An Inventory Model Incorporating Deterioration And Partial Backordering

Abstract

This study develops an inventory model for deteriorating items that incorporates partial backordering under realistic operational and financial conditions. The model addresses the practical challenges of managing inventory where products experience time-dependent deterioration and shortages occur due to demand uncertainty or supply disruptions. Unlike traditional inventory models, this framework integrates exponential time-dependent demand, variable deterioration rates, and partial backordering to reflect real-world customer behavior where only a fraction of unmet demand is willing to wait. The mathematical model employs differential equations to determine optimal replenishment times, cycle lengths, and order quantities that minimize total average costs including holding costs, deterioration costs, shortage costs, and lost sales. The analysis considers multiple scenarios involving trade credit policies, interest rates, and payment delays between suppliers and retailers in a two-echelon supply chain. Numerical illustrations demonstrate that optimal solutions differ between individual stakeholders and the overall supply chain, with system-wide cost minimization typically achieved at moderate order frequencies. Results indicate that progressive credit periods marginally increase order quantities but significantly reduce annual total costs. The model provides decision-makers with a practical tool for optimizing inventory policies under deterioration, shortages, and financial constraints in contemporary market conditions.

DOI: https://doi-ds.org/doilink/01.2026-68834452