Scheduling Imprecise Computation Tasks on Parallel Machines to Minimize Linear and Non-Linear Error Penalties: Reviews, Links and Improvements

We study scheduling problems with controllable processing times on parallel machines, in which the decision-maker selects an actual processing time for each job from a given interval. The chosen values of the processing times must be such that each job can be preemptively scheduled within a given time interval, and it is required to minimize a certain cost function that depends on the chosen times. Using a popular interpretation of these models, we formulate these problems in terms of scheduling imprecise computation tasks, with the objective functions that depend on errors of computation. We prove that all problems traditionally considered within the body of research on scheduling imprecise computation tasks on parallel machines are no harder computationally than their counterparts with ...xed processing times. As a rule, we achieve these best possible algorithms not by building specialized procedures, but rather by adapting advanced methods for solving network ‡ow problems and techniques of submodular optimization.