Sustainable policies for a disruptions-tolerant production network model with green investment and incentive scheme amid various quality inspection setups

In the realm of contemporary production inventory literature, prevailing models have showcased resilience in the face of various potential disruptions. Concurrently, there emerges a burgeoning advocacy for phased methodologies that harmonize with the imperative carbon emission reduction objectives delineated in the Paris Agreement. Numerous other researchers put thrusts on manufacturers’ different inspection policies aiming to ensure product quality. Thus, a potential research gap exists in integrating the aforementioned aspects into a unified production inventory model. This study addresses this gap by developing a novel disruption-tolerant discrete-time multi-nodal production inventory model. The proposed model incorporates potential disruptions from random machinery breakdowns and volatile demand rates, while considering the manufacturer’s green investments within a carbon cap-and-trade framework. Through the amalgamation of final one-time and operant inspection policies, this study develops six increasingly intricate iterations of the proposed model. Then, this study demonstrates the global optimality of the generalized model by establishing its equivalence with a standard quadratic integer programming problem. Analytical insights emphasize the strategic importance of green investments by manufacturers, thereby highlighting their role in enhancing operational resilience against machinery breakdowns under environmental sustainability and quality assurance objectives. Numerical results indicate that the integration of in-line inspection stations minimally impacts total costs and advocates manufacturers for some efficient quality-control measures. Also, this study emphasizes balancing the optimal level of green investment with operational efficiency and cost considerations in navigating regulatory requirements and evolving customer preferences.