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This work deals with the inventory, purchase and delivery optimization problem in the supply chain. The formulation of two problems is presented involving several decision levels. The first one optimizes the company inventory and purchase tasks in a medium-term horizon planning, assuming that the total amount purchased is delivered at the beginning of each period. Then, in a more detailed formulation, the purchased amount is distributed among several deliveries giving rise to a non-linear non-convex problem. Some transformation techniques are evaluated to overcome the non-convexities in order to find a global solution in a reasonable execution time. Finally, the results obtained considering some possible scenarios are analyzed and compared.