New complexity results for parallel identical machine scheduling problems with preemption, release dates and regular criteria

New complexity results for parallel identical machine scheduling problems with preemption, release dates and regular criteria

In this paper, we are interested in parallel identical machine scheduling problems with preemption and release dates in case of a regular criterion to be minimized. We show that solutions having a permutation flow shop structure are dominant if there exists an optimal solution with completion times scheduled in the same order as the release dates, or if there is no release date. We also prove t...

Refining the boundary between P and NP for identical machine scheduling problems with preemption and release dates

Minimizing Total Tardiness in Parallel-Machine Scheduling with Release Dates

The considered problem is the scheduling of a set of N jobs on M identical parallel machines in order to minimize the total tardiness without any preemption or splitting. Each job has its own processing time, release date and due date. All the machines are considered identical (with same speed) and available during all the scheduling period. This problem is NP-hard. An exact resolution, an Ant ...

Single Machine Scheduling with Release Dates

We consider the scheduling problem of minimizing the average weighted completion time of n jobs with release dates on a single machine. We first study two linear programming relaxations of the problem, one based on a time-indexed formulation, the other on a completiontime formulation. We show their equivalence by proving that a O(n logn) greedy algorithm leads to optimal solutions to both relax...

Integrated network design and scheduling problems with parallel identical machines: Complexity results and dispatching rules

We consider the class of integrated network design and scheduling (INDS) problems that focus on selecting and scheduling operations that will change the characteristics of a network, while being specifically concerned with the performance of the network over time. Motivating applications of INDS problems include infrastructure restoration after an extreme event and building humanitarian logisti...