scholarly journals Minimizing Total Weighted Completion Time on Single Machine with Past-Sequence-Dependent Setup Times and Exponential Time-Dependent and Position-Dependent Learning Effects

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Kaibiao Sun ◽  
Hongxing Li
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Processing Time ◽  
Setup Times ◽  
Time Dependent ◽  
Total Weighted Completion Time ◽  
Learning Effects ◽  
Exponential Time ◽  
Weighted Completion Time ◽  
Dependent Learning

This paper addresses a single-machine problem in which the past-sequence-dependent (p-s-d) setup times and exponential time-dependent and position-dependent learning effects are considered. By the exponential time-dependent learning effect, it means that the processing time of a job is defined by an exponent function of the total actual processing time of the already processed jobs. The setup times are proportional to the length of the already processed jobs. The aim is to minimize the total weighted completion time, this is an NP-hard problem. Under certain conditions, it is shown that the classical WSPT rule is optimal for the problem.

Scheduling Jobs with Truncated Exponential Sum-of-Logarithm-Processing-Times Based and Position-based Learning Effects

2015 ◽  
Vol 32 (04) ◽  
pp. 1550026 ◽  
Author(s):  
Yuan-Yuan Lu ◽  
Fei Teng ◽  
Zhi-Xin Feng
Keyword(s):  
Single Machine ◽  
Minimization Problem ◽  
Completion Time ◽  
Heuristic Algorithms ◽  
Exponential Sum ◽  
Total Weighted Completion Time ◽  
Learning Effects ◽  
Processing Times ◽  
Time Minimization ◽  
Weighted Completion Time

In this study, we consider a scheduling problem with truncated exponential sum-of-logarithm-processing-times based and position-based learning effects on a single machine. We prove that the shortest processing time (SPT) rule is optimal for the makespan minimization problem, the sum of the θth power of job completion times minimization problem, and the total lateness minimization problem, respectively. For the total weighted completion time minimization problem, the discounted total weighted completion time minimization problem, the maximum lateness minimization problem, we present heuristic algorithms (the worst-case bound of these heuristic algorithms are also given) according to the corresponding single machine scheduling problems without learning considerations. It also shows that the problems of minimizing the total tardiness, the total weighted completion time and the discounted total weighted completion time are polynomially solvable under some agreeable conditions on the problem parameters.

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.

scholarly journals Single-Machine Scheduling with Accelerating Learning Effects

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
T. C. E. Cheng ◽  
Shih-Chang Tseng ◽  
Peng-Jen Lai ◽  
Wen-Chiung Lee
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Learning Effect ◽  
Single Machine Scheduling ◽  
Total Tardiness ◽  
Total Weighted Completion Time ◽  
Learning Effects ◽  
Optimal Solutions ◽  
New Model ◽  
Weighted Completion Time

Scheduling with learning effects has been widely studied. However, there are situations where the learning effect might accelerate. In this paper, we propose a new model where the learning effect accelerates as time goes by. We derive the optimal solutions for the single-machine problems to minimize the makespan, total completion time, total weighted completion time, maximum lateness, maximum tardiness, and total tardiness.

scholarly journals Branch and Bound Method to Solve Multi Objectives Function

2016 ◽  
Vol 12 (3) ◽  
pp. 5964-5974
Author(s):  
Tahani Jabbar Kahribt ◽  
Mohammed Kadhim Al- Zuwaini
Keyword(s):  
Lower Bounds ◽  
Branch And Bound ◽  
Single Machine ◽  
Upper Bound ◽  
Completion Time ◽  
Heuristic Method ◽  
Total Weighted Completion Time ◽  
Branch And Bound Method ◽  
Special Cases ◽  
Weighted Completion Time

This paper  presents  a  branch  and  bound  algorithm  for  sequencing  a  set  of  n independent  jobs  on  a single  machine  to  minimize sum of the discounted total weighted completion time and maximum lateness,  this problems is NP-hard. Two lower bounds were proposed and heuristic method to get an upper bound. Some special cases were  proved and some dominance rules were suggested and proved, the problem solved with up to 50 jobs.

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