Optimal Production and Inventory Policies for Delayed Deteriorating Items with Stock-Dependent Demand and Partial Backlogging under Two-Phase Production: Insights from COVID-19 Disruptions

Abstract

The COVID-19 pandemic exposed critical weaknesses in global supply chains, necessitating strong and sustainable inventory strategies for perishable goods. This study proposes an economic production quantity (EPQ) model for items subject to delayed deterioration under a two-phase production framework with shortages and partial backlogging. The production process is divided into two distinct phases representing different stages of disruption and recovery. During the production period, demand is assumed constant, whereas in the non-production period, demand depends on the available stock level, reflecting post-pandemic consumer behavior in which product visibility influences purchasing decisions. The model incorporates a finite freshness period, after which deterioration begins, making it suitable for products such as meat, bread, and cassava. Shortages are permitted and partially backlogged to capture realistic market responses. The objective is to determine the optimal production cycle and inventory levels that minimize the total system cost, including production, holding, deterioration, shortage, lost sales, and environmental costs. The purpose is to determine the optimal cycle length and inventory level for each cycle to minimize total cost. The necessary and sufficient conditions are provided to show the existence and uniqueness of the optimal solution. Also, the decision rule of the Newton-Raphson method has been used to determine the optimal solutions for the nonlinear optimization problem. Numerical illustrations and sensitivity analyses are presented to examine the impact of key parameters, including demand sensitivity, deterioration rate, and backlog fraction, on optimal decisions. The results demonstrate that the proposed framework provides practical insights for manufacturers seeking to stabilize operations, reduce waste, and enhance profitability in the post-COVID-19 recovery phase.