scholarly journals Single-Machine Parallel-Batch Scheduling with Nonidentical Job Sizes and Rejection

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 258
Author(s):  
Miaomiao Jin ◽  
Xiaoxia Liu ◽  
Wenchang Luo
Keyword(s):  
Integer Programming ◽  
Single Machine ◽  
Heuristic Algorithms ◽  
Batch Processing ◽  
Batch Scheduling ◽  
Scheduling Problem ◽  
Programming Formulation ◽  
Processing Times ◽  
Batch Processing Machine ◽  
Rejection Penalty

We investigate the single-machine parallel-batch scheduling problem with nonidentical job sizes and rejection. In this problem, a set of jobs with different processing times and nonidentical sizes is given to be possibly processed on a parallel-batch processing machine. Each job is either accepted and then processed on the machine or rejected by paying its rejection penalty. Preemption is not allowed. Our task is to choose the accepted jobs and schedule them as batches on the machine to minimize the makespan of the accepted jobs plus the total rejection penalty of the rejected jobs. We provide an integer programming formulation to exactly solve our problem. Then, we propose three fast heuristic algorithms to solve the problem and evaluate their performances by using a small numerical example.

scholarly journals Scheduling Jobs with Maintenance Subject to Load-Dependent Duration on a Single Machine

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Yawei Qi ◽  
Long Wan ◽  
Zhigang Yan
Keyword(s):  
Integer Programming ◽  
Single Machine ◽  
Numerical Experiments ◽  
Heuristic Algorithms ◽  
Programming Model ◽  
Scheduling Problem ◽  
Np Hard ◽  
Ordinary Sense ◽  
Starting Time ◽  
Special Case

This paper investigates a scheduling problem on a single machine with maintenance, in which the starting time of the maintenance is given in advance but its duration depends on the load of the machine before the maintenance. The goal is to minimize the makespan. We formulate it as an integer programming model and show that it is NP-hard in the ordinary sense. Then, we propose an FPTAS and point out that a special case is polynomial solvable. Finally, we design fast heuristic algorithms to solve the scheduling problem. Numerical experiments are implemented to evaluate the performance of the proposed heuristic algorithms. The results show the proposed heuristic algorithms are effective.

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.

scholarly journals Approximation Algorithm for the Single Machine Scheduling Problem with Release Dates and Submodular Rejection Penalty

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 133 ◽  
Author(s):  
Xiaofei Liu ◽  
Weidong Li
Keyword(s):  
Single Machine ◽  
Exact Algorithm ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Release Dates ◽  
Scheduling Problem ◽  
Combinatorial Algorithm ◽  
Processing Times ◽  
Primal Dual ◽  
Rejection Penalty

In this paper, we consider the single machine scheduling problem with release dates and nonmonotone submodular rejection penalty. We are given a single machine and multiple jobs with probably different release dates and processing times. For each job, it is either accepted and processed on the machine or rejected. The objective is to minimize the sum of the makespan of the accepted jobs and the rejection penalty of the rejected jobs which is determined by a nonmonotone submodular function. We design a combinatorial algorithm based on the primal-dual framework to deal with the problem, and study its property under two cases. For the general case where the release dates can be different, the proposed algorithm have an approximation ratio of 2. When all the jobs release at the same time, the proposed algorithm becomes a polynomial-time exact algorithm.

Single-machine batch scheduling problem with job rejection and resource dependent processing times

2018 ◽  
Vol 52 (2) ◽  
pp. 315-334 ◽  
Author(s):  
Weifan Huang ◽  
Chin-Chia Wu ◽  
Shangchia Liu
Keyword(s):  
Resource Allocation ◽  
Single Machine ◽  
Setup Time ◽  
Batch Scheduling ◽  
Nonrenewable Resource ◽  
Job Rejection ◽  
Processing Times ◽  
Programming Solution ◽  
First Job ◽  
Rejection Penalty

This paper addresses single-machine batch scheduling with job rejection and convex resource allocation. A job is either rejected, in which case a rejection penalty will be incurred, or accepted and processed on the machine. The accepted jobs are combined to form batches containing contiguously scheduled jobs. For each batch, a batch-dependent machine setup time, which is a function of the number of batches processed previously, is required before the first job in the batch is processed. Both the setup times and job processing times are controllable by allocating a continuously divisible nonrenewable resource to the jobs. The objective is to determine an accepted job sequence, a rejected job set, a partition of the accepted job sequence into batches, and resource allocation that jointly minimize a cost function based on the total delivery dates of the accepted jobs, and the job holding, resource consumption, and rejection penalties. An dynamic programming solution algorithm with running time O (n6) is developed for the problem. It is also shown that the case of the problem with a common setup time can be solved in O (n5) time.

scholarly journals A Novel Fast Parallel Batch Scheduling Algorithm for Solving the Independent Job Problem

2020 ◽  
Vol 10 (2) ◽  
pp. 460
Author(s):  
Bin Zhang ◽  
Dawei Wu ◽  
Yingjie Song ◽  
Kewei Liu ◽  
Juxia Xiong
Keyword(s):  
Approximation Algorithm ◽  
Production Scheduling ◽  
Manufacturing Systems ◽  
Scheduling Algorithm ◽  
Fast Algorithms ◽  
Batch Scheduling ◽  
Scheduling Problem ◽  
Total Size ◽  
Processing Times ◽  
Batch Processing Machine

With the rapid economic development, manufacturing enterprises are increasingly using an efficient workshop production scheduling system in an attempt to enhance their competitive position. The classical workshop production scheduling problem is far from the actual production situation, so it is difficult to apply it to production practice. In recent years, the research on machine scheduling has become a hot topic in the fields of manufacturing systems. This paper considers the batch processing machine (BPM) scheduling problem for scheduling independent jobs with arbitrary sizes. A novel fast parallel batch scheduling algorithm is put forward to minimize the makespan in this paper. Each of the machines with different capacities can only handle jobs with sizes less than the capacity of the machine. Multiple jobs can be processed as a batch simultaneously on one machine only if their total size does not exceed the machine capacity. The processing time of a batch is determined by the longest of all the jobs processed in the batch. A novel and fast 4.5-approximation algorithm is developed for the above scheduling problem. For the special case of all the jobs having the same processing times, a simple and fast 2-approximation algorithm is achieved. The experimental results show that fast algorithms further improve the competitive ratio. Compared to the optimal solutions generated by CPLEX, fast algorithms are capable of generating a feasible solution within a very short time. Fast algorithms have less computational costs.

A Batch Scheduling Problem with Two Agents

2015 ◽  
Vol 32 (06) ◽  
pp. 1550044 ◽  
Author(s):  
Byung-Cheon Choi ◽  
Myoung-Ju Park
Keyword(s):  
Approximation Algorithm ◽  
Optimality Conditions ◽  
Single Machine ◽  
Completion Time ◽  
Polynomial Algorithm ◽  
Batch Scheduling ◽  
Scheduling Problem ◽  
Np Hard ◽  
Due Date ◽  
Processing Times

In this paper, we consider a two-agent batch scheduling problem on a single machine such that the processing times of agent 1 and the due date of agent 2 in the same batch are identical. The objective is to minimize the total completion time of agent 1 with a constraint on the maximum tardiness of agent 2. First, we propose the optimality conditions. Then, we show that the problem is strongly NP-hard. Finally, we prove the problem remains NP-hard even for the case with one batch of agent 2, and develop a pseudo-polynomial algorithm and an approximation algorithm for this case.

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.

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