A new algorithm for multidimensional scheduling problems

In this work we consider the hybrid flexible flowline (HFFL) problem with a set of additional constraints that apply in real-world industrial environments. A set of n jobs has to be scheduled on a set of m ordered stages. All jobs are available at time 0, and job preemption is not allowed. Each stage i consists in mi parallel unrelated machines. Jobs might skip stages; we denote the stages visited by job j as the set Fj . At each stage i in Fj , job j should be processed by exactly one machine in the set of eligible machines Eij . Precedence constraints among jobs refrain job j from starting in the first stage before ending the process of its predecessor jobs Pj in the last stage. Setup times Siljk depend on both the previous job j and the next job k, and on the stage i and machine l where the setup is executed. These times can be anticipatory or non-anticipatory. Time lags lagilj between finishing a job j at stage i and starting the job at the next stage, can be positive or negative and depend on the machine l that job j is assigned to at stage i. Machines release dates are given by the input parameter relij. The goal is to find a schedule that minimises the makespan, that is, the maximum job completion time. The gap between HFFL theory and scheduling practice is named in two reviews on HFFL problems [1, 2]. For a more recent review, see [3].