SCHEDULING ON TWO PARALLEL MACHINES WITH TWO DEDICATED SERVERS

2017 ◽  
Vol 58 (3-4) ◽  
pp. 314-323
Author(s):  
YIWEI JIANG ◽  
PING ZHOU ◽  
HUIJUAN WANG ◽  
JUELIANG HU
Keyword(s):  
Processing Time ◽  
Parallel Machines ◽  
List Scheduling ◽  
Np Hard ◽  
Worst Case ◽  
Identical Machines ◽  
Loading And Unloading ◽  
Parallel Identical Machines ◽  
Dedicated Servers ◽  
Nonpreemptive Scheduling

We study a nonpreemptive scheduling on two parallel identical machines with a dedicated loading server and a dedicated unloading server. Each job has to be loaded by the loading server before being processed on one of the machines and unloaded immediately by the unloading server after its processing. The loading and unloading times are both equal to one unit of time. The goal is to minimize the makespan. Since the problem is NP-hard, we apply the classical list scheduling and largest processing time heuristics, and show that they have worst-case ratios, $8/5$ and $6/5$, respectively.

Preemptive Scheduling of Stochastic Jobs with a Two-Stage Processing Time Distribution on M + 1 Parallel Machines

1992 ◽  
Vol 6 (2) ◽  
pp. 171-191 ◽  
Author(s):  
Chueng-Chiu Huang ◽  
Gideon Weiss
Keyword(s):  
Processing Time ◽  
Parallel Machines ◽  
Optimal Solution ◽  
General Distribution ◽  
Constant Independent ◽  
Expected Number ◽  
Total Flowtime ◽  
Optimal Decisions ◽  
Identical Machines ◽  
Parallel Identical Machines

We analyze the optimal preemptive sequencing of n jobs on M + 1 parallel identical machines to minimize expected total flowtime. The running times of the jobs are independent samples from the distribution Pr(X = H) = p, Pr(X = H + T) = 1 − p, where H, T are random variables of general distribution. Preemption of a job is allowed when H is completed. This problem does not have a simple optimal solution. We show that the scheme of shortest expected remaining processing time first (SERPT) is close to optimal in two senses. The expected flowtime under SERPT and under the optimal policy differ by no more than a constant, independent of the number of jobs, and the expected number of optimal decisions that are not according to SERPT is bounded by a constant, independent of the number of jobs.

TWO-STAGE FLOWSHOP SCHEDULING PROBLEMS WITH IDENTICAL AND BATCH PROCESSORS

2010 ◽  
Vol 27 (05) ◽  
pp. 617-627 ◽  
Author(s):  
WEN-WEI WANG ◽  
LONG-MIN HE ◽  
MING-BAO CHENG
Keyword(s):  
Approximation Algorithm ◽  
Processing Time ◽  
Parallel Machines ◽  
Np Hard ◽  
Scheduling Problems ◽  
Flowshop Scheduling ◽  
Two Stage ◽  
Worst Case ◽  
Flowshop Scheduling Problem ◽  
Stage 1

This paper considers minimizing total completion time in a two-stage flowshop scheduling problem with m identical parallel machines at Stage 1 and a batch processor at Stage 2. We prove that the problem when all jobs have same processing time at Stage 2 is NP – hard and gave a two-approximation algorithm in O(n3) time. In the case that all jobs have arbitrary processing time at Stage 1 and at Stage 2, we give an approximation algorithm after pointing out that in this case the problem is strongly NP – hard. Hundreds of instances of a numerical experiment show that the worst-case ratio of this approximation algorithm is nearing 2.

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 under a Grade of Service Provision

2011 ◽  
Vol 101-102 ◽  
pp. 484-487
Author(s):  
Yong Wu ◽  
Min Ji ◽  
Qi Fan Yang
Keyword(s):  
Service Provision ◽  
Competitive Ratio ◽  
Processing Time ◽  
Optimal Algorithm ◽  
Online Version ◽  
Scheduling Problems ◽  
Grade Of Service ◽  
Identical Machines ◽  
Machine Covering ◽  
Parallel Identical Machines

Two semi-online scheduling problems on two parallel identical machines under a grade of service (GoS) provision were studied. The goal is to maximize the minimum machine load. For the semi-online version where the largest processing time of all jobs is known in advance, we show that no competitive algorithm exists. For the semi-online version where the optimal offline value is known in advance, we propose an optimal algorithm with competitive ratio 2.

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

1986 ◽  
Vol 23 (3) ◽  
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.

Scheduling on two parallel machines with two dedicated servers

2017 ◽  
Vol 58 ◽  
pp. 314
Author(s):  
Yiwei Jiang ◽  
Ping Zhou ◽  
Huijuan Wang ◽  
Jueliang Hu
Keyword(s):  
Parallel Machines ◽  
Dedicated Servers

scholarly journals Semi-Online Scheduling on Two Machines withGoSLevels and Partial Information of Processing Time

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Taibo Luo ◽  
Yinfeng Xu
Keyword(s):  
Processing Time ◽  
Parallel Machines ◽  
Partial Information ◽  
Online Scheduling ◽  
Scheduling Problems ◽  
Total Processing Time ◽  
Grade Of Service ◽  
Two Machines

This paper investigates semi-online scheduling problems on two parallel machines under a grade of service (GoS) provision subject to minimize the makespan. We consider three different semi-online versions with knowing the total processing time of the jobs with higherGoSlevel, knowing the total processing time of the jobs with lowerGoSlevel, or knowing both in advance. Respectively, for the three semi-online versions, we develop algorithms with competitive ratios of3/2,20/13, and4/3which are shown to be optimal.

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