Effect of In-Process Inspection on Highly Imperfect Production System Considering Environmental Deliberations

The aim of almost every production firm is to gain maximum profit along with customer satisfaction. The formation of imperfect products is an obvious process in a production system, which is not a good thing from a business point of view. This paper considers an inventory model for an imperfect production system. All the imperfect products are assumed to be reworkable. An investment occurs for in-process inspection to reduce the rate of formation of imperfect items. A comparison is performed with a production system without in-process inspection to demonstrate the effectiveness of the model. The study shows that the implementation of in-process inspection significantly reduces the total cost of the system as compared to a production system without in-process inspection. The results obtained show that the use of in-process inspection can reduce the total cost by up to 9.3%. Moreover, reducing the formation of defective items saves energy as well as resources. In addition, to reduce carbon emissions, a penalty is implemented on carbon emissions caused by manufacturing, reworking, disposal, and indirect emissions caused by the transportation of disposed items to the treatment facility. As everyone should now be concerned about the environment, green technology is implemented to reduce the amount of carbon emissions to some extent. A classical optimization technique is used to achieve decision variables, i.e., optimal production quantity (Q), fraction of profit invested in in-process inspection (Pf), and green technology investment (G), such that the total cost of the system is minimized. A sensitivity analysis is performed to determine the effects of various parameters on the decision variables and total cost. Maple 18 and Mathematica 11 software are used for mathematical work and graphical representation.