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.

scholarly journals Infinity substitute in exactly minimizing total tardiness in tight-tardy progressive 1-machine scheduling by idling-free preemptions of equal-length jobs

2019 ◽  
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Integer Linear Programming ◽  
Linear Programming Problem ◽  
Job Scheduling ◽  
Computation Time ◽  
Total Tardiness ◽  
Scheduling Problem ◽  
Integer Linear Programming Problem ◽  
Job Scheduling Problem

A schedule ensuring the exactly minimal total tardiness can be found by the respective integer linear programming problem with infinities. In real computations, the infinity which shows that the respective states are either forbidden or impossible is substituted with a sufficiently great positive integer. An open question is whether the substitute can be selected so that the computation time would be decreased. The goal is to ascertain how the increment of the infinity substitute in the respective model influences the computation time of exact schedules. If the influence appears to be significant, then a recommendation on selecting the infinity substitute is to be stated in order to decrease the computation time. A pattern of generating instances of the job scheduling problem is provided. The instances of the job scheduling problem are generated so that schedules which can be obtained trivially, without the exact model, are excluded. Nine versions of the infinity substitute have been proposed. The increment of the infinity substitute in the model of total tardiness exact minimization rendered to solving an integer linear programming problem involving the branch-and-bound approach may have bad influence on the computation time of exact schedules. At least, the greater value of the infinity substitute cannot produce an optimal schedule faster in tight-tardy progressive 1-machine scheduling by idling-free preemptions of equal-length jobs. Roughly the best value of the infinity substitute is the maximal value taken over all the finite triple-indexed weights in the model and increased then by 1. The influence of the “max” infinity substitution is extremely significant. Compared to the case when the infinity is substituted with a sufficiently great integer, the “max” infinity substitution saves up to 50 % of the computation time. This saves hours and even days or months when up to 8 jobs of a few equal processing periods are scheduled for a few thousands of cycles or longer. Therefore, it is strongly recommended always to select the infinity substitute as less as possible in order to decrease the computation time.

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.

A two-agent single-machine scheduling problem to minimize the total cost with release dates

2015 ◽  
Vol 21 (3) ◽  
pp. 805-816 ◽  
Author(s):  
Du-Juan Wang ◽  
Yunqiang Yin ◽  
Wen-Hsiang Wu ◽  
Wen-Hung Wu ◽  
Chin-Chia Wu ◽  
...  
Keyword(s):  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Release Dates ◽  
Scheduling Problem ◽  
Total Cost

scholarly journals A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 61
Author(s):  
Wencheng Wang ◽  
Xiaofei Liu
Keyword(s):  
Approximation Algorithm ◽  
Single Machine ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Single Machine Scheduling ◽  
Release Time ◽  
Release Dates ◽  
Scheduling Problem ◽  
Release Times

In this paper, we consider parallel-machine scheduling with release times and submodular penalties (P|rj,reject|Cmax+π(R)), in which each job can be accepted and processed on one of m identical parallel machines or rejected, but a penalty must paid if a job is rejected. Each job has a release time and a processing time, and the job can not be processed before its release time. The objective of P|rj,reject|Cmax+π(R) is to minimize the makespan of the accepted jobs plus the penalty of the rejected jobs, where the penalty is determined by a submodular function. This problem generalizes a multiprocessor scheduling problem with rejection, the parallel-machine scheduling with submodular penalties, and the single machine scheduling problem with release dates and submodular rejection penalties. In this paper, inspired by the primal-dual method, we present a combinatorial 2-approximation algorithm to P|rj,reject|Cmax+π(R). This ratio coincides with the best known ratio for the parallel-machine scheduling with submodular penalties and the single machine scheduling problem with release dates and submodular rejection penalties.

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