This work reviews lean literature on the supply chain focused on the operational approach, from the lean management to the Kanban system. But, the main issue of this work is to analyze the behavior of a lean supply chain using a Kanban system managing the planning in two different ways. The difference between both is related to the production order or sequence to follow: the product with fewer inventories in stock (the most critical to run out) or the one which requires less set-up time to optimize unproductive times. The study the behavior of the supply chain, it would be done through simulation with many different scenarios: 5 different demands, each one with two coefficients of variance, 4 different batch sizes, 4 different compositions of production and process saturation and ensuring different service levels between 92% and 98%. To compare these supply chain models, an approach of the supply chain using the EOQ (Economic Order Quantity) system will be also simulated in the same conditions but with one batch size, the most economic one.