Maryam Dehghanbaghi - Department of Industrial Engineering, Robat karim Branch, Islamic Azad University, Tehran Iran.
Azadeh Dabbaghi - Research Institute of Petroleum Industry, Tehran, Iran.

After the second-hand products return to the second-hand markets, either goods, parts, or materials are reused or disposed. For optimum sales, these products are under the process of determining the optimal warranty period and warranty policy, so that both the seller's profit and the consumer's profit are met. Therefore, estimating the warranty costs for future claims on second-hand products is very necessary. In this paper, a hybrid stochastic model is presented to improve the reliability of second-hand products under the free repair replacement warranty policy to determine the level of upgrade, with the aim of reducing warranty costs. Using the upgrade actions, the model, based on three approaches, minimal-perfect repair, virtual age, and improvement factor, is developed for estimating the warranty costs of second-hand products. The contribution of this research is the application of three upgrade approaches in the warranty cost model simultaneously to estimate the warranty costs and optimum upgrade level more realistic. Finally, under different product lifetime, a numerical example and sensitivity analysis are provided. Evaluation is presented in four lifetimes for second-hand products ranging from one to four years for which the optimum upgrade level and the warranty period are determined. The results show that the higher the level of second-hand product upgrades to a certain extent, the higher the savings, but the more upgrades are not cost-effective for second-hand products.

Warranty, Second-hand product, Warranty costs, Stochastic modeling, Upgrade