We provide several non-approximability results for deterministic scheduling problems whose objective is to minimize the total job completion time. Unless P = NP, none of the problems under consideration can be approximated in polynomial time within arbitrarily good precision. Most of our results are derived by Max SNP hardness proofs. Among the investigated problems are: scheduling unrelated ma...

W consider both branch-and-cut and column-generation approaches for the problem of finding a minimumcost assignment of jobs with release dates and deadlines to unrelated parallel machines. Results are presented for several variants both with and without constraint programming. Among the variants, the most effective strategy is to combine a tight and compact, but approximate, mixed integer progr...

We present a general time-indexed formulation that contains scheduling problems with unrelated parallel machines. We derive a class of basic valid inequalities for this formulation, and we show that a subset of these inequalities are facet-defining. We characterize all facet-defining inequalities with right-hand side 1. Further, we show how to efficiently separate these inequalities.

This work deals with the problem of scheduling n independent jobs on m unrelated parallel machines with the objective of minimizing the makespan (the total elapsed time from the start of execution until all jobs have been completed). Preemption is not allowed. This way a job, once assigned to a particular machine, may not be removed until it has finished its execution. All the machines start wo...

We consider mechanism design issues for scheduling problems and we survey some recent developments on this important problem in Algorithmic Game Theory. We treat both the related and the unrelated version of the problem. 1 The scheduling problem The problem of scheduling unrelated machines [21, 14] is one of the most fundamental algorithmic problems: There are n machines and m tasks∗ and machin...

The Price of Anarchy [Koutspoupias and Papadimitriou, 1999] is the, by now celebrated, ratio used to measure how system performance is affected by the selfish behaviour of agents using it. In this work we show bounds on the Price of Anarchy for problems of restricted scheduling of selfish jobs on related and unrelated machines.

Motivated by the problem to approximate all feasible schedules by one schedule in a given scheduling environment, we introduce in this paper the concepts of strong simultaneous approximation ratio (SAR) and weak simultaneous approximation ratio (WAR). Then we study the two parameters under various scheduling environments, such as, nonpreemptive, preemptive or fractional scheduling on identical,...

The paper addresses the problem of scheduling in the two-stage flowshop with parallel unrelated machines and renewable resource constraints. The objective is minimization of makespan. The problem is NP-hard. Fast heuristic algorithms using list scheduling and greedy strategies are proposed. For evaluation of the performance of the algorithms computational experiments are performed on randomly g...

Scheduling jobs on unrelated parallel machines so as to minimize makespan is one of the basic problems in the area of machine scheduling. In the first part of the paper, we prove that the power of preemption, i.e., the worst-case ratio between the makespan of an optimal nonpreemptive and that of an optimal preemptive schedule, is at least 4. This matches the upper bound proposed in Lin and Vitt...

We present an unified approach to study online scheduling problems in the resource augmentation/speed scaling models. Potential function method is extensively used for analyzing algorithms in these models; however, they yields little insight on how to construct potential functions and how to design algorithms for related problems. In the paper, we generalize and strengthen the dual-fitting tech...