Scheduling identical jobs on uniform parallel machines with random processing times

1998 ◽  
Vol 35 (1-2) ◽  
pp. 109-112 ◽  
Author(s):  
Mohamed I. Dessouky ◽  
Richard L. Marcellus ◽  
Li Zhang
Keyword(s):  
Parallel Machines ◽  
Processing Times ◽  
Identical Jobs

scholarly journals Workload Balancing on Identical Parallel Machines: Theoretical and Computational Analysis

2021 ◽  
Vol 11 (8) ◽  
pp. 3677
Author(s):  
Yassine Ouazene ◽  
Nhan-Quy Nguyen ◽  
Farouk Yalaoui
Keyword(s):  
Computational Analysis ◽  
Parallel Machines ◽  
Production Systems ◽  
Identical Parallel Machines ◽  
Workload Balancing ◽  
Processing Times ◽  
Use Of Resources ◽  
Maximum Completion Time ◽  
Completion Times ◽  
Identical Jobs

This paper considers the problem of assigning nonpreemptive jobs on identical parallel machines to optimize workload balancing criteria. Since workload balancing is an important practical issue for services and production systems to ensure an efficient use of resources, different measures of performance have been considered in the scheduling literature to characterize this problem: maximum completion time, difference between maximum and minimum completion times and the Normalized Sum of Square for Workload Deviations. In this study, we propose a theoretical and computational analysis of these criteria. First, we prove that these criteria are equivalent in the case of identical jobs and in some particular cases. Then, we study the general version of the problem using jobs requiring different processing times and establish the theoretical relationship between the aforementioned criteria. Based on these theoretical developments, we propose new mathematical formulations to provide optimal solutions to some unsolved instances in order to enhance the latest benchmark presented in the literature.

scholarly journals Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flowtime

1986 ◽  
Vol 23 (03) ◽  
pp. 841-847 ◽  
Author(s):  
R. R. Weber ◽  
P. Varaiya ◽  
J. Walrand
Keyword(s):  
Processing Time ◽  
Parallel Machines ◽  
Preemptive Scheduling ◽  
Total Reward ◽  
Processing Times ◽  
Identical Machines ◽  
Scheduling Strategies

A number of jobs are to be processed using a number of identical machines which operate in parallel. The processing times of the jobs are stochastic, but have known distributions which are stochastically ordered. A reward r(t) is acquired when a job is completed at time t. The function r(t) is assumed to be convex and decreasing in t. It is shown that within the class of non-preemptive scheduling strategies the strategy SEPT maximizes the expected total reward. This strategy is one which whenever a machine becomes available starts processing the remaining job with the shortest expected processing time. In particular, for r(t) = – t, this strategy minimizes the expected flowtime.

SEMI-ONLINE MACHINE COVERING

2007 ◽  
Vol 24 (03) ◽  
pp. 373-382 ◽  
Author(s):  
SHENG-YI CAI
Keyword(s):  
Competitive Ratio ◽  
Completion Time ◽  
Online Algorithm ◽  
Parallel Machines ◽  
Identical Parallel Machines ◽  
Processing Times ◽  
First Case ◽  
Machine Covering

This paper investigates two different semi-online versions of the machine covering, which is the problem of assigning a set of jobs to a system of m(m ≥ 3) identical parallel machines so as to maximize the earliest machine completion time. In the first case, we assume that the largest processing times is known in advance. In the second case, we assume that the total processing times of all jobs is known in advance. For each version we propose a semi-online algorithm and investigate its competitive ratio. The competitive ratio of each algorithm is [Formula: see text], which is shown to be the best possible competitive ratio for each semi-online problem.

Scheduling jobs with exponential processing times on parallel machines

1988 ◽  
Vol 25 (04) ◽  
pp. 752-762 ◽  
Author(s):  
Tapani Lehtonen
Keyword(s):  
Binomial Distribution ◽  
Parallel Machines ◽  
Essential Feature ◽  
Stochastic Order ◽  
Partial Solution ◽  
Flow Time ◽  
Optimal Assignment ◽  
Processing Times ◽  
Expected Makespan

We consider a system where jobs are processed by parallel machines. The processing times are exponentially distributed. An essential feature is that the assignment of the jobs to the machines is decided before the system starts to work. We consider both the flow time and the makespan. In the case of the flow time we allow both the machines and the jobs to be non-homogeneous. The optimization is by minimizing the flow time in the sense of stochastic order and the optimal assignment is obtained for this case. The case of the makespan is harder. We consider the expected makespan and as a partial solution we prove an optimality result for the case where there are two non-homogeneous machines and the jobs are homogeneous. It turns out that the optimal assignment can be expressed by using a quantile of a binomial distribution.

scholarly journals Preemptive Scheduling with Controllable Processing Times on Parallel Machines

2015 ◽  
Vol 3 (1) ◽  
pp. 68-76
Author(s):  
Guiqing Liu ◽  
Kai Li ◽  
Bayi Cheng
Keyword(s):  
Polynomial Time ◽  
Resource Use ◽  
Parallel Machines ◽  
Optimal Algorithm ◽  
Parallel Machine Scheduling ◽  
Controllable Processing Times ◽  
Scheduling Problems ◽  
Processing Times ◽  
Online Problems ◽  
Machine Scheduling Problems

AbstractThis paper considers several parallel machine scheduling problems with controllable processing times, in which the goal is to minimize the makespan. Preemption is allowed. The processing times of the jobs can be compressed by some extra resources. Three resource use models are considered. If the jobs are released at the same time, the problems under all the three models can be solved in a polynomial time. The authors give the polynomial algorithm. When the jobs are not released at the same time, if all the resources are given at time zero, or the remaining resources in the front stages can be used to the next stages, the offline problems can be solved in a polynomial time, but the online problems have no optimal algorithm. If the jobs have different release dates, and the remaining resources in the front stages can not be used in the next stages, both the offline and online problems can be solved in a polynomial time.

Parallel-batching scheduling with nonlinear processing times on a single and unrelated parallel machines

2018 ◽  
Vol 78 (4) ◽  
pp. 693-715 ◽  
Author(s):  
Min Kong ◽  
Xinbao Liu ◽  
Jun Pei ◽  
Panos M. Pardalos ◽  
Nenad Mladenovic
Keyword(s):  
Parallel Machines ◽  
Unrelated Parallel Machines ◽  
Parallel Batching ◽  
Processing Times ◽  
Nonlinear Processing

On almost optimal priority rules for preemptive scheduling of stochastic jobs on parallel machines

1995 ◽  
Vol 27 (03) ◽  
pp. 821-839 ◽  
Author(s):  
Gideon Weiss
Keyword(s):  
Single Machine ◽  
Parallel Machines ◽  
Preemptive Scheduling ◽  
Priority Rule ◽  
Priority Rules ◽  
Holding Costs ◽  
Processing Times ◽  
Stochastic Processing ◽  
Stochastic Processing Times

We consider scheduling a batch of jobs with stochastic processing times on single or parallel machines, with the objective of minimizing the expected holding costs. Preemption of jobs is allowed, and the holding costs of preempted jobs may depend on the stage of completion. We provide a new proof of the optimality of a Gittins priority rule for the single machine and use the same proof to show that the Gittins priority rule is nearly optimal for parallel machines.

On almost optimal priority rules for preemptive scheduling of stochastic jobs on parallel machines

1995 ◽  
Vol 27 (3) ◽  
pp. 821-839 ◽  
Author(s):  
Gideon Weiss
Keyword(s):  
Single Machine ◽  
Parallel Machines ◽  
Preemptive Scheduling ◽  
Priority Rule ◽  
Priority Rules ◽  
Holding Costs ◽  
Processing Times ◽  
Stochastic Processing ◽  
Stochastic Processing Times

We consider scheduling a batch of jobs with stochastic processing times on single or parallel machines, with the objective of minimizing the expected holding costs. Preemption of jobs is allowed, and the holding costs of preempted jobs may depend on the stage of completion. We provide a new proof of the optimality of a Gittins priority rule for the single machine and use the same proof to show that the Gittins priority rule is nearly optimal for parallel machines.

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