scholarly journals Approximation Algorithm for the Single Machine Scheduling Problem with Release Dates and Submodular Rejection Penalty

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 133 ◽  
Author(s):  
Xiaofei Liu ◽  
Weidong Li
Keyword(s):  
Single Machine ◽  
Exact Algorithm ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Release Dates ◽  
Scheduling Problem ◽  
Combinatorial Algorithm ◽  
Processing Times ◽  
Primal Dual ◽  
Rejection Penalty

In this paper, we consider the single machine scheduling problem with release dates and nonmonotone submodular rejection penalty. We are given a single machine and multiple jobs with probably different release dates and processing times. For each job, it is either accepted and processed on the machine or rejected. The objective is to minimize the sum of the makespan of the accepted jobs and the rejection penalty of the rejected jobs which is determined by a nonmonotone submodular function. We design a combinatorial algorithm based on the primal-dual framework to deal with the problem, and study its property under two cases. For the general case where the release dates can be different, the proposed algorithm have an approximation ratio of 2. When all the jobs release at the same time, the proposed algorithm becomes a polynomial-time exact algorithm.

An Optimal Algorithm for Scheduling with Variable Job Processing Times and Rejection

2015 ◽  
Vol 775 ◽  
pp. 449-452
Author(s):  
Ji Bo Wang ◽  
Chou Jung Hsu
Keyword(s):  
Objective Function ◽  
Polynomial Time ◽  
Single Machine ◽  
Processing Time ◽  
Optimal Algorithm ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Processing Times ◽  
Rejection Penalty

This paper studies a single machine scheduling problem with rejection. Each job has a variable processing time and a rejection penalty. The objective function is to minimize the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs. We show that the problem can be solved in polynomial time.

A two-agent single-machine scheduling problem to minimize the total cost with release dates

2015 ◽  
Vol 21 (3) ◽  
pp. 805-816 ◽  
Author(s):  
Du-Juan Wang ◽  
Yunqiang Yin ◽  
Wen-Hsiang Wu ◽  
Wen-Hung Wu ◽  
Chin-Chia Wu ◽  
...  
Keyword(s):  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Release Dates ◽  
Scheduling Problem ◽  
Total Cost

scholarly journals A Single-Machine Scheduling Problem with Uncertainty in Processing Times and Outsourcing Costs

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Myoung-Ju Park ◽  
Byung-Cheon Choi
Keyword(s):  
Single Machine ◽  
Operating Cost ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Performance Measure ◽  
Total Weighted Completion Time ◽  
Maximum Deviation ◽  
Scheduling Problem ◽  
Processing Times ◽  
Special Cases

We consider a single-machine scheduling problem with an outsourcing option in an environment where the processing time and outsourcing cost are uncertain. The performance measure is the total cost of processing some jobs in-house and outsourcing the rest. The cost of processing in-house jobs is measured as the total weighted completion time, which can be considered the operating cost. The uncertainty is described through either an interval or a discrete scenario. The objective is to minimize the maximum deviation from the optimal cost of each scenario. Since the deterministic version is known to be NP-hard, we focus on two special cases, one in which all jobs have identical weights and the other in which all jobs have identical processing times. We analyze the computational complexity of each case and present the conditions that make them polynomially solvable.

scholarly journals A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 61
Author(s):  
Wencheng Wang ◽  
Xiaofei Liu
Keyword(s):  
Approximation Algorithm ◽  
Single Machine ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Single Machine Scheduling ◽  
Release Time ◽  
Release Dates ◽  
Scheduling Problem ◽  
Release Times

In this paper, we consider parallel-machine scheduling with release times and submodular penalties (P|rj,reject|Cmax+π(R)), in which each job can be accepted and processed on one of m identical parallel machines or rejected, but a penalty must paid if a job is rejected. Each job has a release time and a processing time, and the job can not be processed before its release time. The objective of P|rj,reject|Cmax+π(R) is to minimize the makespan of the accepted jobs plus the penalty of the rejected jobs, where the penalty is determined by a submodular function. This problem generalizes a multiprocessor scheduling problem with rejection, the parallel-machine scheduling with submodular penalties, and the single machine scheduling problem with release dates and submodular rejection penalties. In this paper, inspired by the primal-dual method, we present a combinatorial 2-approximation algorithm to P|rj,reject|Cmax+π(R). This ratio coincides with the best known ratio for the parallel-machine scheduling with submodular penalties and the single machine scheduling problem with release dates and submodular rejection penalties.

Sign in / Sign up

Export Citation Format

Share Document