Single machine group scheduling with resource dependent setup and processing times

2005 ◽  
Vol 162 (1) ◽  
pp. 112-121 ◽  
Author(s):  
Adam Janiak ◽  
Mikhail Y. Kovalyov ◽  
Marie-Claude Portmann
Keyword(s):  
Single Machine ◽  
Group Scheduling ◽  
Processing Times ◽  
Machine Group

scholarly journals Single-Machine Group Scheduling Problems with Deterioration to Minimize the Sum of Completion Times

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Yong He ◽  
Li Sun
Keyword(s):  
Single Machine ◽  
Group Scheduling ◽  
Scheduling Problems ◽  
Minimization Problems ◽  
Processing Times ◽  
Machine Group ◽  
Polynomially Solvable ◽  
Decreasing Functions ◽  
Completion Times ◽  
Sum Of Completion Times

We consider two single-machine group scheduling problems with deteriorating group setup and job processing times. That is, the job processing times and group setup times are linearly increasing (or decreasing) functions of their starting times. Jobs in each group have the same deteriorating rate. The objective of scheduling problems is to minimize the sum of completion times. We show that the sum of completion times minimization problems remains polynomially solvable under the agreeable conditions.

scholarly journals Single-Machine Group Scheduling Problems with Variable Job Processing Times

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Ping Ji ◽  
Lin Li
Keyword(s):  
Single Machine ◽  
Minimization Problem ◽  
Deteriorating Jobs ◽  
Setup Time ◽  
Resource Consumption ◽  
Group Scheduling ◽  
Scheduling Problems ◽  
Processing Times ◽  
Machine Group ◽  
Total Resource

This paper considers two resource constrained single-machine group scheduling problems. These problems involve variable job processing times (general position-dependent learning effects and deteriorating jobs); that is, the processing time of a job is defined by the function that involves its starting time and position in the group, and groups’ setup time is a positive strictly decreasing continuous function of the amount of consumed resource. Polynomial time algorithms are proposed to optimally solve the makespan minimization problem under the constraint that the total resource consumption does not exceed a given limit and the total resource consumption minimization problem under the constraint that the makespan does not exceed a given limit, respectively.

Single-machine group scheduling with new models of position-dependent processing times

2018 ◽  
Vol 117 ◽  
pp. 1-5 ◽  
Author(s):  
Xin Zhang ◽  
Lijuan Liao ◽  
Wenya Zhang ◽  
T.C.E. Cheng ◽  
Yuanyuan Tan ◽  
...  
Keyword(s):  
Single Machine ◽  
Group Scheduling ◽  
Processing Times ◽  
Machine Group ◽  
New Models

scholarly journals Single Machine Group Scheduling with Position Dependent Processing Times and Ready Times

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Xingong Zhang ◽  
Qiulian Xie
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Setup Time ◽  
Solution Procedure ◽  
Release Time ◽  
Group Scheduling ◽  
Processing Times ◽  
Machine Group ◽  
Special Case ◽  
Nondecreasing Order

We investigate a single machine group scheduling problem with position dependent processing times and ready times. The actual processing time of a job is a function of positive group-dependent job-independent positional factors. The actual setup time of the group is a linear function of the total completion time of the former group. Each job has a release time. The decision should be taken regarding possible sequences of jobs in each group and group sequence to minimize the makespan. We show that jobs in each group are scheduled in nondecreasing order of its release time and the groups are arranged in nondecreasing order of some certain conditions. We also present a polynomial time solution procedure for the special case of the proposed problem.

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