OPTIMAL SEMI-ONLINE ALGORITHMS FOR m-BATCH-MACHINE FLOW SHOP SCHEDULING

2012 ◽  
Vol 04 (04) ◽  
pp. 1250051 ◽  
Author(s):  
MING LIU ◽  
CHENGBIN CHU
Keyword(s):  
Online Algorithms ◽  
Processing Time ◽  
Flow Shop ◽  
Optimal Algorithm ◽  
Flow Shop Scheduling ◽  
Shop Scheduling ◽  
Batch Machine ◽  
Processing Times ◽  
Batch Processing Machine ◽  
Over Time

This paper deals with semi-online scheduling on m-batch-machine flow shop. The objective is to minimize the makespan. A parallel batch processing machine can handle up to B jobs simultaneously. We study an unbounded model where B = ∞. The jobs that are processed together construct a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is given by the longest processing time of any job in the batch. The problem is online in the sense that jobs arrive over time. Let pi, j(i = 1,…,m) denote the processing time of job Jj on machines Mi, respectively. Let Jj+1 be the following job of Jj in a job instance. We study semi-online problem with jobs' nondecreasing processing times. We focus on the case where p1, j = ⋯ = pm, j for i = 1, …, m and pi, j+1 ≥ βpi, j (β ≥ 1). For this problem, we propose an optimal algorithm [Formula: see text] with a competitive ratio [Formula: see text].

scholarly journals Minimizing the Makespan for Scheduling Problems with General Deterioration Effects

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xianyu Yu ◽  
Yulin Zhang ◽  
Kai Huang
Keyword(s):  
Processing Time ◽  
Flow Shop ◽  
Single Machine Scheduling ◽  
Flow Shop Scheduling ◽  
Scheduling Problems ◽  
Shop Scheduling ◽  
Processing Times ◽  
Polynomially Solvable ◽  
Machine Scheduling Problems ◽  
Normal Processing

This paper investigates the scheduling problems with general deterioration models. By the deterioration models, the actual processing time functions of jobs depend not only on the scheduled position in the job sequence but also on the total weighted normal processing times of the jobs already processed. In this paper, the objective is to minimize the makespan. For the single-machine scheduling problems with general deterioration effects, we show that the considered problems are polynomially solvable. For the flow shop scheduling problems with general deterioration effects, we also show that the problems can be optimally solved in polynomial time under the proposed conditions.

scholarly journals A Heuristic Approach to Flow Shop Scheduling Problem in Which Processing Times Are Associated with Their Respective Probabilities with No-Idle Constraint

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Deepak Gupta ◽  
Harminder Singh
Keyword(s):  
Processing Time ◽  
Flow Shop ◽  
Flow Shop Scheduling ◽  
Scheduling Problem ◽  
Flowshop Scheduling ◽  
Numerical Illustration ◽  
Fixed Sequence ◽  
Shop Scheduling ◽  
General Flow ◽  
Processing Times

This paper is an attempt to study general flow shop scheduling problem in which processing time of jobs is associated with probabilities under no-idle constraint. The objective of this paper is to develop a heuristic algorithm to flowshop scheduling so that no machine remains idle during working for any given sequence of jobs. The proposed algorithm is simple, and easy to understand and provides an important tool in many practical situations for minimizing the expected hiring cost of the machines for a fixed sequence of job processing. A numerical illustration is also given to justify the proposed algorithm.

The Research of Heuristic Algorithm for Flow Shop Scheduling Problem

2012 ◽  
Vol 605-607 ◽  
pp. 528-531
Author(s):  
Dan Tang ◽  
Hong Ping Shu
Keyword(s):  
Heuristic Algorithm ◽  
Processing Time ◽  
Flow Shop ◽  
Heuristic Method ◽  
Flow Shop Scheduling ◽  
Scheduling Problem ◽  
Average Quality ◽  
Simulation Experiments ◽  
Shop Scheduling ◽  
Better Than

For the flow shop scheduling problem which aims to minimize makespan, this paper gives a new derivation about its mathematical definition, and mining characteristics of the problem itself further. By which analysis, the new heuristic method proposed in the paper shorten the waiting time of each job as much as possible on the basis of reduce the processing time of the first machine and last job. The result of simulation experiments shows that, our new heuristic algorithm has good performance, and the average quality and stability of scheduling sequences generated by new method is significantly better than other heuristic algorithm which has the same complexity.

Flow shop scheduling with flexible processing times

OR Spectrum ◽  
2018 ◽  
Vol 40 (3) ◽  
pp. 809-829 ◽  
Author(s):  
Matthias Bultmann ◽  
Sigrid Knust ◽  
Stefan Waldherr
Keyword(s):  
Flow Shop ◽  
Flow Shop Scheduling ◽  
Shop Scheduling ◽  
Processing Times

Two-Machine Ordered Flow Shop Scheduling with Generalized Due Dates

2020 ◽  
Vol 37 (01) ◽  
pp. 1950032
Author(s):  
Myoung-Ju Park ◽  
Byung-Cheon Choi ◽  
Yunhong Min ◽  
Kyung Min Kim
Keyword(s):  
Flow Shop ◽  
Flow Shop Scheduling ◽  
Due Dates ◽  
Shop Scheduling ◽  
Processing Times ◽  
Specific Position ◽  
Polynomially Solvable ◽  
Definition Of ◽  
Tardy Jobs ◽  
Np Hardness

We consider a two-machine flow shop scheduling with two properties. The first is that each due date is assigned for a specific position different from the traditional definition of due dates, and the second is that a consistent pattern exists in the processing times within each job and each machine. The objective is to minimize maximum tardiness, total tardiness, or total number of tardy jobs. We prove the strong NP-hardness and inapproximability, and investigate some polynomially solvable cases. Finally, we develop heuristics and verify their performances through numerical experiments.

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