Optimization of Production Inventory under Weibull Deterioration and Price Discount Conditions: A Mathematical Modeling and Sensitivity Analysis Approach

Abstract

This study presents an integrated production-inventory model that incorporates Weibull deterioration and price discount considerations to optimize inventory strategies for perishable goods. The model is developed under the assumptions of deterministic demand, continuous replenishment, and the absence of shortages, while deterioration is governed by a three-parameter Weibull distribution. A mathematical formulation based on differential equations is established to represent inventory behavior during both production and non-production periods. The model accounts for setup costs, holding costs, production costs, deterioration losses, and discount incentives to derive a Total Variable Cost (TVC) function. Analytical methods are employed to determine the optimal cycle time that minimizes overall cost. A numerical illustration using realistic parameter values demonstrates the efficiency and applicability of the proposed model. In addition, a comprehensive sensitivity analysis evaluates the impact of key parameters such as setup cost, production rate, demand level, and deterioration rate on optimal inventory policies. The findings highlight the practical relevance of the proposed framework for decision-making in industries managing deteriorating products. The results provide valuable managerial insights to improve cost efficiency, enhance production planning, and promote operational sustainability.