Stochastic and Markov chain approach to optimize re-manufacturing and outsourcing in the closed loop supply chain.

The turbulent and dynamic environment of today's business world has become increasingly challenging for organizations operating in different business areas. In such a situation, in order to get rid of these conditions, moving forward and towards the perspective of the new horizons of prosperity and survival is the dream of many of them. In the meantime, according to the specific circumstances and requirements that govern each institution or organization, and in order to achieve their desired productivity, they use certain strategies and programs that outsourcing is one of these strategies. Today, organizations are outsourcing to boost competitive ability and profit and focus on their competitive edge.In this research, a mathematical programming approach is proposed to optimize the issue of outsourcing in the supply chain. In this approach, at first the mathematical model of the problem showed and then in order to solve the problem of the theory of Markov chains described. The objective function of the problem involves minimizing the cost of purchasing, outsourcing and lost demand. In order to solve the problem, three genetic metamorphic algorithms, gray wolves and antlion have been used. After examining the numerical expressions, Gray wolf's algorithm has the highest level of performance. In order to expand the applied dimensions of research in real-world conditions, a company (MPEICO) that manufactures insulators is considered as the case study..