Abstract
In this paper we present a decomposition algorithm for maximizing a linear function over a submodular polyhedron intersected with a box. Apart from this contribution to submodular optimization, our results extend the toolkit available in deterministic machine scheduling with controllable processing times. We demonstrate how this method can be applied to developing fast algorithms for minimizing total compression cost for preemptive schedules on parallel machines with respect to given release dates and a common deadline. Obtained scheduling algorithms are faster and easier to justify than those previously known in the scheduling literature.
Highlights
In scheduling with controllable processing times, the actual durations of the jobs are not fixed in advance, but have to be chosen from a given interval
We present a decomposition algorithm for maximizing a linear function over a submodular polyhedron intersected with a box
We demonstrate how this method can be applied to several scheduling problems, in which it is required to minimize the total penalty for choosing actual processing times, known as total compression cost
Summary
In scheduling with controllable processing times, the actual durations of the jobs are not fixed in advance, but have to be chosen from a given interval. This area of scheduling has been active since the 1980s, see surveys [16] and [22]. As established in [23,24], there is a close link between scheduling with controllable processing times and linear programming problems with submodular constraints. This allows us to use the achievements of submodular optimization [4,21] for design and justification of scheduling algorithms. Our papers [25,27] can be viewed as convincing examples of such a positive mutual influence of scheduling and submodular optimization
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
