Total Weighted Completion Time Minimization in a Problem of Scheduling Deteriorating Jobs

2002 ◽  
pp. 265-271 ◽  
Author(s):  
Aleksander Bachman ◽  
Adam Janiak
Keyword(s):  
Completion Time ◽  
Deteriorating Jobs ◽  
Total Weighted Completion Time ◽  
Time Minimization ◽  
Weighted Completion Time

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.

Minimizing the total weighted completion time of deteriorating jobs

2002 ◽  
Vol 81 (2) ◽  
pp. 81-84 ◽  
Author(s):  
Aleksander Bachman ◽  
Adam Janiak ◽  
Mikhail Y. Kovalyov
Keyword(s):  
Completion Time ◽  
Deteriorating Jobs ◽  
Total Weighted Completion Time ◽  
Weighted Completion Time

scholarly journals A Heuristic’s Job Order Gain in Pyramidal Preemptive Job Scheduling Problems for Total Weighted Completion Time Minimization

2019 ◽  
Vol 22 ◽  
pp. 1-8
Author(s):  
Vadim Romanuke
Keyword(s):  
Completion Time ◽  
Job Scheduling ◽  
Relative Difference ◽  
Total Weighted Completion Time ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Release Date ◽  
Time Minimization ◽  
Weighted Completion Time ◽  
Processing Period

A possibility of speeding up the job scheduling by a heuristic based on the shortest processing period approach is studied in the paper. The scheduling problem is such that the job volume and job priority weight are increasing as the job release date increases. Job preemptions are allowed. Within this model, the input for the heuristic is formed by either ascending or descending job order. Therefore, an estimator of relative difference in duration of finding an approximate schedule by these job orders is designed. It is ascertained that the job order results in different time of computations when scheduling at least a few hundred jobs. The ascending-order solving becomes on average by 1 % to 2.5 % faster when job volumes increase steeply. As the steepness of job volumes decreases, this gain vanishes and, eventually, the descending-order solving becomes on average faster by up to 4 %. The gain trends of both job orders slowly increase as the number of jobs increases.

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