Dynamic lot-sizing model under perishability, substitution, and limited storage capacity

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.