This paper addresses a supply chain management problem with consideration of production and distribution activities. The formulation is based on a mixed-integer bi-level programming approach as a mathematical model of the leader-follower game. A hybrid evolutionary-deterministic strategy has been developed and the performance of the solution method is evaluated by numerical experiments based on a ficticious hydrogen energy system. The experimental results obtained show that the resolution method is efficient and promising for dealing with multi-objective optimization cases.The National Council of Science and Technology of Mexico (Consejo Nacional de Ciencia y Tecnologia, CONACYT). Bourse reference: 2018-000003-01EXTF-00046, supported this w...