Optimal price and pro rata decisions for combined warranty policies with different repair options

Abstract

A repairable product under a non-renewing combined warranty policy that is subject to a displaced log-linear demand function of the product's price and pro rata period length is considered. Expressions for the manufacturer's long-run average profit per unit time under replacement, minimal and general repair options are obtained. In addition, expressions for the stationary points and second-order conditions of the profit function are presented. Numerical illustrations that demonstrate optimal product pricing, pro rata length determination, and repair option selection to maximize the manufacturers, profit are given.

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

“…Huang, Liu, and Murthy (2007) develop a model to determine the optimal product reliability, price and warranty strategy to achieve the maximum total integrated profit for a general repairable multi-component product sold under a free replacement-repair warranty strategy. Matis, Jayaraman, and Rangan (2008) explore the optimal price and pro rate warranty length for a multi-component product with considering the different repair options on the com-ponents. Bai and Pham (2006) investigate optimisation of warranty policies for single products composed of multiple components.…”

Notice of Retraction: Survey on research and development of product warranty

“…Matis et al [9] considered repairable product of non-renewing combined warranty policy, and obtained manufacturer's long-run average profit per unit time under replacement, minimal repair and general repair options. Pascual and Ortega [10] confirmed the optimal during time of life cycle and overhaul interval.…”

Modeling and analysis of a warranty policy using new and reconditioned parts

“…The expected forecast sales volume/total demand, D ( w , p ), for the original product is modeled as a displaced log‐linear function of w and p : where D 1 >0, , d 1 >1, and d 2 >0. The constant d 1 is the rate of decrease of the sales volume with the increasing price of the product, d 2 is the rate of increase of the sales volume with the increasing warranty length, D 1 is a demand amplitude factor, and D 2 is a warranty displacement constant.…”

“…This paper is a complete overhaul and extension of the conference paper and is extended by improving the literature review, defining a more accurate acquisition cost function for the reconditioned components, developing the mathematical formulation for the expected number of failures per product sold, using a different and well‐established total demand function , introducing the recovery cost discussed previously, and proving local optimality using the Hessian matrix. Furthermore, five new sets of numerical experiments are designed and run, and the results are fully analyzed and discussed to derive managerial insights.…”