Mathematical inventory model links preservation, carbon costs and green-sensitive demand

A mathematical inventory study reports that moderate investment in preserving deteriorating products, combined with a suitable period of trade credit, can lower total average cost when carbon emissions, pricing, shortages and environmentally sensitive demand are considered together. The findings come from a computational optimization model rather than a field trial, so they describe results under the model’s assumptions rather than measured benefits for particular businesses or industries. The framework was developed for deteriorating items whose demand responds to selling price and the product’s “green degree,” an environmental attribute used in the study to represent environmentally aware consumer demand.

Ordering, holding and preservation are linked to carbon prices, while part of the unmet demand is backlogged and a permissible trade-credit period allows payment to be delayed. Researchers minimized total average cost over two decision variables: the shortage point, denoted μ, and preservation investment, denoted ξ. The optimization was performed in Mathematica.

Convexity was established analytically using a positive-definite Hessian and also examined graphically. The study analyzed three trade-credit cases through numerical examples and subjected the results to an extensive sensitivity analysis covering variations of plus or minus 20 percent in the model parameters. Across the tested cases, total cost proved most sensitive to demand and pricing parameters and to shortage cost.

This sensitivity result indicates that assumptions about market demand, product pricing and the financial consequences of unmet demand can strongly influence the model’s calculated optimum. The analysis also found that combining a moderate level of preservation investment with an appropriately chosen trade-credit period reduced total average cost while supporting the study’s sustainability objective. The model consequently treats preservation, credit terms, pricing and replenishment decisions as elements of a coordinated system rather than independent controls.

Its managerial implications concern the selection of pricing, replenishment timing, preservation spending and credit-term design within the tested scenarios. The research does not establish a universal investment level or credit period: the reported optimum depends on demand behavior, shortage costs, carbon prices and other assumptions built into the mathematical framework. As an early-access peer-reviewed modeling study, it offers a way to compare interconnected cost and environmental factors but does not provide empirical evidence from operating companies or real-world implementation.

Subject of Research: Mathematical optimization of sustainable inventory decisions for deteriorating products

Article Title: A sustainable inventory model for deteriorating items with preservation investment, carbon-emission costs and trade credit under price and green sensitive demand

Article References: Verma, S. K., Singhwal, P., Malik, A. K., & Kaushik, J. (2026). A sustainable inventory model for deteriorating items with preservation investment, carbon-emission costs and trade credit under price and green sensitive demand. Discover Sustainability. https://doi.org/10.1007/s43621-026-04675-8

Image Credits: AI Generated

DOI: 10.1007/s43621-026-04675-8

Keywords: inventory modeling, deteriorating products, preservation investment, carbon costs, trade credit, green-sensitive demand, sustainable operations, shortage optimization, sustainable, inventory, model, deteriorating