Optimising sustainable inventory management: incorporating advertising, time, price-dependent demand and preservation technology investment with carbon emissions in non-vanishing inventory scenarios

This paper presents a comprehensive framework for sustainable inventory management tailored to the needs of retailers and customers. Our model investigates various factors influencing inventory dynamics, including demand dynamics dependent on time, price, and advertisement, preservation technologies investment for deterioration reduction, and carbon emissions due to holding and transportation. We consider two cases: shortages with partial backlogging and non-vanishing inventory situations. Non-vanishing inventory comprises products with extended shelf life, like electronics or furniture, contrasting perishable goods. We analytically solve this model, illustrating examples of both cases. Our analysis highlights the effectiveness of preservation technologies in reducing deterioration rates and their impact on overall profits. Efficient inventory management practices, such as optimising order quantities and managing backlogs, are crucial in minimising losses from unsold inventory. Visual representations, like concavity graphs, offer insights into decision variable-total profit relationships, enriching our understanding of inventory management dynamics.