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.

A value-at-risk approach to optimisation of warranty policy

“…Ladany and Shore (2007) address a method to determine the optimal warranty period with considering the products lifetime and market demand. Lin, Wang, and Chin (2009) optimise the price, warranty length and production rate of a one component system dynamically. Wu, Chou, and Huang (2009) develop a decision model to determine the optimal price, the length of warranty and the production rate to maximise profit based on the pre-determined life cycle in a static demand market.…”

“…In the literature, the sales volume of product k, M k , is expressed by a function of product price P k and length of warranty T k in different forms, including linear (Lin et al, 2009;Yazdian et al, 2016) and non-linear ones (Huang et al, 2007;Ladany & Shore, 2007;Xie, Liao, & Zhu, 2014). For simplicity, a linearity form, introduced by Yazdian et al (2016), is used in this paper.…”

After-sales service competition in a supply chain: Does uncertainty affect the conflict between profit maximization and customer satisfaction?

“…In academic research, warranty length is a common research theme (e.g., Chien 2005Chien , 2012Jack and Murthy 2006;Lin et al, 2009;Chen, et al, 2010;Wu and Longhurst, 2011;Bouguerra, et al, 2012). Also, research on warranty often sets up two types of warranty, base warranty and extended warranty (e.g., Wu and Longhurst 2011;Bouguerra, et al, 2012), as we assume two types of after-sales service plans, base and optional services.…”

Understanding multi-stage diffusion process in presence of attrition of potential market and related pricing policy

“…It may be noted that there is always an objective difference between the customers attitude towards the price and the manufacturers perception of the price. The manufacturer sets prices with the aim to maximize the overall profit of the firm, while at the same time, the customers are considered to be coherent in the attempts to make a purchase when the price is lower [30]. Therefore, there should be a tradeoff between the customers utility and the sellers aim to maximize the profit.…”