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Nowadays, environment is an important concern of industries parallel to the economy. In this direction, an joint vendor-buyer model is exhibited where the system reliability and inspection errors are discussed along with the carbon emission issue. The main goal of this model is to obtain the optimum investment, shipment size, reliability and lead time even the inspection errors present in the system. A reliability dependent unit production cost is utilized to raise the machinery system reliability. Transportation of products use the single-setup-multi-unequal-delivery (SSMUD) policy reduced carbon emission. Mathematical problem is solved analytically and found a quasi-closed-form solution. Total cost is minimized with the optimum level of decision variables. The globality of the decision are proved by Hessian matrix. Results prove that the total cost is minimized even though the optimum solutions are obtained in quasi-closed-form. Numerical example is elaborated to test the validity of the model numerically and lastly clarify the comparison among SSSD, SSMD, and SSMUD policies.

<abstract><p>A long-run manufacturing system can experience machine breakdown at any time for various reasons such as unskilled labor or outdated machinery technology. In an integrated green inventory model, the produced green products cannot all be perfect throughout a cycle, particularly when machines malfunction. Therefore, an inspection policy is introduced to clean the production process from unusable defect products, the correctness of which depends on the discussion of the inspected errors. The perfect products detected via the inspection process are delivered to the retailer as well as the market. To transport green products, it is essential to control the capacity of the containers and the quantities of green products transported per batch. In this study, the greenhouse gas equivalence factor of CO$ _2 $ emissions is calculated for all green products' manufacturing and transportation mediums. These types of energies are used in the manufacturing process: electricity, natural gas, and coal. Whereas within transportation, four transportation modes are considered: railways, roadways, airways, and waterways. The retailer can agree to transport their inventories to the customers' house according to their requirement by requiring a third-party local agency via outsourcing criteria. The model solves the problem of CO$ _2 $ emissions through production and transportation within the machine breakdown.</p></abstract>