Scheduling parallel machines with resource-dependent processing times

A two-stage resource allocation model for lifeline systems quick response with vulnerability analysis

“…Furthermore, since the resource allocation problem could be generalized to the unrelated parallel machine scheduling problems, many heuristic algorithms could also be used to solve the resource allocation problem (Lin, Pfund, & Fowler, 2011;Su & Lien, 2009;Yeh, Lai, Lee, & Chuang, 2014).…”

Parallel machine scheduling with additional resources: Notation, classification, models and solution methods

“…A number of studies assume that the flexible resource may be allocated freely among the machines, but the resulting resource assignment must remain fixed for the whole scheduling horizon (Daniels et al, 1999;Ruiz-Torres and Centeno, 2007;Sue and Lien, 2009). Daniels et al (1996) refer to this case as static problem.…”

“…They state that loading one machine at a time outperforms the approach of simultaneously loading all machines. Finally, in a recent study, Sue and Lien (2009) develop two heuristic algorithms for the same static UPMFRS problem. The former assigns jobs to the machines first and then deploys the resources to jobs while the latter proceeds in the reverse manner.…”

A Direct Proof of the 4/3 Bound of LPT Scheduling Rule

“…There is a rich literature on this problem (see, e.g., [2][3][4]). This problem is routinely encountered in many real-life applications such as production lines, shipping docks, universities, and computer systems [5,6].…”