scholarly journals Comparison of Two Integer Programming Formulations for a Single Machine Family Scheduling Problem to Minimize Total Tardiness

Procedia CIRP ◽  
2014 ◽  
Vol 19 ◽  
pp. 174-179 ◽  
Author(s):  
Oliver Herr ◽  
Asvin Goel
Keyword(s):  
Integer Programming ◽  
Single Machine ◽  
Total Tardiness ◽  
Scheduling Problem

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.

Minimizing Total Earliness and Total Tardiness on Single Machine with Release Dates

2011 ◽  
Vol 5 ◽  
pp. 30-43
Author(s):  
Elkanah Oyetunji ◽  
Ayodeji E. Oluleye
Keyword(s):  
Single Machine ◽  
Single Machine Scheduling ◽  
Total Tardiness ◽  
Release Dates ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Bicriteria Scheduling ◽  
Linear Composite ◽  
Effectiveness And Efficiency ◽  
Machine Scheduling Problems

This paper considers the bicriteria scheduling problem of minimizing the total earliness and the total tardiness on a single machine with release dates. In view of the fact that the problem has been characterized as NP-Hard, we propose two approximation algorithms (labeled as ETA1 and ETA2) for solving the problem. The proposed algorithms were compared with the MA heuristic selected from the literature. The two criteria (the total earliness and the total tardiness) were aggregated together into a linear composite objective function (LCOF). The performances of the algorithms were evaluated based on both effectiveness and efficiency. The algorithms were tested on a set of 1200 randomly generated single machine scheduling problems. Experimental results show that both the ETA1 and ETA2 algorithms outperformed (in terms of effectiveness and efficiency) the MA heuristic under all the considered problem sizes. Also, the ETA1 algorithm outperformed the ETA2 algorithm when the number of jobs (n) ranges between 20 and 500.

scholarly journals JOB ORDER INPUT FOR EFFICIENT EXACT MINIMIZATION OF TOTAL TARDINESS IN TIGHT-TARDY PROGRESSIVE SINGLE MACHINE SCHEDULING WITH IDLING-FREE PREEMPTIONS

2020 ◽  
Vol 1 (1) ◽  
pp. 19-36
Author(s):  
V.V. Romanuke ◽  
Keyword(s):  
Linear Programming ◽  
Single Machine ◽  
Job Scheduling ◽  
Computation Time ◽  
Single Machine Scheduling ◽  
Total Tardiness ◽  
Release Dates ◽  
Scheduling Problem ◽  
Speed Up ◽  
Job Scheduling Problem

Abstract. A schedule ensuring the exactly minimal total tardiness can be found with the respective integer linear programming problem. An open question is whether the exact schedule computation time changes if the job release dates are input into the model in reverse order. The goal is to ascertain whether the job order in tight-tardy progressive single machine scheduling with idling-free preemptions influences the speed of computing the exact solution. The Boolean linear programming model provided for finding schedules with the minimal total tardiness is used. To achieve the said goal, a computational study is carried out with the purpose of estimating the averaged computation time for both ascending and descending orders of job release dates. Instances of the job scheduling problem are generated so that schedules which can be obtained trivially, without the exact model, are excluded. As in the case of equal-length jobs, it has been ascertained that the job order really influences the speed of computing schedules whose total tardiness is minimal. Scheduling two to five jobs is executed on average faster by the descending job order input, where 1 to 3 % speed-up is expected. Further increment of the number of jobs to be scheduled cannot guarantee any speed-up even on average. This result is similar to that in the case of equal-length jobs, but there is no regularity in such an efficient job order input. Without any assurance for a single job scheduling problem, the efficient exact minimization of total tardiness by the descending job order input must be treated as on average only.

A New Decomposition Approach for the Single Machine Total Tardiness Scheduling Problem

1998 ◽  
Vol 49 (10) ◽  
pp. 1101 ◽  
Author(s):  
F. Della Croce ◽  
R. Tadei ◽  
P. Baracco ◽  
A. Grosso
Keyword(s):  
Single Machine ◽  
Total Tardiness ◽  
Scheduling Problem ◽  
Decomposition Approach

SOME IMPROVED ALGORITHMS ON THE SINGLE MACHINE HIERARCHICAL SCHEDULING WITH TOTAL TARDINESS AS THE PRIMARY CRITERION

2010 ◽  
Vol 27 (05) ◽  
pp. 577-585 ◽  
Author(s):  
CHENG HE ◽  
YIXUN LIN ◽  
JINJIANG YUAN
Keyword(s):  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Total Tardiness ◽  
Scheduling Problem ◽  
Np Hard ◽  
Assignment Problems ◽  
Running Time ◽  
Minimization Problems ◽  
Hierarchical Minimization

It is well-known that a single machine scheduling problem of minimizing the total tardiness is NP-hard. Recently, Liu, Ng and Cheng solved some special hierarchical minimization problems with total tardiness as the primary criterion by the Algorithm TAP (Two Assignment Problems) in O(n3) time. And in this paper we present some algorithms for these problems with running time O(n log n).

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.

Sign in / Sign up

Export Citation Format

Share Document