This paper presents an algorithm for automated proof nets construction in the non-commutative multiplicative linear logic (NCMLL) that is a logic useful for applications as planning, concurrency or sequentiality. The properties of this algorithm can be proved from a recently defined graph-theoretic characterization of non-commutative proof nets. Involving simple construction principles improved in the commutative case, it induces also a new proof search method for NCMLL. Moreover the relationships between non-commutative linear logic and Lambek calculus lead to a new method for automatic construction of proof nets for this calculus.