Interval differential equation approach for inventory systems with green and price-dependent nonlinear demand

The highly competitive and volatile nature of the current marketing environment makes it challenging to predict demand and other uncertain costs. To address this uncertainty, this study employs an interval-valued optimization technique. We propose an economic order quantity (EOQ) model within an interval framework, where the demand rate is represented as an interval-valued power function dependent on the green level, selling price, and time. Furthermore, the retailer’s purchasing and holding costs are treated as interval values; the purchasing cost is dependent on the green level, while the holding cost varies over time. The model also permits fully backlogged shortages, which are considered interval values. A parametric method is utilized to convert the differential equation for the inventory level from its interval form into a crisp equivalent. The resulting maximization problem is then solved using the Teaching-learning-based optimizer algorithm (TLBOA), after being converted to a crisp problem using interval order relations and the center-radius optimization approach. Finally, a numerical example is provided to illustrate and validate the proposed model, followed by a post-optimality analysis to examine the impact of various parameters on the optimal policy. (AMS classification code: 90B05, 49M37, 90C70, 90C59)