عنوان مقاله [English]
The increasing importance of customer's trust and demand diversification has turned the attention to warranty policy and supplying a family of products. In this respect, while retaining the benefits of mass production and flexibility each member shows to a specific segment of demand, appropriate models have not been sufficiently developed. This paper presents a maximization profit model by simultaneously optimizing the price and warranty length for products in a family of products through application of Markov chains. A continuous Markov model was used to calculate the steady state probabilities that the products need for warranty services. Then, the optimal prices and warranty lengths for all products were determined using a mathematical model to maximize the profitability of the products. The problem was formulated in two scenarios of fixed time and renewable warranty policies. Given the integer warranty length, the problem was a mixed nonlinear integer programming. Numerical samples for the problems solved by GAMS software and sensitivity analysis for the important parameters were also investigated. The results showed that the model was sensitive mostly in the case of price and warranty length elasticity. Moreover, the share of each product in total production did not change much under the influence of capacity change. This study can help manufacturers optimize the main variables of a product including reliability, price, and warranty period simultaneously at the product development stage (design and engineering). The proposed model can be operationally used by the managers for decision-making on the price and warranty length for a family product.