Single machine scheduling problem with controllable processing times and resource dependent release times

2007 ◽  
Vol 181 (2) ◽  
pp. 645-653 ◽  
Author(s):  
Byung-Cheon Choi ◽  
Suk-Hun Yoon ◽  
Sung-Jin Chung
Keyword(s):  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Controllable Processing Times ◽  
Scheduling Problem ◽  
Processing Times ◽  
Release Times

Single Machine Scheduling with Discretely Compressible Processing Times

2013 ◽  
Vol 787 ◽  
pp. 1020-1024
Author(s):  
Shu Xia Zhang ◽  
Yu Zhong Zhang
Keyword(s):  
Dynamic Programming ◽  
Single Machine ◽  
Processing Time ◽  
Machine Scheduling ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Processing Times ◽  
Release Times

In this paper, we address the single machine scheduling problem with discretely compressible processing times, where processing any job with a compressed processing time incurs a corresponding compression cost. We consider the following problem: scheduling with discretely compressible processing times to minimize makespan with the constraint of total compression cost. Jobs may have different release times. We design a pseudo-polynomial time algorithm by approach of dynamic programming and an FPTAS.

scholarly journals Dynamic Restructuring Framework for Scheduling with Release Times and Due-Dates

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1104 ◽  
Author(s):  
Nodari Vakhania
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Due Dates ◽  
Processing Times ◽  
Release Times ◽  
Special Case

Scheduling jobs with release and due dates on a single machine is a classical strongly NP-hard combination optimization problem. It has not only immediate real-life applications but also it is effectively used for the solution of more complex multiprocessor and shop scheduling problems. Here, we propose a general method that can be applied to the scheduling problems with job release times and due-dates. Based on this method, we carry out a detailed study of the single-machine scheduling problem, disclosing its useful structural properties. These properties give us more insight into the complex nature of the problem and its bottleneck feature that makes it intractable. This method also helps us to expose explicit conditions when the problem can be solved in polynomial time. In particular, we establish the complexity status of the special case of the problem in which job processing times are mutually divisible by constructing a polynomial-time algorithm that solves this setting. Apparently, this setting is a maximal polynomially solvable special case of the single-machine scheduling problem with non-arbitrary job processing times.

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.

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