scholarly journals Cost-allocation problems for fuzzy agents in a fixed-tree network

2022 ◽  
Author(s):  
Julio R. Fernández ◽  
Inés Gallego ◽  
Andrés Jiménez-Losada ◽  
Manuel Ordóñez
Keyword(s):  
Spanning Tree ◽  
Cost Allocation ◽  
Minimum Cost ◽  
Maintenance Costs ◽  
Tree Networks ◽  
Tree Network ◽  
Classic Problem ◽  
Entire Time ◽  
Allocation Problems ◽  
Fixed Tree

AbstractCost-allocation problems in a fixed network are concerned with distributing the costs for use by a group of clients who cooperate in order to reduce such costs. We work only with tree networks and we assume that a minimum cost spanning tree network has already been constructed and now we are interested in the maintenance costs. The classic problem supposes that each agent stays for the entire time in the same node of the network. This paper introduces cost-allocation problems in a fixed-tree network with a set of agents whose activity over the nodes is fuzzy. Agent’s needs to pay for each period of time may differ. Moreover, the agents do not always remain in the same node for each period. We propose the extension of a very well-known solution for these problems: Bird’s rule.

A claims problem approach to the cost allocation of a minimum cost spanning tree

2021 ◽  
Author(s):  
José-Manuel Giménez-Gómez ◽  
Josep E. Peris ◽  
Begoña Subiza
Keyword(s):  
Spanning Tree ◽  
Cost Allocation ◽  
Minimum Cost ◽  
Claims Problem ◽  
The Cost

A cost allocation rule for -hop minimum cost spanning tree problems

2012 ◽  
Vol 40 (1) ◽  
pp. 52-55 ◽  
Author(s):  
G. Bergantiños ◽  
M. Gómez-Rúa ◽  
N. Llorca ◽  
M. Pulido ◽  
J. Sánchez-Soriano
Keyword(s):  
Spanning Tree ◽  
Cost Allocation ◽  
Minimum Cost ◽  
Allocation Rule

scholarly journals Network Connectivity Game

2021 ◽  
Vol 28 (2) ◽  
pp. 73-87
Keyword(s):  
Spanning Tree ◽  
Cost Allocation ◽  
Network Connectivity ◽  
Minimum Cost ◽  
Common Source ◽  
Network Nodes ◽  
Network Cost ◽  
Cost Efficient ◽  
The Cost ◽  
Tree Games

We investigate the cost allocation strategy associated with the problem of providing service /communication between all pairs of network nodes. There is a cost associated with each link and the communication between any pair of nodes can be delivered via paths connecting those nodes. The example of a cost efficient solution which could provide service for all node pairs is a (non-rooted) minimum cost spanning tree. The cost of such a solution should be distributed among users who might have conflicting interests. The objective of this paper is to formulate the above cost allocation problem as a cooperative game, to be referred to as a Network Connectivity (NC) game, and develop a stable and efficient cost allocation scheme. The NC game is related to the Minimum Cost Spanning Tree games and to the Shortest Path games. The profound difference is that in those games the service is delivered from some common source node to the rest of the network, while in the NC game there is no source and the service is established through the two-way interaction among all pairs of participating nodes. We formulate Network Connectivity (NC) game and construct an efficient cost allocation algorithm which finds some points in the core of the NC game. Finally, we discuss the Egalitarian Network Cost Allocation (ENCA) rule and demonstrate that it finds an additional core point.

On Analyzing Cost Allocation Problems: Cooperation Building Structures and Order Problem Representations

2018 ◽  
Vol 20 (04) ◽  
pp. 1850007
Author(s):  
John Kleppe ◽  
Peter Borm ◽  
Ruud Hendrickx ◽  
Hans Reijnierse
Keyword(s):  
Cost Allocation ◽  
Minimum Cost ◽  
Cost Functions ◽  
Building Structures ◽  
Order Problem ◽  
Core Element ◽  
Initial Allocation ◽  
Allocation Problems ◽  
Sequencing Situations ◽  
Problem Representations

To analyze cost allocation problems, this paper identifies associated cooperation building structures, with joint cost functions, and corresponding efficient order problem representations, with individualized cost functions. This paper presents an approach that, when applicable, offers a way not only to adequately model a cost allocation problem by means of a cooperative cost game, but also to construct a core element of such a game by means of a generalized Bird allocation. We apply the approach to both existing and new classes of cost allocation problems related to operational research problems: sequencing situations without initial ordering, maintenance problems, minimum cost spanning tree situations, permutation situations without initial allocation, public congestion network situations, traveling salesman problems, shared taxi problems and traveling repairman problems.

Minimum-cost spanning tree as a path-finding problem

1988 ◽  
Vol 26 (6) ◽  
pp. 291-293 ◽  
Author(s):  
Bruce M. Maggs ◽  
Serge A. Plotkin
Keyword(s):  
Spanning Tree ◽  
Minimum Cost ◽  
Path Finding

scholarly journals FUZZY SHORTEST ROUTE ALGORITHM FOR TELEPHONE LINE CONNECTION USING THE LC-MST ALGORITHM

2015 ◽  
Vol 2 (2) ◽  
pp. 37-39
Author(s):  
Vijayalakshmi D ◽  
Kalaivani R
Keyword(s):  
Transmission Lines ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Minimum Cost ◽  
Distribution Networks ◽  
Minimum Length ◽  
Fuzzy Graph ◽  
Telephone Line ◽  
Water Pipelines ◽  
Communication Links

In computer science, there are many algorithms that finds a minimum spanning tree for a connected weighted undirected fuzzy graph. The minimum length (or cost) spanning tree problem is one of the nicest and simplest problems in network optimization, and it has a wide variety of applications. The problem is tofind a minimum cost (or length) spanning tree in G. Applications include the design of various types of distribution networks in which the nodes represent cities, centers etc.; and edges represent communication links (fiber glass phone lines, data transmission lines, cable TV lines, etc.), high voltage power transmissionlines, natural gas or crude oil pipelines, water pipelines, highways, etc. The objective is to design a network that connects all the nodes using the minimum length of cable or pipe or other resource in this paper we find the solution to the problem is to minimize the amount of new telephone line connection using matrixalgorithm with fuzzy graph.

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