scholarly journals Single-Machine Scheduling Problems with the General Sum-of-Processing-Time and Position-Dependent Effect Function

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Kunping Shen ◽  
Yuke Chen ◽  
Shangchia Liu
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Completion Time ◽  
Processing Time ◽  
Objective Functions ◽  
Dependent Effect ◽  
Effect Function ◽  
Processing Times ◽  
Time Problem ◽  
Normal Processing

This paper considers the combination of the general sum-of-processing-time effect and position-dependent effect on a single machine. The actual processing time of a job is defined by functions of the sum of the normal processing times of the jobs processed and its position and control parameter in the sequence. We consider two monotonic effect functions: the nondecreasing function and the nonincreasing function. Our focus is the following objective functions, including the makespan, the sum of the completion time, the sum of the weighted completion time, and the maximum lateness. For the nonincreasing effect function, polynomial algorithm is presented for the makespan problem and the sum of completion time problem, respectively. The latter two objective functions can also be solved in polynomial time if the weight or due date and the normal processing time satisfy some agreeable relations. For the nondecreasing effect function, assume that the given parameter is zero. We also show that the makespan problem can remain polynomially solvable. For the sum of the total completion time problem and a 1 is the deteriorating rate of the jobs, there exists an optimal solution for a 1 ≥ M ; a V-shaped property with respect to the normal processing times is obtained for 0 < a 1 ≤ 1 . Finally, we show that the sum of the weighted completion problem and the maximum lateness problem have polynomial-time solutions for a 1 > M under some agreeable conditions, respectively.

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.

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.

scholarly journals Single-Machine Scheduling with Rejection and an Operator Non-Availability Interval

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 668 ◽  
Author(s):  
Lili Zuo ◽  
Zhenxia Sun ◽  
Lingfa Lu ◽  
Liqi Zhang
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Single Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Scheduling Problems ◽  
Objective Functions ◽  
Rejection Cost ◽  
Scheduling With Rejection

In this paper, we study two scheduling problems on a single machine with rejection and an operator non-availability interval. In the operator non-availability interval, no job can be started or be completed. However, a crossover job is allowed such that it can be started before this interval and completed after this interval. Furthermore, we also assume that job rejection is allowed. That is, each job is either accepted and processed in-house, or is rejected by paying a rejection cost. Our task is to minimize the sum of the makespan (or the total weighted completion time) of accepted jobs and the total rejection cost of rejected jobs. For two scheduling problems with different objective functions, by borrowing the previous algorithms in the literature, we propose a pseudo-polynomial-time algorithm and a fully polynomial-time approximation scheme (FPTAS), respectively.

SCHEDULING PROBLEMS WITH THE EFFECTS OF DETERIORATION AND LEARNING

2007 ◽  
Vol 24 (02) ◽  
pp. 245-261 ◽  
Author(s):  
JI-BO WANG ◽  
T. C. EDWIN CHENG
Keyword(s):  
Performance Measures ◽  
Single Machine ◽  
Completion Time ◽  
Flow Shop ◽  
Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Scheduling Problems ◽  
Processing Times ◽  
Weighted Completion Time ◽  
Machine Scheduling Problems

This paper deals with the machine scheduling problems with the effects of deterioration and learning. In this model the processing times of jobs are defined as functions of their starting times and positions in a sequence. We introduce polynomial solutions for some single machine problems and flow shop problems. The performance measures include makespan, total completion time, total weighted completion time, and maximum lateness.

scholarly journals Parallel-Batch Scheduling with Two Models of Deterioration to Minimize the Makespan

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Cuixia Miao
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Processing Time ◽  
Parallel Machine ◽  
Batch Scheduling ◽  
Approximation Schemes ◽  
Time Approximation ◽  
Identical Parallel Machine ◽  
Parallel Machine Problem ◽  
Machine Problem

We consider the bounded parallel-batch scheduling with two models of deterioration, in which the processing time of the first model ispj=aj+αtand of the second model ispj=a+αjt. The objective is to minimize the makespan. We presentO(n log n)time algorithms for the single-machine problems, respectively. And we propose fully polynomial time approximation schemes to solve the identical-parallel-machine problem and uniform-parallel-machine problem, respectively.

scholarly journals Hierarchical minimization of two maximum costs on a bounded serial-batching machine

2020 ◽  
Author(s):  
Cheng He ◽  
Hao Lin ◽  
Li Li
Keyword(s):  
Processing Time ◽  
Optimization Problem ◽  
Setup Time ◽  
Time Algorithm ◽  
Hierarchical Optimization ◽  
Objective Functions ◽  
Processing Times ◽  
Hierarchical Minimization ◽  
Batching Machine ◽  
Special Case

This paper studies a hierarchical optimization problem of scheduling $n$ jobs on a serial-batching machine, in which two objective functions are maximum costs. By a hierarchical optimization problem, we mean the problem of optimizing the secondary criterion under the constraint that the primary criterion is optimized. A serial-batching machine is a machine that can handle up to $b$ jobs in a batch and jobs in a batch start and complete respectively at the same time and the processing time of a batch is equal to the sum of the processing times of jobs in the batch. When a new batch starts, a constant setup time $s$ occurs. We confine ourselves to the bounded model, where $b<n$. We present an $O(n^4)$-time algorithm for this hierarchical optimization problem. For the special case where two objective functions are maximum lateness, we give an $O(n^3\log n)$-time algorithm.

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