Improved Rejection Penalty Algorithm with Multiprocessor Rejection Technique

This paper deals with multiprocessor scheduling with rejection technique where each job is provided with processing time and a given penalty cost. If the job satisfies the acceptance condition, it will schedule in the least loaded identical parallel machine else job is rejected. In this way its penalty cost is calculated. Our objective is to minimize the makespan of the scheduled job and to minimize the sum of the penalties of rejected jobs. We have merged ‘CHOOSE ‘and ‘REJECTION PENALTY’ algorithm to reduce the sum of penalties cost and makespan. Our proposed ‘Improved Reject penalty algorithm’ reduce competitive ratio, which in turn enhances the efficiency of the on-line algorithm. By applying our new on-line technique, we got the lower bound of our algorithm is is 1.286 which is far better from the existing algorithms whose competitive ratio is at 1.819. In our approach we have consider non-preemption scheduling technique

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

Order Acceptance and Scheduling: A Taxonomy and Review

Over the past 20 years, the topic of order acceptance has attracted considerable attention from those who study scheduling and those who practice it. In a firm that strives to align its functions so that profit is maximized, the coordination of capacity with demand may require that business sometimes be turned away. In particular, there is a trade-off between the revenue brought in by a particular order, and all of its associated costs of processing. The present study focuses on the body of research that approaches this trade-off by considering two decisions: which orders to accept for processing, and how to schedule them. This paper presents a taxonomy and a review of this literature, catalogs its contributions and suggests opportunities for future research in this area

An online scheduling algorithm for a two-layer multiprocessor architecture

In this paper we give online algorithms and competitive ratio bounds for a scheduling problem on the following two-layer architecture. The architecture consists of two sets of processors; within each set the processors are identical while both the processors themselves and their numbers may differ between the sets. The scheduler has to make an online assigment of jobs to one of the two processor sets. Jobs, assigned to a processor set, are then sceduled in an optimal offline preemptive way within the processor set considered. The scheduler's task is to minimize the maximum of the two makespans of the processor sets

Maximizing total job value on a single machine with job selection

This paper describes a single machine scheduling problem of maximizing total job value with a machine availability constraint. The value of each job decreases over time in a stepwise fashion. Several solution properties of the problem are developed. Based on the properties, a branch-and-bound algorithm and a heuristic algorithm are derived. These algorithms are evaluated in the computational study and the results show that the heuristic algorithm provides effective solutions within short computation times

Maximizing total job value on a single machine with job selection

This paper describes a single machine scheduling problem of maximizing total job value with a machine availability constraint. The value of each job decreases over time in a stepwise fashion. Several solution properties of the problem are developed. Based on the properties, a branch-and-bound algorithm and a heuristic algorithm are derived. These algorithms are evaluated in the computational study and the results show that the heuristic algorithm provides effective solutions within short computation times

Scheduling with Outliers

In classical scheduling problems, we are given jobs and machines, and have to schedule all the jobs to minimize some objective function. What if each job has a specified profit, and we are no longer required to process all jobs -- we can schedule any subset of jobs whose total profit is at least a (hard) target profit requirement, while still approximately minimizing the objective function? We refer to this class of problems as scheduling with outliers. This model was initiated by Charikar and Khuller (SODA'06) on the minimum max-response time in broadcast scheduling. We consider three other well-studied scheduling objectives: the generalized assignment problem, average weighted completion time, and average flow time, and provide LP-based approximation algorithms for them. For the minimum average flow time problem on identical machines, we give a logarithmic approximation algorithm for the case of unit profits based on rounding an LP relaxation; we also show a matching integrality gap. For the average weighted completion time problem on unrelated machines, we give a constant factor approximation. The algorithm is based on randomized rounding of the time-indexed LP relaxation strengthened by the knapsack-cover inequalities. For the generalized assignment problem with outliers, we give a simple reduction to GAP without outliers to obtain an algorithm whose makespan is within 3 times the optimum makespan, and whose cost is at most (1 + \epsilon) times the optimal cost.Comment: 23 pages, 3 figure

Batch Scheduling with Proportional-Linear Deterioration and Outsourcing

We consider the bounded parallel-batch scheduling with proportional-linear deterioration and outsourcing, in which the actual processing time is pj=αj(A+Dt) or pj=αjt. A job is either accepted and processed in batches on a single machine by manufactures themselves or outsourced to the third party with a certain penalty having to be paid. The objective is to minimize the maximum completion time of the accepted jobs and the total penalty of the outsourced jobs. For the pj=αj(A+Dt) model, when all the jobs are released at time zero, we show that the problem is NP-hard and present a pseudo-polynomial time algorithm, respectively. For the pj=αjt model, when the jobs have distinct m (<n) release dates, we provide a dynamic programming algorithm, where n is the number of jobs