Polynomial-time solvable cases of the capacitated multi-echelon shipping network scheduling problem with delivery deadlines

2012 ◽  
Vol 137 (2) ◽  
pp. 263-271 ◽  
Author(s):  
Gang Wang ◽  
Lei Lei
Keyword(s):  
Polynomial Time ◽  
Scheduling Problem ◽  
Network Scheduling

scholarly journals The Complexity Landscape of Resource-Constrained Scheduling

2020 ◽  
Author(s):  
Robert Ganian ◽  
Thekla Hamm ◽  
Guillaume Mescoff
Keyword(s):  
Artificial Intelligence ◽  
Polynomial Time ◽  
Project Scheduling ◽  
Scheduling Problem ◽  
Comprehensive Understanding ◽  
Resource Constrained ◽  
Special Cases ◽  
Project Scheduling Problem ◽  
Np Complete ◽  
New Algorithms

The Resource-Constrained Project Scheduling Problem (RCPSP) and its extension via activity modes (MRCPSP) are well-established scheduling frameworks that have found numerous applications in a broad range of settings related to artificial intelligence. Unsurprisingly, the problem of finding a suitable schedule in these frameworks is known to be NP-complete; however, aside from a few results for special cases, we have lacked an in-depth and comprehensive understanding of the complexity of the problems from the viewpoint of natural restrictions of the considered instances. In the first part of our paper, we develop new algorithms and give hardness-proofs in order to obtain a detailed complexity map of (M)RCPSP that settles the complexity of all 1024 considered variants of the problem defined in terms of explicit restrictions of natural parameters of instances. In the second part, we turn to implicit structural restrictions defined in terms of the complexity of interactions between individual activities. In particular, we show that if the treewidth of a graph which captures such interactions is bounded by a constant, then we can solve MRCPSP in polynomial time.

An Ordered Flow Shop with Two Agents

2016 ◽  
Vol 33 (05) ◽  
pp. 1650037 ◽  
Author(s):  
Byung-Cheon Choi ◽  
Myoung-Ju Park
Keyword(s):  
Polynomial Time ◽  
Processing Time ◽  
Flow Shop ◽  
Fixed Number ◽  
Scheduling Problem ◽  
Np Hard ◽  
Two Agents ◽  
Agent Scheduling ◽  
Polynomially Solvable ◽  
Machine Problem

In this paper, we consider a two-agent scheduling problem in an [Formula: see text]-machine ordered flow shop where each agent is responsible for his own set of jobs and wishes to minimize the makespan. Since the problem is NP-hard, we develop a pseudo-polynomial time approach for the case with a fixed number of machines and investigate the conditions that make the problem polynomially solvable. Finally, we consider a three-machine problem with a special processing time structure, and demonstrate its polynomiality.

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