Stochastic analysis of an imperfect production-inventory system with consideration of random machine breakdown, rework, inspection, and environmental emissions

Incorporation of production disruption, quality, inspection, and environmental concerns in the production and inventory model has obtained significant attention in literature; nevertheless, researchers study these subjects individually. It is necessary to jointly incorporate all those aspects in a single research study to support decision making, and gain new insights for complexities in practice. This paper takes the initiative in this respect and proposes a production-inventory model with imperfect quality and disruption from a sustainable point of view. The objective is to determine the optimal rate of production and to examine the impact of emission penalty cost on production. By using the renewal reward theorem, models are formulated. The developed models are examined numerically and compared to investigate the optimal policies. The sensitivity analysis concludes that under a low emission cost, a certain level of emission beyond the permissible emission limit is acceptable, whereas the low production rate is best when the high penalty cost is imposed.