This paper presents a new mixed-integer goal programming (MIGP) model for a parallel machine scheduling problem with sequence-dependent setup times and release dates. Two objectives are considered in the model to minimize the total weighted flow time and the total weighted tardiness simultaneously. Due to the com-plexity of the above model and uncertainty involved in real-world scheduling probl...

We consider the problem of scheduling n jobs on m identical parallel machines. An optimal schedule to the proposed problem is defined as one that gives the smallest makespan (the completion time of the last job on any one of the parallel machines) among the set of all schedules with optimal total flowtime (the sum of the completion times of all jobs). We propose two new simple heuristic algorit...

We consider the problem of minimizing flow time on a single machine supporting preemption that can reject jobs at a cost. Even if all jobs have the same rejection cost, we show that no online algorithm can have competitive ratio better than (2+ √ 2)/2 ≈ 1.707 in general or e/(e− 1) ≈ 1.582 if all jobs are known to have the same processing time. We also give an optimal offline algorithm for unit...

For the NP-hard problem of scheduling n jobs in a two-machine flow shop so as to minimize the total completion time, we present two equivalent lower bounds that are computable in polynomial time. We formulate the problem by the use of positional completion time variables, which results in two integer linear programming formulations with O(n2) variables and O(n) constraints. Solving the linear p...

We consider an uncertain single-machine scheduling problem, in which the processing time of a job can take any real value from a given closed interval. The criterion is to minimize the sum of weighted completion times of the n jobs, a weight being associated with each job. For a job permutation, we study the stability box, which is a subset of the stability region. We derive an O(n log n) algor...

In this paper we confront the job shop scheduling problem with total flow time minimization. We start extending the disjunctive graph model used for makespan minimization to represent the version of the problem with total flow time minimization. Using this representation, we adapt local search neighborhood structures originally defined for makespan minimization. The proposed neighborhood struct...

We consider the problem of minimizing the total flow time of multiple jobs in a pool of multiple homogenous machines, where the jobs arrive over time and have to be served with phase precedence. This is a common occurrence in job scheduling for the increasingly popular data center oriented systems, where jobs need to be processed through a MAP and Reduce procedure before leaving the system. For...

This paper addresses scheduling n jobs in a two-machine flow shop to minimize the total completion time, subject to the condition that the jobs are processed in the same given sequence on both machines. A new concept of optimal schedule block is introduced, and polynomial time dynamic programming algorithms employing this concept are derived for two specific problems. In the first problem, the ...