Single Machine Scheduling with Release Dates

We consider the scheduling problem of minimizing the average weighted completion time of n jobs with release dates on a single machine. We first study two linear programming relaxations of the problem, one based on a time-indexed formulation, the other on a completiontime formulation. We show their equivalence by proving that a O(n log n) greedy algorithm leads to optimal solutions to both relaxations. The proof relies on the notion of mean busy times of jobs, a concept which enhances our understanding of these LP relaxations. Based on the greedy solution, we describe two simple randomized approximation algorithms, which are guaranteed to deliver feasible schedules with expected objective value within factors of 1.7451 and 1.6853, respectively, of the optimum. They are based on the concept of common and independent a-points, respectively. The analysis implies in particular that the worst-case relative error of the LP relaxations is at most 1.6853, and we provide instances showing that it is at least e/(e - 1) 1.5819. Both algorithms may be derandomized, their deterministic versions running in O(n2 ) time. The randomized algorithms also apply to the on-line setting, in which jobs arrive dynamically over time and one must decide which job to process without knowledge of jobs that will be released afterwards

Single machine scheduling problems with release dates

The single machine scheduling problems have been extensively studied with various criteria to be optimized and under various assumptions. In this work, we review some results obtained recently in the case of different release dates. Most problems with different release dates are NP-hard. Some researchers have proved some dominance properties or sufficient conditions for local optimality which lead to an optimal schedule in some specificic cases. We present some properties or conditions for two regular criteria, total tardiness and total flow time

An Exact Approach to Early/Tardy Scheduling with Release Dates

In this paper we consider the single machine earliness/tardiness scheduling problem with di?erent release dates and no unforced idle time. The problem is decomposed into a weighted earliness subproblem and a weighted tardiness subproblem. Lower bounding procedures are proposed for each of these subproblems, and the lower bound for the original problem is then simply the sum of the lower bounds for the two subproblems. The lower bounds and several versions of a branch-and-bound algorithm are then tested on a set of randomly generated problems, and instances with up to 30 jobs are solved to optimality. To the best of our knowledge, this is the first exact approach for the early/tardy scheduling problem with release dates and no unforced idle time.scheduling, early/tardy, release dates, lower bounds, branch-and-bound

Heuristics for the Early/Tardy Scheduling Problem with Release Dates

In this paper we consider the single machine earliness/tardiness scheduling problem with di?erent release dates and no unforced idle time. We analyse the performance of several dispatch rules, a greedy procedure and a decision theory local search heuristic. The dispatch rules use a lookahead parameter whose value must be specified. We perform some experiments to determine an appropriate value for this parameter. The use of dominance rules to improve the solutions obtained by these heuristics is also considered. The computational results show that the use of the dominance rules can indeed improve the solution quality with little additional computational e?ort. To the best of our knowledge, this is the first analysis of heuristic performance for the early/tardy scheduling problem with release dates and no unforced idle time.scheduling, early/tardy, release dates, heuristics

Bounded single-machine parallel-batch scheduling with release dates and rejection

Author name used in this publication: T. C. E. Cheng2008-2009 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Approximation Results for Preemptive Stochastic Online Scheduling

We present first constant performance guarantees for preemptive stochastic scheduling to minimize the sum of weighted completion times. For scheduling jobs with release dates on identical parallel machines we derive policies with a guaranteed performance ratio of 2 which matches the currently best known result for the corresponding deterministic online problem. Our policies apply to the recently introduced stochastic online scheduling model inwhich jobs arrive online over time. In contrast to the previously considered nonpreemptivesetting, our preemptive policies extensively utilize information on processing time distributions other than the first (and second) moments. In order to derive our results we introduce a new nontrivial lower bound on the expected value of an unknown optimal policy that we derive from an optimal policy for the basic problem on a single machine without release dates. This problem is known to be solved optimally by a Gittins index priority rule. This priority index also inspires the design of our policies.computer science applications;

Application of submodular optimization to single machine scheduling with controllable processing times subject to release dates and deadlines

In this paper, we study a scheduling problem on a single machine, provided that the jobs have individual release dates and deadlines, and the processing times are controllable. The objective is to find a feasible schedule that minimizes the total cost of reducing the processing times. We reformulate the problem in terms of maximizing a linear function over a submodular polyhedron intersected with a box. For the latter problem of submodular optimization, we develop a recursive decomposition algorithm and apply it to solving the single machine scheduling problem to achieve the best possible running time

Solving two production scheduling problems with sequence-dependent set-up times

In today�s competitive markets, the importance of good scheduling strategies in manufacturing companies lead to the need of developing efficient methods to solve complex scheduling problems. In this paper, we studied two production scheduling problems with sequence-dependent setups times. The setup times are one of the most common complications in scheduling problems, and are usually associated with cleaning operations and changing tools and shapes in machines. The first problem considered is a single-machine scheduling with release dates, sequence-dependent setup times and delivery times. The performance measure is the maximum lateness. The second problem is a job-shop scheduling problem with sequence-dependent setup times where the objective is to minimize the makespan. We present several priority dispatching rules for both problems, followed by a study of their performance. Finally, conclusions and directions of future research are presented.Production-scheduling, set-up times, priority dispatching rules