Optimal Inventory Management with Time-Varying Exponential Demand, Weibull Decay, Partial Shortages, and Permissible Payment Delays

Abstract

 This study presents a comprehensive inventory model that integrates exponential demand, gradual deterioration following a Weibull distribution, and partial backlogging, under a trade credit policy framework. The primary objective is to develop a price and lot-sizing model suitable for retail environments where suppliers permit a delay in payments—a realistic and common trade credit scenario. The model assumes that demand increases exponentially over time, while items deteriorate gradually rather than instantaneously. Additionally, the possibility of shortages is allowed, with partial backlogging occurring only during the shortage period for the remaining unmet demand. To determine the optimal ordering policy, the first and second order conditions are established, leading to the development of a structured algorithm aimed at minimizing the total cost. The algebraic approach, combined with cost minimization techniques, enables the identification of multiple optimal values across different inventory scenarios. The model addresses practical conditions often faced in retail inventory systems, such as payment flexibility, time-sensitive demand, and limited backordering capabilities. This framework provides a robust and realistic measurement model for inventory control, allowing businesses to strategically balance ordering decisions, holding costs, shortage implications, and the benefits of deferred payments. The findings contribute to the advancement of inventory theory by offering a refined decision-making tool that accommodates both market dynamics and supplier-buyer financial arrangements.