three aspects. First, the single-period satisfaction property fails to hold under limited storage capacity and time-varying unit ordering costs. Second, the forecast horizon inconsistently increases with joint setup costs or storage capacity. Third, the total costs fail to decrease with increasing storage capacity or product lifetime.

中文翻译：

---

易腐烂、替代和有限存储容量下的动态批量模型

摘要 包括血液、药品和农产品在内的各种商品在自然界中易腐烂，需要特殊的储存条件，例如控制温度。然而，扩大冷库的空间是昂贵的。因此，存储容量往往制约着易腐品行业企业的运营效率。众多企业采取产品替代、多品联合采购等政策，实现高效库存管理，降低运营成本。本文考虑了在产品替代和有限存储容量下易腐烂库存的两种产品动态批量调整问题。本研究旨在确定订购、库存、以及在以下标准下的计划范围内的替代决策：（i）库存持有成本和变质率取决于年龄，（ii）单向产品替代和两种产品的联合订购是可能的，以及（iii）存储容量有一个限制库存数量的上限。本研究的贡献概括为三点。首先，我们开发了一种动态规划算法，通过使用两个结构属性来解决存储容量约束下易腐烂库存和需求替代的动态批量调整问题。其次，我们通过使用边际分析方法获得一般问题的预测范围，并通过建立两种产品的再生点的单调性来获得单位订购成本不变的情况。第三，我们通过使用详细的实例测试台来确定存储容量、产品寿命、联合设置和库存成本对预测范围长度和总成本的影响。主要发现还从三个方面进行了讨论。首先，单期满意度属性在有限的存储容量和随时间变化的单位订购成本下无法成立。其次，预测范围随着联合设置成本或存储容量的增加而不一致。第三，总成本未能随着存储容量或产品寿命的增加而降低。在有限的存储容量和随时间变化的单位订购成本下，单期满意度属性无法保持。其次，预测范围随着联合设置成本或存储容量的增加而不一致。第三，总成本未能随着存储容量或产品寿命的增加而降低。在有限的存储容量和随时间变化的单位订购成本下，单期满意度属性无法保持。其次，预测范围随着联合设置成本或存储容量的增加而不一致。第三，总成本未能随着存储容量或产品寿命的增加而降低。