977 research outputs found
How the structure of precedence constraints may change the complexity class of scheduling problems
This survey aims at demonstrating that the structure of precedence
constraints plays a tremendous role on the complexity of scheduling problems.
Indeed many problems can be NP-hard when considering general precedence
constraints, while they become polynomially solvable for particular precedence
constraints. We also show that there still are many very exciting challenges in
this research area
Preemptive scheduling on uniform parallel machines with controllable job processing times
In this paper, we provide a unified approach to solving preemptive scheduling problems with uniform parallel machines and controllable processing times. We demonstrate that a single criterion problem of minimizing total compression cost subject to the constraint that all due dates should be met can be formulated in terms of maximizing a linear function over a generalized polymatroid. This justifies applicability of the greedy approach and allows us to develop fast algorithms for solving the problem with arbitrary release and due dates as well as its special case with zero release dates and a common due date. For the bicriteria counterpart of the latter problem we develop an efficient algorithm that constructs the trade-off curve for minimizing the compression cost and the makespan
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 that, for a subclass of these problems, the completion times of all jobs
can be ordered in an optimal solution. Using these two results, we provide new
results on polynomially solvable problems and hence refine the boundary between
P and NP for these problems
Parallel machine scheduling with release dates, due dates and family setup times
In manufacturing, there is a fundamental conflict between efficient production and delivery performance. Maximizing machine utilization by batching similar jobs may lead to poor delivery performance. Minimizing customers' dissatisfaction may lead to an inefficient use of the machines. In this paper, we consider the problem of scheduling n independent jobs with release dates, due dates, and family setup times on m parallel machines. The objective is to minimize the maximum lateness of any job. We present a branch-and-bound algorithm to solve this problem. This algorithm exploits the fact that an optimal schedule is contained in a specific subset of all feasible schedules. For lower bounding purposes, we see setup times as setup jobs with release dates, due dates and processing times. We present two lower bounds for the problem with setup jobs, one of which proceeds by allowing preemption
Single-machine scheduling with stepwise tardiness costs and release times
We study a scheduling problem that belongs to the yard operations component of the railroad planning problems, namely the hump sequencing problem. The scheduling problem is characterized as a single-machine problem with stepwise tardiness cost objectives. This is a new scheduling criterion which is also relevant in the context of traditional machine scheduling problems. We produce complexity results that characterize some cases of the problem as pseudo-polynomially solvable. For the difficult-to-solve cases of the problem, we develop mathematical programming formulations, and propose heuristic algorithms. We test the formulations and heuristic algorithms on randomly generated single-machine scheduling problems and real-life datasets for the hump sequencing problem. Our experiments show promising results for both sets of problems
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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
08071 Abstracts Collection -- Scheduling
From 10.02. to 15.02., the Dagstuhl Seminar 08071 ``Scheduling\u27\u27 was held
in the International Conference and Research Center (IBFI), Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
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