Modelling of an imprecise sustainable production control problem with interval valued demand via improved centre-radius technique and sparrow search algorithm

The modelling and optimization of a manufacturing systems in the context of sustainable production under uncertainty remain a pivotal focus in control theory. The goal of this research is to develop a robust decision-making framework for a production-inventory system characterised by imperfect production with reworking processes, and interval valued non-linear demand rate which is dependent on green level, selling price, warranty period, and time. This study also considers the impact of carbon emission regulation taxes to demonstrate how CO2 emission control influences the best-found policy of the proposed system. To fulfil the goal, an interval-valued optimal control problem (IVOCP) is constructed using generalised variational principle and corresponding highly nonlinear interval maximization problem is obtained. To tackle this interval optimisation problem, an improved c-r optimisation technique and the meta-heuristic algorithm Sparrow Search algorithm (SSA) are employed. The best-found solution for the corresponding problem is numerically illustrated through four distinct scenarios based on the presence of green investment levels and warranty periods in the demand rate. The obtained best found results are compared by some other metaheuristic algorithms. Additionally, statistical tests and non-parametric tests are conducted to assess the effectiveness, consistency, and stability of the algorithms. Furthermore, sensitivity analyses have been made to observe how inventory system parameters impact the optimal policy. Based on these analyses, managerial insights are derived to aid in decision-making processes.