Production System for Delayed Deterioration Inventories with Two-Level Production Rate, Stock-Dependent Demand Rate and Linear Holding Cost Under Trade Credit Policy

Abstract

This paper introduces an optimized total variable cost model for a production inventory system dealing with delayed deteriorating items. The model incorporates a two-level production rate and a stock-dependent demand rate, all operating under a trade credit policy. The demand rate remains constant during the inventory build-up period, but post-production, before deterioration, it varies based on product availability and nature. The inventory depletes to zero in the model’s final stage due to the combined impact of constant demand and deterioration rates. To characterize the optimality of the analytical results, the paper utilizes theorems and lemmas. The model’s dynamics are described by differential equations, which are solved using MATLAB. A numerical experiment is conducted to demonstrate the practicality of the developed models. Additionally, a sensitivity analysis is performed to illustrate how changes in selected system parameters affect the total variable costs determined in the numerical example. The paper concludes with suggestions and recommendations aimed at reducing the total variable cost. Ultimately, it is demonstrated that the developed model surpasses the one presented in the working paper. The proposed model could be used in inventory management and control of items that exhibit delayed in deterioration to minimises the total variable cost when sudden distraction of production process occurred as revealed by the the result presented.