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In response to the digital revolution, nowadays, many companies operate online and offline businesses in parallel to ensure their future competitiveness. This research examines the inventory strategy for multi-product vendor-buyer supply chain systems, considering space constraints and carbon emissions, in order to improve competence in managing online and offline integrated orders. We amalgamate costs and emissions in transport and storage. Here, we divide the warehouse of the buyer into two stages: one for satisfying online orders and the other for satisfying offline orders. We also assume that additional crashing costs reduce the lead times for receiving products in the buyer’s warehouse. This study demonstrates a mathematical model in the form of a constrained non-linear programme (NLP) and derives a Lagrangian multiplier method to solve it. An iterative solution procedure is designed in order to attain sustainable manufacturing decisions, which are illustrated numerically.

Many nations have created ecological policies and regulations to prevent industries from emitting excessive amounts of carbon emissions into the environment. While significant progress has been achieved in the direction of sustainable growth, many nations still rely on nonrenewable energy sources. This study explores the viability of investing in green technology to achieve the optimal decisions (lot sizes, lead time, and green investment amount) in a two-echelon supply chain system by considering human error with two carbon emission strategies: carbon taxes and limited carbon emissions. It entails the inspection of every shipped lot by the buyer to identify defective products that could have resulted from the vendor’s production process. We show a constrained non-linear program and design a calculus-optimization technique to solve it. The methodology used in this research is the quantitative method, which is based on the principles of operations research, and the models are built on mathematically oriented inventory theory. The results imply that an outsized ecological carbon footprint can be reduced without compromising customer service by designing optimal inventory strategies. The findings also confirm that green investment is the greatest economical method for reducing carbon emissions and system costs.