Optimizing the economic lot size of a three-stage supply chain with backordering derived without derivatives

Multi-stage supply chain management integration provides a key to successful international business operations. This is because the integrated approach improves the global system performance and cost efficiency. The integrated production inventory models using differential calculus to solve the multi-variable problems are prevalent in operational research. This paper extends the integrated vendor–buyer inventory problem by Yang and Wee [Yang, P.C., Wee, H.M., 2002. The economic lot size of the integrated vendor–buyer system derived without derivatives. Optimal Control Applications and Methods 23, 163–169] to solve the multi-variable problems in the supply chain, and simplifies the solution procedure using a simple algebraic method. As a result, the solution procedure may be easily understood and applied so as to derive the optimal solution.