Dynamic optimisation of price, warranty length and production rate

Abstract

This study investigates a marketing and production problem that uses price, warranty length and production rate as simultaneous dynamic decision variables. Furthermore, this study was conducted under a policy of free replacement of defective items; and under conditions where demand was dynamic and dependent on price, warranty and cumulative sales. A continuous profit maximisation model was formulated, which first considers the expected warranty cost per item. Then, it considers the steps for dynamic optimisation, which eventually derive the optimal price, warranty length and production rate. Discretisation was then applied to the profit maximisation model and a digital computer was used to identify the optimal control paths, obtaining a finite solution that is a set of real numbers for practical application. A model-driven Decision Support System is finally established, which provides a graphical user interface for overcoming the complexity of the analytical process. Subsequently, the proposed system was tested and the analytical solution was verified using several demand functions for additive lifetime distributions, thereby demonstrating the system's effectiveness.