Scheduling n independent jobs on m Unrelated Parallel Machines (SUM) is the problem of assigning n jobs j = 1, .., n to m machines i = 1, .., m so that each job is processed without interruption on one of the machines, and at any time, every machine processes at most one job. The objective is to minimize the makespan of the schedule. SUM is an NP-hard problem even when the number of machines is...

The problem of Scheduling n Independent Jobs on m Unrelated Parallel Machines, when the number of machines m is xed, is considered. The standard problem of minimizing the makespan of the schedule (SUM) and the bicriteria problem of scheduling with bounded makespan and cost (SUMC) are addressed, and randomized fully linear time approximation schemes are shown for both of them. While matching the...

This paper introduces a stochastic scheduling problem. In this problem a directed acyclic graphs (DAG) represents the precedence relations among m tasks that n workers are scheduled to execute. The question is to find a schedule Σ such that if tasks are assigned to workers according toΣ , the expected time needed to execute all the tasks is minimized. The timeneeded to execute task t byworkerw ...

We show that the problems of minimizing total completion time and of minimizing the number of late jobs on unrelated parallel machines, when preemption is allowed, are both NP-hard in the strong sense. The former result settles a long-standing open question. A special case of the unrelated machine model is the identical machine model with the restriction that a job can only be processed on a sp...

Motivated by applications in energy-efficient scheduling in data centers, Khuller, Li, and Saha introduced the machine activation problem as a generalization of the classical optimization problems of minimum set cover and minimum makespan scheduling on parallel machines. In this problem, a set of n jobs have to be distributed among a set of m (unrelated) machines, given the processing time of e...

We consider the problem of scheduling n jobs to minimize the makespan on m unrelated machines, where job j requires time pij if processed on machine i. A classic algorithm of Lenstra et al. [5] yields the best known approximation ratio of 2 for the problem. Improving this bound has been a prominent open problem for over two decades. In this paper we obtain a tighter bound for a wide subclass of...

We study a problem of optimal scheduling and lot-sizing a number of products on m unrelated parallel machines to satisfy given demands. A sequence dependent setup time is required between lots of different products. The products are assumed to be all continuously divisible or all discrete. The criterion is to minimize the time, at which all the demands are satisfied, Cmax, or the maximum latene...

This paper presents an empirical comparison of polynomial-time approximation algorithms and local search heuristics for the problem of minimizing total weighted completion time on unrelated parallel machines. Algorithms with a worst-case performance guarantee are based on rounding a fractional solution to an LP-rela....<ation or to a convex quadratic programming relaxation. We also investigate ...

We study the scheduling problem on unrelated machines in the mechanism design setting. This problem was proposed and studied in the seminal paper of Nisan and Ronen [NR99], where they gave a 1.75-approximation randomized truthful mechanism for the case of two machines. We improve this result by a 1.6737-approximation randomized truthful mechanism. We also generalize our result to a 0.8368m-appr...

A methodology for minimizing the weighted tardiness of jobs in unrelated parallel machining scheduling with sequence-dependent setups is presented in this paper. To comply with industrial situations, the dynamic release of jobs and dynamic availability of machines are assumed. Recognizing the inherent difficulty in solving industrial-size problems efficiently, six different search algorithms ba...