The impact of R&D expenditures and screening in an economic production rate (EPR) inventory model for a flawed production system with imperfect screening under an interval-valued environment

Abstract

In this paper, a single product of a single manufacturing unit for an imperfect production inventory system is modelled to minimize the total cost of a production cycle. A large fraction of defective items is passed to customers by manufacturers due to imperfect screening method so manufacturer replace them with new ones while incurring penalties. This fraction depends on the investment of research and development (R&D). This paper optimizes the R&D cost to minimize the defective items produced in a production line. The demand function depends on the selling price, advertisement cost, and product quality. The quality of the produce items is measured by screening time effort and investment in R&D. Further, we considered all the costs of the production cycle in interval-valued form and elaborately discuss the application of interval metric in the total cost interval objective function. A necessary and sufficient conditions are derived for the proposed model with the help of modified KKT conditions. Results show that applying screening and R&D costs significantly reduces the number of defective items and simultaneously reduces the total cost. A numerical example is presented along with sensitivity analyses on different parameters with the help of MATLAB software.