We show how to approximate in NC the problem of Scheduling Unrelated Parallel Machines, for a xed number of machines. We develop a (2 + ")-approximate parallel algorithm for the problem. Our approach shows how to relate the linear program obtained by relaxing the integer programming formulation of the problem with a linear program formulation that is positive and in the packing/covering form. T...

This work deals with the parallel machines scheduling problem which consists in the assignment of n jobs on m parallel machines. The most general variant of this problem is when the processing time depends on the machine to which each job is assigned to. This case is known as the unrelated parallel machines problem. Similarly to most of the literature, this paper deals with the minimization of ...

In this paper we consider the problem of scheduling jobs on parallel identical machines, where the processing times of jobs are uncertain: only interval bounds of processing times are known. The optimality criterion of a schedule is the total completion time. In order to cope with the uncertainty we consider the maximum regret objective and we seek a schedule which performs well under all possi...

We investigate approximation algorithms for the classical minimum makespan scheduling problem, focusing on instances where the rank of the matrix describing the processing times of the jobs is bounded. A bounded rank matrix arises naturally when the processing time of a job on machine depends upon a bounded set of resources. A bounded rank matrix also shows up when jobs have varying degrees of ...

We consider the distributed scheduling problem on parallel machines with central objective of maximizing number on-time jobs. Jobs are self-interested utility-maximizers that can choose they processed and exclusively interested in reducing their own private function. Each machine processes jobs according to a local policy. discuss Nash equilibria resulting schedules perform thorough analysis (a...

Theories of language production need to account for how speakers produce prosodic structure. Very few models have addressed the role of prosodic phrasing in speech planning, and little experimental work examining this question has been conducted so far. Four studies designed to investigate the effect of phrase length and prosodic phrasing on speech planning are presented. The first experiment e...

Abstract This paper addresses the unrelated parallel machine scheduling problem with sequence and dependent setup times eligibility constraints. The objective is to minimize maximum completion time (makespan). Instances of more than 500 jobs 50 machines are not uncommon in industry. Such large instances become increasingly challenging provide high-quality solutions within limited amount computa...

This paper studies the customer order scheduling problem in context of additive manufacturing. The study discusses an integrated involving nesting parts as well batches nested onto unrelated parallel machines. A mixed-integer programming model is presented, based on existing formulations from literature, that integrates different materials and sequence-dependent setup times. Additionally, a met...

This paper reviews results related to the parallel machine scheduling problem under availability constraints. The motivation of this paper comes from the fact that no survey focusing on this specific problem was published. The problems of single machine, identical, uniform, and unrelated parallel machines under different constraints and optimizing various objective functions were analyzed. For ...

In this work we propose new randomized rounding algorithms for matroid intersection and matroid base polytopes. We prove concentration inequalities for polynomial objective functions and constraints that has numerous applications and can be used in approximation algorithms for Minimum Quadratic Spanning Tree, Unrelated Parallel Machines Scheduling and Scheduling with Time Windows and Nonlinear ...