A Generalized Minimum Cost Flow Model for Multiple Emergency Flow Routing

During real-life disasters, that is, earthquakes, floods, terrorist attacks, and other unexpected events, emergency evacuation and rescue are two primary operations that can save the lives and property of the affected population. It is unavoidable that evacuation flow and rescue flow will conflict with each other on the same spatial road network and within the same time window. Therefore, we propose a novel generalized minimum cost flow model to optimize the distribution pattern of these two types of flow on the same network by introducing the conflict cost. The travel time on each link is assumed to be subject to a bureau of public road (BPR) function rather than a fixed cost. Additionally, we integrate contraflow operations into this model to redesign the network shared by those two types of flow. A nonconvex mixed-integer nonlinear programming model with bilinear, fractional, and power components is constructed, and GAMS/BARON is used to solve this programming model. A case study is conducted in the downtown area of Harbin city in China to verify the efficiency of proposed model, and several helpful findings and managerial insights are also presented.

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Efficient Algorithms for Identifying Loop Formation and Computing θ Value for Solving Minimum Cost Flow Network Problems

WSEAS TRANSACTIONS ON CIRCUITS AND SYSTEMS ◽

10.37394/23201.2021.20.14 ◽

2021 ◽

Vol 20 ◽

pp. 107-117

Author(s):

TIMOTHY MICHAEL CHÁVEZ ◽

DUC THAI NGUYEN

Keyword(s):

Real Life ◽

Minimum Cost ◽

Simplex Algorithm ◽

Efficient Algorithms ◽

Computer Implementation ◽

Loop Formation ◽

Minimum Cost Flow ◽

Flow Network ◽

Network Problems ◽

Cost Flow

While the minimum cost flow (MCF) problems have been well documented in many publications, due to its broad applications, little or no effort have been devoted to explaining the algorithms for identifying loop formation and computing the θ value needed to solve MCF network problems. This paper proposes efficient algorithms, and MATLAB computer implementation, for solving MCF problems. Several academic and real-life network problems have been solved to validate the proposed algorithms; the numerical results obtained by the developed MCF code have been compared and matched with the built-in MATLAB function Linprog() (Simplex algorithm) for further validation.

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The Minimum Cost Flow Problem of Uncertain Random Network

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595918500161 ◽

2018 ◽

Vol 35 (03) ◽

pp. 1850016

Author(s):

Soheila Abdi ◽

Fahimeh Baroughi ◽

Behrooz Alizadeh

Keyword(s):

Flow Model ◽

Flow Problem ◽

Random Network ◽

Minimum Cost ◽

Random Variable ◽

Minimum Cost Flow ◽

Feasible Set ◽

Uncertain Random Network ◽

Minimum Cost Flow Problem ◽

Cost Flow

The aim of this paper is to present a novel method for solving the minimum cost flow problem on networks with uncertain-random capacities and costs. The objective function of this problem is an uncertain random variable and the constraints of the problem do not make a deterministic feasible set. Under the framework of uncertain random programming, a corresponding [Formula: see text]-minimum cost flow model with a prespecified confidence level [Formula: see text], is formulated and its main properties are analyzed. It is proven that there exists an equivalence relationship between this model and the classical deterministic minimum cost flow model. Then an algorithm is proposed to find the maximum amount of [Formula: see text] such that for it, the feasible set of [Formula: see text]-minimum cost flow model is nonempty. Finally, a numerical example is presented to illustrate the efficiency of our proposed method.

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A Minimum-Cost Flow Model for Workload Optimization on Cloud Infrastructure

2017 IEEE 10th International Conference on Cloud Computing (CLOUD) ◽

10.1109/cloud.2017.68 ◽

2017 ◽

Cited By ~ 2

Author(s):

Frederick Nwanganga ◽

Mandana Saebi ◽

Gregory Madey ◽

Nitesh Chawla

Keyword(s):

Flow Model ◽

Minimum Cost ◽

Cloud Infrastructure ◽

Minimum Cost Flow ◽

Cost Flow

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A New Method for Solving Single- and Multi-Objective Capacitated Solid Minimum Cost Flow Problems under Uncertainty

Journal of Intelligent Systems ◽

10.1515/jisys-2015-0108 ◽

2016 ◽

Vol 25 (2) ◽

pp. 159-183

Author(s):

Manjot Kaur ◽

Rehan Sadiq

Keyword(s):

Fuzzy Sets ◽

Fuzzy Set ◽

Intuitionistic Fuzzy Set ◽

Real Life ◽

Minimum Cost ◽

Minimum Cost Flow ◽

Multi Objective ◽

Flow Problems ◽

Cost Flow ◽

Minimum Cost Flow Problems

AbstractIn real life, a person may assume that an object belongs to a set, but it is possible that he (she) is not sure about it. In other words, there may be hesitation or confusion whether an object belongs to a set or not. In fuzzy set theory, there is no means to incorporate such type of hesitation or confusion. A possible solution is to use intuitionistic fuzzy set [K. T. Atanassov, Intutionistic fuzzy sets, Fuzzy Sets Syst.20 (1986), 87–96]. In this article, the concept of unbalanced fully fuzzy multi-objective capacitated solid minimum cost flow (SMCF) problems is generalized by unbalanced intuitionistic fully fuzzy multi-objective capacitated SMCF (CSMCF) problems and new methods are proposed for solving these problems. The main advantage of the proposed methods over the existing methods is that all the unbalanced fully fuzzy single- and multi-objective CSMCF problems that can be solved by the existing methods can also be solved by the proposed method.

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A minimum cost flow model for level of repair analysis

International Journal of Production Economics ◽

10.1016/j.ijpe.2010.03.025 ◽

2011 ◽

Vol 133 (1) ◽

pp. 233-242 ◽

Cited By ~ 17

Author(s):

R.J.I. Basten ◽

M.C. van der Heijden ◽

J.M.J. Schutten

Keyword(s):

Flow Model ◽

Minimum Cost ◽

Minimum Cost Flow ◽

Cost Flow ◽

Level Of Repair Analysis

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Risk-Based Minimum Cost Flow Model for AGVs Path Planning

The Open Automation and Control Systems Journal ◽

10.2174/1874444301810010001 ◽

2018 ◽

Vol 10 (1) ◽

pp. 1-7

Author(s):

Hamed Fazlollahtabar

Keyword(s):

Path Planning ◽

Flow Model ◽

Minimum Cost ◽

Minimum Cost Flow ◽

Cost Flow

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Practical extensions to a minimum cost flow model for level of repair analysis

European Journal of Operational Research ◽

10.1016/j.ejor.2010.11.015 ◽

2011 ◽

Vol 211 (2) ◽

pp. 333-342 ◽

Cited By ~ 12

Author(s):

R.J.I. Basten ◽

M.C. van der Heijden ◽

J.M.J. Schutten

Keyword(s):

Flow Model ◽

Minimum Cost ◽

Minimum Cost Flow ◽

Cost Flow ◽

Level Of Repair Analysis

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Model and Algorithm for Vehicle Routing Problem with Time Windows and a Limited Number of Vehicles

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.482-484.2322 ◽

2012 ◽

Vol 482-484 ◽

pp. 2322-2326 ◽

Cited By ~ 2

Author(s):

Yong Ji Jia ◽

Chang Jun Wang

Keyword(s):

Vehicle Routing ◽

Vehicle Routing Problem ◽

Time Window ◽

Programming Model ◽

Search Algorithm ◽

Time Windows ◽

Real Life ◽

Mixed Integer ◽

Routing Problem ◽

Number Of Customers

In this paper, a useful variant of the vehicle routing problem, Vehicle Routing Problem with Time Windows and a limited number of vehicles (m-VRPTW) is given. The problem is to serve a number of customers at minimum cost by using a limited number of vehicles, without violating the time window constraint and the vehicle capacity constraint. The feasible solution of m-VRPTW may contain some unserved customers and third-party vehicles, such as taxies, are hired to serve these unserved customers. The mixed integer programming model of m-VRPTW is proposed and a two-phase algorithm based on insertion algorithm and tabu search algorithm is proposed to solve it. Experimental results show that our algorithm can yield effective and efficient solution and be capable of dealing with the m-VRPTW problems in real life conditions.

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