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@article{204239,
        author = {BAPAN PARYA and Dhrub Kumar Singh},
        title = {Developing mathematical models that incorporate the decline in quality of inventory items, where demand is influenced by both price and stock levels, and also considers the impact of quantity discounts.},
        journal = {International Journal of Innovative Research in Technology},
        year = {2026},
        volume = {13},
        number = {1},
        pages = {1145-1154},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=204239},
        abstract = {This study develops an integrated deterministic inventory model for a two-echelon supply chain consisting of a single manufacturer and a single retailer dealing with deteriorating items having a fixed lifetime. The proposed model incorporates advertisement- and stock-dependent demand, preservation technology investment, shortages with partial backordering, and quantity discount policies. Two scenarios are analyzed: (i) a system without quantity discount and (ii) a coordinated system where the retailer adjusts order quantities in exchange for quantity discounts offered by the manufacturer. Preservation technology is employed to reduce the deterioration rate and improve inventory performance. The objective is to minimize the total integrated supply chain cost by optimizing the backorder rate and preservation investment. Mathematical formulations are developed for both manufacturer and retailer, and the joint total cost functions are derived. Computational algorithms are proposed to obtain optimal solutions for the decision variables. Numerical results demonstrate that implementing a quantity discount policy significantly reduces preservation costs, backorder rates, and overall system costs. Sensitivity analysis further reveals the effects of deterioration rate, preservation efficiency, advertisement frequency, and holding costs on system performance. The findings indicate that coordinated quantity discount strategies combined with optimal preservation investment can enhance supply chain efficiency and profitability while reducing inventory-related costs.},
        keywords = {Integrated inventory model, Deteriorating items, Quantity discount, Preservation technology, Stock-dependent demand, Advertisement-dependent demand, Backordering, Supply chain coordination.},
        month = {June},
        }