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@article{204421,
        author = {Somen Guha and Dhrub Kumar Singh},
        title = {A Mathematical Inventory Model for deteriorating items with price and time dependent demand rate -a deterministic approach.},
        journal = {International Journal of Innovative Research in Technology},
        year = {2026},
        volume = {13},
        number = {1},
        pages = {2122-2127},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=204421},
        abstract = {Inventory management is a vital component of modern production and supply chain systems, particularly when dealing with deteriorating products whose demand is influenced by both time and selling price. This study develops a deterministic inventory model for deteriorating items under a demand rate that depends simultaneously on time and price. The proposed model reflects realistic market situations where customer demand initially increases or decreases over time and is inversely affected by product price.
The model incorporates key inventory factors such as deterioration, shortages, time-dependent holding cost, variable pricing, and instantaneous replenishment. Two forms of demand functions are considered: increasing time-price dependent demand and decreasing time-price dependent demand. Mathematical expressions for inventory level, deterioration quantity, order quantity, shortage quantity, holding cost, and profit function are derived using differential equations. The objective is to determine the optimal selling price and replenishment policy that maximize the average profit per unit time.
Optimality conditions are obtained by applying first- and second-order optimization techniques. A numerical example is presented to demonstrate the applicability of the model and to compare different demand strategies. The results indicate that inventory policies based on both time and price-dependent demand provide better profit outcomes than policies considering only one factor. The analysis further reveals that the demand function incorporating positive time influence offers superior profitability and managerial insights under suitable market conditions.
The proposed model provides a practical decision-making framework for inventory managers dealing with deteriorating products in competitive markets. It highlights the importance of integrating pricing decisions with demand dynamics and inventory control to achieve maximum profitability and efficient inventory management.},
        keywords = {Deteriorating Items; Deterministic Inventory Model; Price-Dependent Demand; Time-Dependent Demand; Inventory Control; Optimal Pricing Policy; Shortage Management; Profit Maximization.},
        month = {June},
        }