Abstract:
In the classical scheduling models, it is always assumed that for any job. We have to process it, however, in the real world; we can choose not to process a job. For example, the processing time is too long or the processing penalty is expensive. So it is worthwhile for us to send it outside to be processed or purchased by paying some money, we call the problem scheduling with rejection. The task we are about to research is how we choose the job to be processed or rejected, and how we arrange for the processing orders of the jobs so as to optimize the objective function value. In this paper, we consider the scheduling with rejection to minimize the total weighted completion time with the constraint of total rejection penalties on m identical parallel machines. We show that it is NPhard and design a pseudopolynomial time algorithm as well as an FPTAS through dynamic programming.

Abstract:
This paper addresses the two-machine flowshop scheduling problem with separate setup times to minimize makespan or total completion time (TCT). Setup times are relaxed to be random variables rather than deterministic as commonly used in the OR literature. Moreover, distribution-free setup times are used where only the lower and upper bounds are given. Global and local dominance relations are developed for the considered flowshops and an illustrative numerical example is given.

Abstract:
This paper considers a (twoparty) Nash bargaining problem involving job scheduling. In this problem, each party can only offer one machine to process jobs so that the cooperation between them is necessary. It implies two parties should first negotiate a reasonable partition of all the jobs to make the corresponding cooperative (processing) profit allocation scheme, i.e. the bargaining solution, acceptable to each party. This paper derives the Nash bargaining solution(s) of the case where the processing time of each job is the same and each party’s processing cost is determined by his total completion time.

Abstract:
In this paper we consider the problem of scheduling jobs on parallel identical machines, where the processing times of jobs are uncertain: only interval bounds of processing times are known. The optimality criterion of a schedule is the total completion time. In order to cope with the uncertainty we consider the maximum regret objective and we seek a schedule which performs well under all possible instantiations of processing times. Although the deterministic version of the considered problem is solvable in polynomial time, the minmax regret version is known to be weakly NP-hard even for a single machine, and strongly NP-hard for parallel unrelated machines. In this paper we show that the problem is strongly NP-hard also in the case of parallel identical machines.

Abstract:
We consider the problem of two-machine flow-shop scheduling with a single server and equal processing times, we show that this problem is NP -hard in the strong sense and present a busy schedule for it with worst-case bound 7 / 6

Abstract:
This article addresses the problem of single machine scheduling on total loss before completion that arises under disruption environment. Such a problem deals with a situation when, at time t, a disruption unexpectedly occurs after a subset of jobs processed. In such cases continuing with the original schedule is likely to be suboptimal and may be even infeasible. Therefore, a new schedule is needed to process the uncompleted jobs. The approach taken here differs from most rescheduling analysis in that the loss associated with the deviation between the original and the new schedule is included in the model. The authors concentrate on the case in which the weighted shortest processing time (WSPT) rule is optimal for the original problem. According to type of disruption, type of disruption management policy, and objective function, several problems are studied in the paper. In each problem, the authors either find the optimal schedule or obtain some important results.

Abstract:
In this study, the problem of simultaneously minimizing the total completion time and number of tardy jobs with release dates on a single machine is investigated. Three heuristics (called HR4, HR5 and HR6) were proposed for the bicriteria problem and were compared with the branch and bound (BB) procedure in order to evaluate effectiveness. Computational experiments, focusing on both the effectiveness (a measure of the closeness of the value of the performance measure) and efficiency (a measure of the execution time or speed) of the solution methods, were presented.

Abstract:
This paper considers the problem of uniform parallel machine scheduling with unequal release dates so as to minimize total completion times.This problem is proved to an NP-hard problem.Uniform parallel machine scheduling is an important class of parallel machine scheduling problems.The objective of minimizing total completion times is a familiar regular criterion.We build a mathematics model for this problem,and then propose 6 heuristic algorithms by the way of extending the research results of the corresponding problems in the single machine or identical parallel machine cases.An example and the compute results are given and the performance of the algorithms by experiment is also analyzed.

Abstract:
This paper discusses review of literature
of open shop scheduling problems. First, the problem is classified as per
different measures of performance, viz., minimization of makespan, minimization
of sum of completion times of jobs, minimization of sum of weighted completion
times of all jobs, minimization of total tardiness of all jobs, minimization of
sum of weighted tardiness of all jobs, minimization of weighted sum of tardy
jobs, and miscellaneous measures of the open shop scheduling problem. In each
category, the literature is further classified based on approaches used and
then the contributions of researchers in the respective categories are
presented. Directions for future research are discussed in the end.

Abstract:
This paper addresses the single-machine scheduling problem with release times minimizing the total completion time. Under the circumstance of incomplete global information at each decision time, a two-level rolling scheduling strategy (TRSS) is presented to create the global schedule step by step. The estimated global schedules are established based on a dummy schedule of unknown jobs. The first level is the preliminary scheduling based on the predictive window and the second level is the local scheduling for sub-problems based on the rolling window. Performance analysis demonstrates that TRSS can improve the global schedules. Computational results show that the solution quality of TRSS outperforms that of the existing rolling procedure in most cases.