Preemptive models of scheduling with controllable processing times and of scheduling with imprecise computation: A review of solution approaches

This paper provides a review of recent results on scheduling with controllable processing times. The stress is on the methodological aspects that include parametric flow techniques and methods for solving mathematical programming problems with submodular constraints. We show that the use of these methodologies yields fast algorithms for solving problems on single machine or parallel machines, with either one or several objective functions. For a wide range of problems with controllable processing times we report algorithms with the running times which match those known for the corresponding problems with fixed processing times. As a by-product, we present the best possible algorithms for a number of problems on parallel machines that are traditionally studied within the body of research on scheduling with imprecise computation

Decomposition algorithms for submodular optimization with applications to parallel machine scheduling with controllable processing times

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

Polynomial-time approximation schemes for scheduling problems with time lags

We identify two classes of machine scheduling problems with time lags that possess Polynomial-Time Approximation Schemes (PTASs). These classes together, one for minimizing makespan and one for minimizing total completion time, include many well-studied time lag scheduling problems. The running times of these approximation schemes are polynomial in the number of jobs, but exponential in the number of machines and the ratio between the largest time lag and the smallest positive operation time. These classes constitute the first PTAS results for scheduling problems with time lags

Models and algorithms for energy-efficient scheduling with immediate start of jobs

We study a scheduling model with speed scaling for machines and the immediate start requirement for jobs. Speed scaling improves the system performance, but incurs the energy cost. The immediate start condition implies that each job should be started exactly at its release time. Such a condition is typical for modern Cloud computing systems with abundant resources. We consider two cost functions, one that represents the quality of service and the other that corresponds to the cost of running. We demonstrate that the basic scheduling model to minimize the aggregated cost function with n jobs is solvable in O(nlogn) time in the single-machine case and in O(n²m) time in the case of m parallel machines. We also address additional features, e.g., the cost of job rejection or the cost of initiating a machine. In the case of a single machine, we present algorithms for minimizing one of the cost functions subject to an upper bound on the value of the other, as well as for finding a Pareto-optimal solution

Scheduling incompatible tasks on two machines

The paper studies the problem of scheduling tasks on two machines to minimize the makespan. The tasks are assigned to the machine in advance. An incompatibility relation is defined over the tasks which forbids any two incompatible tasks to be processed at the same time. The problem can serve as a mathematical model for some batching problems in which the jobs are grouped in pairs on two machines. A linear-time algorithm is presented

Approximation results for flow shop scheduling problems with machine availability constraints

This paper considers two-machine flow shop scheduling problems with machine availability constraints. When the processing of a job is interrupted by an unavailability period of a machine, we consider both the resumable scenario in which the processing can be resumed when the machine next becomes available, and the semi-resumable scenarios in which some proportion of the processing is repeated but the job is otherwise resumable. For theresumable scenario, problems with non-availability intervals on one of the machines are shown to admit fully polynomial-time approximation schemes that are based on an extended dynamic programming algorithm. For the problem with several non-availability intervals on the first machine, we present a fast 3/2-approximation algorithm. For the problem with one non-availability interval under the semi-resumable scenario, polynomial-time approximation schemes are developed

Computational modeling of electrodepostion in small features under megasonic agitation

This paper considers copper electrodeposition processes in microvias and verifies whether the quality of electroplating can be improved in the presence of acoustic streaming generated by a megasonic transducers placed into a plating cell. Our numerical experiments demonstrate that an improvement of cupric ion transport is observed in the area close to the mouth of a via, and that leads to fillings of better quality compared to those achieved under basic conditions. On the other hand, acoustic streaming inside the via has no major impact. The reasons for this lack of impact are different for blind vias and through vias

Scheduling incompatible tasks on two machines

The paper studies the problem of scheduling tasks on two machines to minimize the makespan. The tasks are assigned to the machine in advance. An incompatibility relation is defined over the tasks which forbids any two incompatible tasks to be processed at the same time. The problem can serve as a mathematical model for some batching problems in which the jobs are grouped in pairs on two machines. A linear-time algorithm is presented.Two machine scheduling Incompatibility graph Max-batch Polynomial algorithm