scholarly journals Scheduling Jobs and a Variable Maintenance on a Single Machine with Common Due-Date Assignment

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Long Wan
Keyword(s):  
Single Machine ◽  
Optimal Solution ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Due Date ◽  
Due Date Assignment ◽  
Common Due Date ◽  
Optimal Polynomial ◽  
Special Case ◽  
Identical Jobs

We investigate a common due-date assignment scheduling problem with a variable maintenance on a single machine. The goal is to minimize the total earliness, tardiness, and due-date cost. We derive some properties on an optimal solution for our problem. For a special case with identical jobs we propose an optimal polynomial time algorithm followed by a numerical example.

THE PROBLEM OF PARTITIONING WITH DUPLICATIONS AND ITS APPLICATIONS

1994 ◽  
Vol 03 (03) ◽  
pp. 395-405
Author(s):  
J. HARALAMBIDES ◽  
S. TRAGOUDAS
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Vlsi Layout ◽  
Optimal Polynomial ◽  
Partitioning Problem ◽  
Polynomially Solvable ◽  
The Cost ◽  
Parallel Graph ◽  
Special Case

The problem of partitioning the elements of a graph G=(V, E) into two equal size sets A and B that share at most d elements such that the total number of edges (u, v), u∈A−B, v∈B−A is minimized, arises in the areas of Hypermedia Organization, Network Integrity, and VLSI Layout. We formulate the problem in terms of element duplication, where each element c∈A∩B is substituted by two copies c′∈A and c″∈B As a result, edges incident to c′ or c″ need not count in the cost of the partition. We show that this partitioning problem is NP-hard in general, and we present a solution which utilizes an optimal polynomial time algorithm for the special case where G is a series-parallel graph. We also discuss special other cases where the partitioning problem or variations are polynomially solvable.

scholarly journals Optimization for Due-Date Assignment Single-Machine Scheduling under Group Technology

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Li-Yan Wang ◽  
Mengqi Liu ◽  
Ji-Bo Wang ◽  
Yuan-Yuan Lu ◽  
Wei-Wei Liu
Keyword(s):  
Single Machine ◽  
Group Technology ◽  
Machine Scheduling ◽  
Time Algorithm ◽  
Single Machine Scheduling ◽  
Due Date ◽  
Optimal Sequence ◽  
Due Date Assignment ◽  
The Common ◽  
Slk Due Date Assignment

In this paper, the single-machine scheduling problem is studied by simultaneously considering due-date assignment and group technology (GT). The objective is to determine the optimal sequence of groups and jobs within groups and optimal due-date assignment to minimize the weighted sum of the absolute value in lateness and due-date assignment cost, where the weights are position dependent. For the common (CON) due-date assignment, slack (SLK) due-date assignment, and different (DIF) due-date assignment, an O n    log    n time algorithm is proposed, respectively, to solve the problem, where n is the number of jobs.

scholarly journals A Note on Two-Agent Scheduling with Resource Dependent Release Times on a Single Machine

2015 ◽  
Vol 2015 ◽  
pp. 1-4 ◽  
Author(s):  
Peng Liu ◽  
Lini Duan
Keyword(s):  
Cost Function ◽  
Single Machine ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Release Time ◽  
Scheduling Problem ◽  
Two Agents ◽  
Release Times ◽  
Agent Scheduling ◽  
Optimal Polynomial

We consider a scheduling problem in which both resource dependent release times and two agents exist simultaneously. Two agents share a common single machine, and each agent wants to minimize a cost function dependent on its own jobs. The release time of eachA-agent’s job is related to the amount of resource consumed. The objective is to find a schedule for the problem of minimizingA-agent’s total amount of resource consumption with a constraint onB-agent’s makespan. The optimal properties and the optimal polynomial time algorithm are proposed to solve the scheduling problem.

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