Investigation of green production inventory problem with selling price and green level sensitive interval-valued demand via different metaheuristic algorithms

In real-life situation, different characteristics of an imperfect production inventory system, viz. demand, production, defectiveness and different costs may be imprecise. To represent the impreciseness of those parameters, several well-known approaches like interval, fuzzy, stochastic and fuzzy-stochastic approaches are applied. Among these approaches, interval approach is more realistic. This work deals with a green production model in interval environment. Due to consideration of interval-valued demand and defective rates, the corresponding differential equations of inventory levels of the proposed model are represented in interval form. With the help of parametric representation of interval, these differential equations are solved. The corresponding profit maximization problem is obtained in the interval form. To transform the said maximization problem into crisp form, interval order relations and centre-radius optimization technique are used and, the transformed problem is solved with the help of different metaheuristic algorithms. Then the proposed model is justified and validated with the help of a numerical example. Finally, the sensitivity analyses are performed to explore the effects of changes of different system parameters on the best found (optimal) policy.