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.

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 Integrated Scheduling Problem on a Single Bounded Batch Machine with an Unavailability Constraint

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Jing Fan
Keyword(s):  
Approximation Algorithm ◽  
Processing Time ◽  
Performance Ratio ◽  
Scheduling Problem ◽  
Total Size ◽  
Batch Machine ◽  
Processing Times ◽  
Production And Distribution ◽  
Machine Setting ◽  
Vehicle Capacity

We consider a scheduling problem where a set of jobs are first processed on a machine with an unavailability interval and, then, delivered to the customer directly. We focus on an integrated schedule of production and distribution such that the sum of the maximum delivery time and total delivery cost is optimized. We study two classes of processing machines in the production part. In the first class, the serial-batch machine, the processing time of a batch is the sum of the processing times of its jobs. In the second class, the parallel-batch machine, the processing time of a batch is the maximum processing time of the jobs contained in the batch. The machine has a fixed capacity, and the jobs are processed in batches under the condition that the total size of the jobs in a batch cannot exceed the machine capacity. Two patterns of job’s processing, i.e., resumable and non-resumable, are considered if it is interrupted by the unavailability interval on the machine. In the distribution part, there are sufficient vehicles with a fixed capacity to deliver the completed jobs. The total size of the completed jobs in one delivery cannot exceed the vehicle capacity. We show that these four problems are NP-hard in the strong sense in which the jobs have the same processing times and arbitrary sizes, and we propose an approximation algorithm for solving these four problems. Moreover, we show that the performance ratio of the algorithm is 2 for the serial-batch machine setting, and the error bound is 71/99 for the parallel-batch machine setting. We also evaluate the performance of the approximation algorithm by the computational results.

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.

Linear Rail Space Dynamic Scheduling Technology for Multi-Tasking Hybrid Assembly Sections

2012 ◽  
Vol 271-272 ◽  
pp. 650-656
Author(s):  
Zhi Bing Lu ◽  
Ai Min Wang ◽  
Cheng Tong Tang ◽  
Jing Sheng Li
Keyword(s):  
Production Scheduling ◽  
Dynamic Scheduling ◽  
Scheduling Algorithm ◽  
Real Data ◽  
Utilization Rate ◽  
Filter Method ◽  
Scheduling Problem ◽  
Rule Based ◽  
Comprehensive Utilization ◽  
Space Production

For the rapid response to production scheduling problem driven by high-density production tasks, a dynamic scheduling technology for the large precision strip products assembly with a mixture of task time nodes and line-rail space is proposed. A scheduling constrained model containing coverage, proximity, timeliness and resource is established. A linear rail space production scheduling technology using heuristic automatic scheduling and event-driven method is put forward. The time rule based on delivery and single completion assembly is formed, at the same time the space rule based on the adjacent rail and comprehensive utilization is researched. Supposing the privilege of single product assembling as the core, the scheduling parts filter method based on multiple constraints and former rules. For the space layout problem, a clingy forward and backward algorithms is proposed to judge the assemble position regarding the space comprehensive utilization rate. The classification of the various disturbances in the actual production is summarized. Three basic algorithms are proposed, including insertion, moving and re-scheduling algorithm, in order to solve the assembly dynamic scheduling problem driven by production disturbance events. Finally, take rocket as the example， the rocket assembly space production scheduling system is developed, combining with the proposed algorithm. The practicability of the system is validated using real data.

A STOCHASTIC BATCHING AND SCHEDULING PROBLEM

2001 ◽  
Vol 15 (4) ◽  
pp. 465-479 ◽  
Author(s):  
Ger Koole ◽  
Rhonda Righter
Keyword(s):  
Optimal Policy ◽  
Semiconductor Manufacturing ◽  
Processing Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Flow Time ◽  
Batch Scheduling ◽  
Scheduling Problem ◽  
Processing Times ◽  
Deterministic Problem

We consider a batch scheduling problem in which the processing time of a batch of jobs equals the maximum of the processing times of all jobs in the batch. This is the case, for example, for burn-in operations in semiconductor manufacturing and other testing operations. Processing times are assumed to be random, and we consider minimizing the makespan and the flow time. The problem is much more difficult than the corresponding deterministic problem, and the optimal policy may have many counterintuitive properties. We prove various structural properties of the optimal policy and use these to develop a polynomial-time algorithm to compute the optimal policy.

scholarly journals Research on Optimization of Production Decision Based on Payment Time and Price Coordination

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Yanyang Yan ◽  
Liang Yuan ◽  
Yemei Li
Keyword(s):  
Mathematical Model ◽  
Supply Chain ◽  
Production Scheduling ◽  
Management Practice ◽  
Scheduling Algorithm ◽  
Scheduling Problem ◽  
Effective Implementation ◽  
The Mathematical Model ◽  
Production Decision

This paper focuses on the coordination and optimization between a manufacturer and multiple retailers in a supply chain. The manufacturer makes product quotes and delivery deadlines for all retailers, and each retailer selects product offers and delivery deadlines based on their own needs. Manufacturers maximize their own total profits by setting optimal quotes and delivery deadlines. This paper constructs the mathematical model of the optimal quotation and delivery deadline and proposes a scheduling algorithm that is different from the general M/M/1 and then studies the production scheduling problem and explores the effective implementation of quotation policy in management practice.

Sign in / Sign up

Export Citation Format

Share Document