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SPECIAL SIMPLEX ALGORITHM FOR MULTI-SECTOR problemS

NUMERISCHE MATHEMATIK 1968年第4期12卷 288-+页

作者： HEESTERMAN, AR Faculty of Commerce and Social Science University of Birmingham 15 Birmingham Great Britain

This paper describes a proposed special algorithm for a certain class of partionable linear programming problems. The matrix defining such a linear programming problem consists of a number of non-zero diagonal blocks,... 详细信息

关键词： Mathematical Method programming problem linear programming problem Special Algorithm Diagonal Block

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An efficient approach for solving type-2 intuitionistic fuzzy solid transportation problems with their equivalent crisp solid transportation problems

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INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT 2024年第9期15卷 4370-4403页

作者： Kumar, P. Senthil Amity Univ Amity Sch Engn & Technol Bengaluru 562110 Karnataka India

It presents the type-2 intuitionistic fuzzy solid transportation problem (type-2 IFSTP) in a real-world situation and introduces an efficient technique based on software codes for solving type-2 IFSTP. It defines various types of intuitionistic fuzzy solid transportation problems (IFSTPs) and presents a mathematical model of full and type-2 IFSTPs. Additionally, the theorem, corollary, and their proof, as well as some results relevant to type-2 IFSTPs, are presented. Both the existing problem's solution and the proposed type-2 IFSTP's solution are compared using software (e.g., Matlab). In particular, solving IFSTPs using Matlab is new in the literature. Shortcomings in the existing results are pointed out and solved. Using the proposed approach, the optimal solution and optimal objective value of both the solid transportation problem (STP) and type-2 IFSTPs are obtained concurrently with one LP model, which is the key objective of this article. It also discusses the time complexity of the existing algorithms for solving STPs with different intuitionistic fuzzy numbers (IFNs). Both the proposed results and the benefits of the proposed methodology are thoroughly discussed. Finally, a sound conclusion and future research directions are provided.

关键词： Type-2 intuitionistic fuzzy solid transportation problem linear programming problem Matlab Solution Software PSK theorem

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Cooperation among liquefied natural gas suppliers: Is rationalization the sole objective?

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ENERGY ECONOMICS 2010年第4期32卷 933-947页

作者： Massol, Olivier Tchung-Ming, Stephane IFP Sch Ctr Econ & Management F-92852 Rueil Malmaison France City Univ London Dept Econ London EC1V 0HB England IFP Econ Studies Div F-92852 Rueil Malmaison France Univ Montpellier I CREDEN F-34054 Montpellier France

This paper examines the development of cooperative strategies between countries exporting Liquefied Natural Gas (LNG) and members of the Gas Exporting Countries Forum (GECF). This economic study focuses specifically on an often-raised scenario: the emergence of a cooperative approach designed with the sole aim of logistic rationalization, and which would not have any effect on LNG prices. We first assess the annual gains that may result from this market-power-free cooperative approach using a simple static transportation model. The numerical results obtained suggest that, in the absence of a gain redistribution policy, this cooperative strategy will probably not be adopted because cooperation would not be a rational move for some exporters. The problem of gain sharing is then formulated using cooperative game theory concepts. Several gain-sharing methods have been studied, including the Shapley value and various nucleolus-inspired concepts. Our results suggest that the choice of a redistribution policy appears relatively restricted. Out of the methods studied, only one - per capita nucleolus - satisfies two key requirements: core belonging and monotonicity (in the aggregate). Lastly, we look at how cooperation may give rise to a coordination cost and try to determine the maximum amount of this cost. In view of the low level of this amount and the relative complexity of the sharing method implemented, we consider that the credibility of a logistic cooperation scenario exempt from market power should be reappraised. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Liquefied natural gas Cooperative game theory linear programming problem

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Two-Stage Transportation problem with Two-Sided Constraints on Consumer Demands and Upper Bounds for Capacity of Intermediate Points

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CYBERNETICS AND SYSTEMS ANALYSIS 2024年第6期60卷 919-929页

作者： Stetsyuk, P. I. Stovba, V. O. Khomiak, O. M. Stetsyuk, M. G. Natl Acad Sci Ukraine VM Glushkov Inst Cybernet Kyiv Ukraine

The authors considered a mathematical model of a two-stage transportation problem with two-sided constraints on consumer demands and upper bounds on the capacities of intermediate points. They substantiated the necessary and sufficient conditions for the consistency of the system of linear constraints for the corresponding linear programming problem. The article presents two mathematical models of a two-stage transportation problem to which one can reduce the original model. It also presents the results of computational experiments on applying the problem described to the optimal set partitioning problem using the CPLEX solver from the NEOS server.

关键词： two-stage transportation problem linear programming problem constraint system consistency optimal set partitioning CPLEX NEOS

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Mathematical Model to Evaluate the Impact of Power Supply Constraint for Electric Vehicles on Transportation Network

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INTERNATIONAL JOURNAL OF INTELLIGENT TRANSPORTATION SYSTEMS RESEARCH 2024年第1期23卷 16-28页

作者： Nakajima, Yuki Shimamoto, Hiroshi Univ Miyazaki Grad Sch Engn 1-1 Gakuen Kibanadai Nishi Miyazaki Japan Univ Miyazaki Dept Civil & Environm Engn 1-1 Gakuen Kibanadai Nishi Miyazaki Japan

This paper proposes the UE-based mathematical model to evaluate driver's choice of vehicle types and paths, explicitly considering the supply power constraint in addition to the charging station capacity constraints. Because the flows of EVs in the proposed model are represented in a path-based manner, we apply a column generation-based algorithm to avoid enumerating all of the possible paths. The contributions of this study are that 1) we consider both pre-trip charging and charging during a trip, and that 2) we focus on the difference in the impact of power supply constraints on vehicles that need to charge during a trip and those that do not. The proposed model is applied to a hypothetical network. As a result, we confirmed that 1) while the share of EVs in the middle distance tends to be higher, the share of EVs in the short and long distances tends to be lower, and that 2) in case of inadequate power supply, the share of EVs in the short and middle distances decreases significantly, whereas the share of EVs remains almost unchanged in long OD.

关键词： Electric Vehicle Mode and Path Choice Power Supply Constraint linear programming problem Column Generation Approach

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Calculation of Phase Equilibria of Pure Light Hydrocarbons Using the PC-SAFT Equation of State and the Direct Energy Minimisation

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MOSCOW UNIVERSITY PHYSICS BULLETIN 2023年第6期78卷 876-886页

作者： Isaeva, A. V. Bevzo, M. O. Lomonosov Moscow State Univ Fac Phys Dept Phys Earth Moscow 119991 Russia

In the oil and gas industry, there is growing interest in using the PC-SAFT equation of state for predicting the phase behaviour and physical properties of hydrocarbons. This article demonstrates how this equation of state can be used in combination with the direct energy minimisation algorithm of an isochoric-isothermal system for calculating vapour-liquid equilibrium parameters of hydrocarbons. The proposed approach is tested on four substances: methane, ethane, propane, and n-butane.

关键词： direct energy minimisation algorithm PC-SAFT equation of state Peng-Robinson equation of state linear programming problem

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On the research of linear programming solving methods for non-hierarchical spare parts supply chain planning

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IFAC-PapersOnLine 2016年第30期49卷 198-203页

作者： Pires, Matheus Cardoso Frazzon, Enzo Morosini Universidade Federal de Santa Catarina Florianópolis Brazil

The relevance of planning non-hierarchical supply chains has increased due to growing collaboration among industrial and logistic organizations once this planning approach aims to optimize the supply chain while preserving each actor's individuality. linear programming is the predominant modelling approach to deal with non-hierarchical supply chains according to the state-of-the-art literature. Metaheuristics and exact methods are the classical solving methods for linear programming problems, with different characteristics in terms of solution quality and capability of handling complex problems in feasible computation time. In this context, this paper evaluates methods to solve linear programming problems considering their capability of dealing with most common decision model types associated with spare parts supply chains applying collaborative planning concepts. The gathered references substantiate the conclusion that, for normal sized problems, the simplex method continues to be the most attractive method. For bigger problems, interior point methods can be a better alternative. And for problems that surpass interior point method capacity, metaheuristics are recommended. © 2016

关键词： linear programming Heuristic algorithms Large scale systems Operations research Optimization problem solving Supply chains Collaborative planning Decision modeling Interior point method linear programming problem Non hierarchical Spare parts Spare parts supply Supply chain planning

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Optimal Signal Timing for Multi-Phase Intersections

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IFAC-PapersOnLine 2018年第9期51卷 476-481页

作者： Mercader, Pedro Ornik, Melkior Gutman, Per-Olof Ioslovich, Ilya Technion - Israel Institute of Technology Haifa Israel University of Texas at Austin AustinTX United States

We present an optimal signal timing policy for multi-phase intersections. The policy is optimal in the sense of minimizing the increase in the number of queuing vehicles, i.e. maximizing throughput, within one signal cycle. By introducing weights in the optimality criterion, our solution also accommodates the setting of prioritized traffic, in which it is more important for certain classes of traffic to wait for a shorter time. The proposed signal timing policy is simple to compute and implement. In particular, we show that the proposed strategy can be computed as a solution to a linear programming problem. Additionally, upon parametrizing the proposed policy with respect to the vehicle queue lengths, we analyze some aspects of the multi-cycle behavior of the closed-loop system generated by the policy, most notably convergence of the queue lengths over time. Finally, we illustrate the proposed control law with two numerical examples, one of which is based on real data collected from an existing complex multi-phase intersection. © 2018

关键词： Traffic signals Closed loop systems linear programming Queueing theory Timing circuits Traffic control linear programming problem Optimal controls Optimal signals Optimality criteria Piecewise affine systems Prioritized traffics Road traffic Vehicle queues

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A Hybrid Difference Scheme under Generalized Approximation Condition in the Space of Undetermined Coefficients

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2018年第8期58卷 1270-1279页

作者： Lobanov, A. I. Mirov, F. Kh. Moscow Inst Phys & Technol Dolgoprudnyi 141700 Moscow Oblast Russia

Construction of difference schemes of high approximation orders for hyperbolic problems is still an important problem. For the construction of grid-characteristic methods, difference schemes were earlier analyzed in the space of undetermined coefficients, where the coefficients of high order derivatives in the first differential approximation of the difference scheme were used as the objective function to be minimized. Other reasonable functionals in the space of undetermined coefficients that are linear in the coefficients of the scheme may be used. By solving a linear programming problem, difference schemes meeting various conditions can be chosen. An example of the linear functional related to the approximation properties of the problem is discussed. It is proposed to call it the generalized approximation condition. Based on this condition, a difference scheme of a novel class is built that has no analogs in the literature. The presentation uses the transport equation with a constant coefficient as an example.

关键词： linear transport equation difference scheme hybrid scheme linear programming problem complementary slackness conditions monotonic scheme Lagrange multipliers

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Gradient Estimation Based Multi-functional Optimization of Dynamical Systems

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IFAC-PapersOnLine 2016年第11期49卷 696-701页

作者： Toyoda, Mitsuru Shen, Tielong Department of Engineering and Applied Sciences Sophia University Tokyo102-8554 Japan

A multi-functional optimization algorithm for dynamical systems is proposed in this paper. The problem is formulated as a receding horizon control problem, and the current control is updated by using the gradient estimation of functionals. In order to achieve the Pareto optimality, the input is improved along the Pareto descent direction, which is given by solving the linear programming problem. As a practical example, the application on the engine simulator is conducted, and the optimization problem, whose torque and emission of NOx are chosen as the objective functionals, is considered. © 2016

关键词： Dynamical systems linear programming Multiobjective optimization Pareto principle Automotive control Gradient estimation linear programming problem Multi functional optimization Numerical solution Optimal controls Optimization problems Receding horizon control

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