A solution approach to minimal average cost flow problem with lower and upper bounds on flows

2022 ◽  
Vol 187 ◽  
pp. 115988
Author(s):  
Zhimin Zou ◽  
Fanrong Xie
Keyword(s):  
Average Cost ◽  
Flow Problem ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Solution Approach ◽  
Cost Flow

A NEW APPROACH FOR SOLVING THE MINIMUM COST FLOW PROBLEM WITH INTERVAL AND FUZZY DATA

2011 ◽  
Vol 19 (01) ◽  
pp. 71-88 ◽  
Author(s):  
MEHDI GHIYASVAND
Keyword(s):  
Flow Problem ◽  
Minimum Cost ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Minimum Cost Flow ◽  
Running Time ◽  
Minimum Cost Flow Problem ◽  
Cost Flow ◽  
Cost Scaling ◽  
The Cost

In particular, imprecise observations or possible perturbations mean that data in a network flows may well be better represented by intervals or fuzzy numbers than crisp quantities. In this paper we first consider the minimum cost flow problem with compact interval-valued lower and upper bounds, flows, and costs. We present a new method that shows this problem is solved using two minimum cost flow problems with crisp data. Then this result is extended to networks with fuzzy lower and upper bounds, flows, and costs. One of the best algorithms to solve the minimum cost flow problem with crisp data is the cost scaling algorithm of Goldberg and Tarjan.17 In this paper, the cost scaling algorithm is modified for fuzzy lower and upper bounds, flows and costs. The running time of the modified algorithm is equal to the running time of the cost scaling algorithm with crisp data.

scholarly journals The inverse maximum flow problem with lower and upper bounds for the flow

2008 ◽  
Vol 18 (1) ◽  
pp. 13-22 ◽  
Author(s):  
Adrian Deaconu
Keyword(s):  
Upper Bound ◽  
Flow Problem ◽  
Maximum Flow ◽  
Upper Bounds ◽  
Initial Vector ◽  
Polynomial Algorithms ◽  
Lower And Upper Bounds ◽  
L1 Norm ◽  
Maximum Flow Problem

The general inverse maximum flow problem (denoted GIMF) is considered, where lower and upper bounds for the flow are changed so that a given feasible flow becomes a maximum flow and the distance (considering l1 norm) between the initial vector of bounds and the modified vector is minimum. Strongly and weakly polynomial algorithms for solving this problem are proposed. In the paper it is also proved that the inverse maximum flow problem where only the upper bound for the flow is changed (IMF) is a particular case of the GIMF problem.

scholarly journals The inverse maximum flow problem under Lk norms

2012 ◽  
Vol 28 (1) ◽  
pp. 59-66
Author(s):  
ADRIAN DEACONU ◽  
◽  
ELEONOR CIUREA ◽  
Keyword(s):  
Polynomial Time ◽  
Flow Problem ◽  
Maximum Flow ◽  
Upper Bounds ◽  
Initial Vector ◽  
Lower And Upper Bounds ◽  
Maximum Flow Problem ◽  
The Given

The problem consists in modifying the lower and upper bounds of a given feasible flow f in a network G so that the given flow becomes a maximum flow in G and the distance between the initial vector of bounds and the modified one measured using Lk norm (k ∈ N∗) is minimum. A fast apriori fesibility test is presented. An algorithm for solving this problem is deduced. Strongly and weakly polynomial time implementations of this algorithm are presented. Some particular cases of the problem are discussed.

An Effective Solution Approach Based on Extension Principle for Fuzzy Minimal Cost Flow Problem

2018 ◽  
Vol 26 (06) ◽  
pp. 997-1015
Author(s):  
Sadegh Niroomand ◽  
Ali Mahmoodirad ◽  
Esmaeil Keshavarz
Keyword(s):  
Flow Problem ◽  
Extension Principle ◽  
Minimal Cost ◽  
Solution Approach ◽  
Real World Applications ◽  
Cost Flow ◽  
Fuzzy Cost ◽  
High Degree ◽  
Solution Methodology ◽  
Minimal Cost Flow

A well-known version of minimal cost flow problem with fuzzy arc costs is focused in this study. The fuzzy arc costs is applied as in most of real-world applications, the parameters have high degree of uncertainty. The goal of this problem is to determine the minimum fuzzy cost of sending and passing a specified flow value in to and from a network. A decomposition-based solution methodology is introduced to tackle this problem. The methodology applies Zadeh’s extension principle to decompose the problem to two upper bound and lower bound problems. These problems are capable of being solved for different α-cut values to construct the fuzzy cost flow value as the objective function value. The efficiency of the proposed solution methodology is studied over some well-known examples of the minimal cost flow problem. The obtained results and the procedure applied to obtain them prove the superiority of the proposed approach comparing to the previous approaches of the literature.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

scholarly journals Relationship between Age and Value of Information for a Noisy Ornstein–Uhlenbeck Process

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 940
Author(s):  
Zijing Wang ◽  
Mihai-Alin Badiu ◽  
Justin P. Coon
Keyword(s):  
Value Of Information ◽  
Markov Models ◽  
Upper Bounds ◽  
Distribution Functions ◽  
Lower And Upper Bounds ◽  
Uhlenbeck Process ◽  
Source Data ◽  
Non Linear ◽  
Queue Model ◽  
Selection Of

The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts.

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