Inventory Control of Perishable Products in a VMI System with the Ability of Replacing Unavailable Products: Stochastic Dynamic Programming Approach

Introduction: Considering the perishability and substitutability of products are among the most significant challenges in the design and optimization of decision-making in Vendor Managed Inventory (VMI) systems. This challenge becomes more pronounced when there is uncertainty in product demand. Therefore, the primary objective of this research is to present a stochastic dynamic programming approach for optimal control of decisions in VMI systems with dynamic demand uncertainty, optimizing the ordering levels and inventory of perishable products in a two-tier network including vendors and buyers.
Methods: After defining the problem of interest in developing VMI systems, considering demand uncertainty and product perishability, the problem is formulated in a multi-period modeling framework, and a stochastic dynamic programming (SDP) approach is used for its formulation. In the proposed SDP model, the objective function is to maximize expected profit by taking into account various costs such as ordering and holding, where the holding cost is dependent on the remaining product life; meaning that as the product approaches its expiration date, the holding cost increases. The proposed SDP model is executed in a recursive manner, and MATLAB software is used for its implementation. Each step of the SDP model is a simpler linear optimization model that is efficiently solved using the CPLEX solver.
Results and discussion (Findings): Numerical results demonstrate the computational effectiveness of the SDP method in solving this problem. Using this approach, it is possible to control different costs in a VMI system and make optimal decisions at different stages under any state, thereby improving profit at the end of the time periods.
Product substitution in the event of a shortage ensures that, firstly, in the case of a shortage at one center and the supplier's inability to replenish, the center offers its excess inventory to prevent the shortage. Secondly, if the inventory in a distribution center approaches its expiration date, spoilage is prevented. Therefore, the substitution capability generally leads to a reduction in shortage costs and spoilage costs. Results related to product shelf life indicate that by considering the remaining shelf life of products in a VMI-based inventory control system, information between the distribution and supply layers can be used to reduce prices, transfer inventory to another center, and even change inventory control policies to not only prevent product spoilage but also reduce shortage and reordering costs. To model this feature, a full shelf life is initially defined for each newly supplied product, and then a set of periods is defined. For each planning period, if the product is not delivered to the end customer (remains in inventory), one period/day is deducted from the initially defined shelf life, and over time, it moves from a fresh state to the category of older products, which are subject to price reductions. Furthermore, comparing the proposed model with substitution capability in the case of a shortage to the case where a shortage is not considered, it is observed that there is a 10.5% improvement in profit.
Conclusion: In the management of modern VMI systems, considering the dynamism in demand behavior and the associated uncertainty is very important and can significantly affect the profitability of enterprises. This importance is doubled when the system in question is managed for the inventory control of perishable products. The SDP approach, by considering potential scenarios of demand uncertainty, enabling substitution, and ultimately paying attention to product shelf life, provides optimal decisions in different situations and not only reduces the risk of decision-making but also leads to a noticeable improvement in final profit compared to nominal quantity models and classical optimization models in the literature.