Abstract: The relevance of planning non-hierarchical supply chains has increased due to growing collaboration among industrial and logistic organizations once this planning approach aims to optimize the supply chain while preserving each actor's individuality. Linear programming is the predominant modelling approach to deal with non-hierarchical supply chains according to the state-of-the-art literature. Metaheuristics and exact methods are the classical solving methods for linear programming problems, with different characteristics in terms of solution quality and capability of handling complex problems in feasible computation time. In this context, this paper evaluates methods to solve linear programming problems considering their capability of dealing with most common decision model types associated with spare parts supply chains applying collaborative planning concepts. The gathered references substantiate the conclusion that, for normal sized problems, the simplex method continues to be the most attractive method. For bigger problems, interior point methods can be a better alternative. And for problems that surpass interior point method capacity, metaheuristics are recommended.
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