List scheduling and beam search methods for an extended version of the flexible job shop scheduling problem

An extended version of the flexible job shop problem is tackled in this work. The considered extension to the classical flexible job shop problem allows the precedences between the operations to be given by an arbitrary directed acyclic graph instead of a linear order. Therefore, the problem consists of allocating the operations to the machines and sequencing them in compliance with the given precedences. The goal in the present work is the minimization of the makespan. A list scheduling algorithm is introduced and its natural extension to a beam search method is proposed. Numerical experiments assess the efficiency of the proposed approaches.