We study the parallel machine scheduling problem to minimize the sum of the weighted completion times of the jobs to be scheduled (problem Pm||ΣwjCj in the standard three-field notation). We use the set covering formulation that was introduced by van den Akker et al. (1999) for this problem,...

We define and solve the robust machine availability problem in a parallel machine environment, which aims to minimize the number of identical machines required while completing all the jobs before a given deadline. Our formulation preserves a user-defined robustness level regarding possible...

We consider an extension of classic parallel machine scheduling where a set of jobs is scheduled on identical parallel machines and an undirected conflict graph is part of the input. Each node in the graph represents a job and an edge implies that its two jobs are conflicting, meaning that they...