NP-hardness of the single-variable-resource scheduling problem to minimize the total weighted completion time

2007 ◽  
Vol 178 (2) ◽  
pp. 631-633 ◽  
Author(s):  
J.J. Yuan ◽  
T.C.E. Cheng ◽  
C.T. Ng
Keyword(s):  
Completion Time ◽  
Resource Scheduling ◽  
Total Weighted Completion Time ◽  
Scheduling Problem ◽  
Single Variable ◽  
Weighted Completion Time ◽  
Np Hardness

scholarly journals The minimization of exact total weighted completion time in the preemptive scheduling problem by subsequent length-equal job importance growth

2018 ◽  
Keyword(s):  
Completion Time ◽  
Optimal Schedule ◽  
Total Weighted Completion Time ◽  
Preemptive Scheduling ◽  
Scheduling Problem ◽  
Exact Model ◽  
Priority Weights ◽  
Weighted Completion Time

For the preemptive scheduling problem in case of subsequent job importance growth, it is studied whether the optimal schedule might be found faster within an exact model. It is ascertained that when the number of jobs up to six (except for the case of four jobs) and there is no randomness in problem forming, a little advantage of weight-descending job order exists only on average. As the number of jobs increases, the advantage of either weight-descending or weight-ascending job order becomes more certain. When priority weights are formed randomly, weight-descending job order is expected to be faster than weight-ascending.

scholarly journals A Competitive Online Algorithm for Minimizing Total Weighted Completion Time on Uniform Machines

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xuyang Chu ◽  
Jiping Tao
Keyword(s):  
Completion Time ◽  
Online Algorithm ◽  
Total Weighted Completion Time ◽  
Scheduling Problem ◽  
Uniform Machines ◽  
Online Setting ◽  
Weighted Completion Time ◽  
Waiting Strategy ◽  
Machine Speed ◽  
Over Time

We consider the classic online scheduling problem on m uniform machines in the online setting where jobs arrive over time. Preemption is not allowed. The objective is to minimize total weighted completion time. An online algorithm based on the directly waiting strategy is proposed. Its competitive performance is proved to be max2smax1−1/2∑si,2smax/1+smax2.5−1/2m by the idea of instance reduction, where sm is the fastest machine speed after being normalized by the slowest machine speed.

scholarly journals Transportation and Batching Scheduling for Minimizing Total Weighted Completion Time

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 819 ◽  
Author(s):  
Hongjun Wei ◽  
Jinjiang Yuan ◽  
Yuan Gao
Keyword(s):  
Computational Complexity ◽  
Approximation Algorithm ◽  
Polynomial Time ◽  
Completion Time ◽  
Total Weighted Completion Time ◽  
Single Vehicle ◽  
Weighted Completion Time ◽  
Np Hardness

We consider the coordination of transportation and batching scheduling with one single vehicle for minimizing total weighted completion time. The computational complexity of the problem with batch capacity of at least 2 was posed as open in the literature. For this problem, we show the unary NP-hardness for every batch capacity at least 3 and present a polynomial-time 3-approximation algorithm when the batch capacity is at least 2.

Single Machine Two-Agent Scheduling with Deteriorating Jobs

2016 ◽  
Vol 33 (05) ◽  
pp. 1650034 ◽  
Author(s):  
Zhenyou Wang ◽  
Cai-Min Wei ◽  
Yu-Bin Wu
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Processing Time ◽  
Deteriorating Jobs ◽  
Single Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Scheduling Problem ◽  
Agent Scheduling ◽  
Polynomially Solvable ◽  
Weighted Completion Time

This paper deals with the single machine scheduling problem with deteriorating jobs in which there are two distinct families of jobs (i.e., two-agent) pursuing different objectives. In this model the processing time of a job is defined as a function that is proportional to a linear function of its stating time. For the following three scheduling criteria: minimizing the makespan, minimizing the total weighted completion time, and minimizing the maximum lateness, we show that some basic versions of the problem are polynomially solvable. We also establish the conditions under which the problem is computationally hard.

A SINGLE-MACHINE TWO-AGENT SCHEDULING PROBLEM BY GA APPROACH

2012 ◽  
Vol 29 (02) ◽  
pp. 1250013 ◽  
Author(s):  
SHUENN-REN CHENG
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Learning Effect ◽  
Control Parameter ◽  
Optimal Schedule ◽  
Total Weighted Completion Time ◽  
Scheduling Problem ◽  
Processing Times ◽  
Agent Scheduling ◽  
Weighted Completion Time

A single-machine two-agent scheduling problem with a truncation learning effect is being addressed in the study. The truncation learning effect means that the actual processing time of a job is a function of the sum of processing times of already scheduled jobs and a control parameter. The aim is to find an optimal schedule to minimize the total weighted completion time of jobs of the first agent under the circumstances that no tardy job is allowed for the second agent. A branch-and-bound and three heuristic-based genetic algorithms (GAs) are proposed to solve the problem. Also presented in the study are the computational results of all proposed algorithms.

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