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An interactive approach for the multi-objective transportation problem with interval parameters

INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2015年第4期53卷 1051-1064页

作者： Yu, Vincent F. Hu, Kuo-Jen Chang, An-Yuan Natl Taiwan Univ Sci & Technol Dept Ind Management Taipei Taiwan Natl Formosa Univ Dept Ind Management Huwei Taiwan Natl Formosa Univ Inst Ind Engn & Management Huwei Taiwan

The basic transportation problem (TP) deals with the transportation of goods from a set of supply points to a set of demand points so as to minimise linear transportation costs. The multi-objective transportation problem (MOTP) extends TP to take into consideration multiple conflicting objectives such as transportation cost, average delivery time of the commodities, unfulfilled demand and so forth. We develop an interactive approach to determine the preferred compromise solution for the MOTP where the coefficients of the objective functions and the source and destination parameters have been expressed as interval values by the decision-maker to deal with the impreciseness in the parameters. The proposed method is applied to a real-world MOTP faced by a leading provider of complete broadband access solutions. Results of the case study indicate that the developed method is a practical technique for solving the MOTP with interval parameters.

关键词： interval programming transportation problem multi-objective decision-making

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A heuristic to minimax absolute regret for linear programs with interval objective function coefficients

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1999年第1期117卷 157-174页

作者： Mausser, HE Laguna, M Univ Colorado Grad Sch Business Adm Boulder CO 80309 USA

Decision makers faced with uncertain information often experience regret upon learning that an alternative action would have been preferable to the one actually selected. Models that minimize the maximum regret can be useful in such situations, especially when decisions are subject to ex post review. Of particular interest are those decision problems that can be modeled as linear programs with interval objective function coefficients. The minimax regret solution for these formulations can be found using an algorithm that, at each iteration, solves first a linear program to obtain a candidate solution and then a mixed integer program (MIP) to maximize the corresponding regret. The exact solution of the MIP is computationally expensive and becomes impractical as the problem size increases. In this paper, we develop a heuristic for the MTP and investigate its performance both alone and in combination with exact procedures. The heuristic is shown to be effective for problems that are significantly larger than those previously reported in the literature. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： probabilistic programming heuristics interval programming regret

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Evaluating Stochastic Methods in Power System Operations with Wind Power

Evaluating Stochastic Methods in Power System Operations wit...

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IEEE International Energy Conference (ENERGYCON)

作者： Wang, Yishen Zhou, Zhi Liu, Cong Botterud, Audun Univ Washington Seattle WA 98195 USA Argonne Natl Lab 9700 S Cass Ave Argonne IL 60439 USA

ISBN: (纸本)9781467384636

Wind power is playing an increasingly important role in electricity markets. However, it's inherent variability and uncertainty cause operational challenges and costs as more operating reserves are needed to maintain system reliability. Several operational strategies have been proposed to address these challenges, including advanced probabilistic wind forecasting techniques, dynamic operating reserves, and various unit commitment (UC) and economic dispatch (ED) strategies under uncertainty. This paper presents a consistent framework to evaluate different operational strategies in power system operations with renewable energy. We use conditional Kernel Density Estimation (KDE) for probabilistic wind power forecasting. Forecast scenarios are generated considering spatio-temporal correlations, and further reduced to lower the computational burden. Scenario-based stochastic programming with different decomposition techniques and interval optimization are tested to examine economic, reliability, and computational performance compared to deterministic UC/ED benchmarks. We present numerical results for a modified IEEE-118 bus system with realistic system load and wind data.

关键词： Electricity Markets Stochastic programming interval programming Dynamic Operating Reserves Decomposition Wind Power

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A scenario-based interval-input output model to analyze the risk of COVID-19 pandemic in port logistics

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JOURNAL OF MODELLING IN MANAGEMENT 2022年第4期17卷 1456-1480页

作者： Sarkar, Bishal Dey Shankar, Ravi Kar, Arpan Kumar Indian Inst Technol Delhi Bharti Sch Telecommun Technol & Management New Delhi India Indian Inst Technol Delhi Dept Management Studies New Delhi India

Purpose Presently, Indian sectors are manifesting a higher level of interdependency and making the economy more vulnerable to human-caused and natural disasters. COVID-19 pandemic creates a devastating effect on the world economy. The Indian economy was expected to lose around (sic) 32,000 crores every day during the first 21 days of complete lockdown. This motivates to conduct the research on how the COVID-19 pandemic affects the port logistics sector and how the effects of COVID-19 on port logistics propagate to other sectors owing to its interconnectedness and affect the economy of the country. Design/methodology/approach The purpose of the study is analyze how perturbation in one sector can affect the system of interdependent sectors and it is done with interdependency analysis. It uses Wassily Leontief's inoperability input-output model (IIM) and interval programming (IP) to develop a framework. IP is used to address situations where assumptions are not valid because of uncertainties associated with disruptive events. Findings The model helps in describing how the effect of the COVID-19 pandemic in port logistics can propagate owing to the interconnectedness across other sectors. The model uses the latest five-year data available on the Organisation for Economic Co-operation and Development database. It uses metrics like inoperability and economic loss to study the consequences of COVID-19 pandemic on various sectors. This study also presents the ranking of the affected sectors based on their inoperability and economic loss Research limitations/implications In the future study, other techniques like dynamic evolution, multiplex network analysis, analytical hierarchy process, pinch analysis, stochastic evolution and pinch graph could be integrated with input-output (I-O) modelling. Integrated stochastic evolution with an I-O model allows capturing the likelihood of the events;it includes probability distributions instead of point estimates for scenario parameter

关键词： Input-output modelling interval programming Port logistics Transportation and storage sector Economic loss Inoperability Logistics Risk analysis Management Modelling

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Exploring the trade-off between liquidity, risk and return under sectoral diversification across distinct economic settings

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JOURNAL OF RISK FINANCE 2021年第2期22卷 130-152页

作者： Henriques, Carla Neves, Elisabete ISCAC Coimbra Business Sch Res Ctr Polytech Inst Coimbra Coimbra Portugal INESC Coimbra Coimbra Portugal UTAD CETRAD Vila Real Portugal

Purpose This paper aims to explore the trade-off between liquidity, risk and return under sectoral diversification across distinct economic settings and investment strategies. Design/methodology/approach A novel multi-objective portfolio model is proposed to assess investment decisions under sectoral diversification, where the objective functions and constraints are interval-valued. The objective functions used are risk minimization (through the semi-absolute deviation measure of risk), maximization of liquidity (using turnover as a proxy) and the maximization of logarithmic return. Besides coherence constraints (imposing that the sum of the percentages of investment assigned to each stock should be equal to 100%), constraints regarding the maximum proportion of capital that can be invested (ensuring a minimum level of diversification) and cardinality constraints (to account for transaction costs) are also imposed. Findings Besides the trade-off between return and risk, the study findings highlight a trade-off between liquidity and return and a positive relationship between risk and liquidity. Under an economic crisis scenario, the trade-off between return and liquidity is reduced. With the economic recovery, the levels of risk increase when contrasted with the setting of the economic crisis. The highest liquidity levels are reached with the economic boom, whereas the highest returns are obtained with the economic recession. Originality/value This paper suggests a new modeling approach for assessing the trade-offs between liquidity, risk and return under different scenarios and investment strategies. A new interactive procedure inspired on the reference point approach is also proposed to obtain possibly efficient portfolios according to the investor's preferences. Regarding previous approaches suggested in the literature, this new procedure allows obtaining both supported and unsupported efficient solutions when cardinality constraints are included.

关键词： Multi-objective portfolio models interval programming Sectoral diversification Trade-off between liquidity Risk and return Euronext FTSE 100 C61 G11

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A multi-objective input-output model to assess E4 impacts of building retrofitting measures to improve energy efficiency

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TECHNOLOGICAL AND ECONOMIC DEVELOPMENT OF ECONOMY 2015年第3期21卷 483-494页

作者： Henriques, Carla Oliveira Coelho, Dulce Helena Antunes, Carlos Henggeler Polytech Inst Coimbra ISCAC Quinta Agr P-3040316 Coimbra Portugal Polytech Inst Coimbra ISEC P-3030199 Coimbra Portugal Univ Coimbra DEEC P-3030290 Coimbra Portugal INESC Coimbra P-3030030 Coimbra Portugal

This paper develops a bottom-up approach in the scope of a multi-objective linear programming model (MOLP) based on Input-Output (I-O) analysis to account for investment options aimed at improving the thermal properties of building envelope (e.g., the insulation of external walls and roof, and the replacement of window frames and window glazing). This methodological framework aims at assessing the trade-offs between the overall employment, GDP and energy savings associated with the building sector (residential, private services and public services). Distinct impacts, namely on direct and indirect employment generation, environment (CO2 emissions), energy security supply (energy imports and renewable energy production) and other relevant economic indicators are also analysed. Different sets of input parameters for the economic context and the environmental impacts have been defined as interval coefficients to account for uncertainty. Robust solutions are then obtained by considering the minimisation of the worst possible deviation of the interval objective functions to the corresponding interval ideal solutions.

关键词： energy efficiency retrofitting measures I-O analysis economy-energy-environment-employment (E4) interactions MOLP interval programming building stock

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Inexact Fuzzy Full-Infinite Mixed-Integer programming Method for an Integrated Air and Waste Management System

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JOURNAL OF URBAN PLANNING AND DEVELOPMENT-ASCE 2011年第4期137卷 370-380页

作者： Su, Jing Xi, Beidou Yao, Bo Huang, Guohe Lu, H. W. He, Li Ji, Danfeng Chinese Res Inst Environm Sci Beijing 100012 Peoples R China Beijing Normal Univ Sch Environm Beijing 100875 Peoples R China Univ Regina Ctr Studies Energy & Environm Regina SK S4S 0A2 Canada

Inexact fuzzy full-infinite mixed-integer programming (IFFMIP) was proposed as an extension of inexact full-infinite programming. It can deal with the uncertainties that exist in most of the parameters as intervals, economic data as functional intervals, fuzzy set in capacity constraint, and discrete variables in a facility-expansion plan. Although many models for dealing with waste planning and the air quality management problem exist, this is the first attempt to integrate waste flow allocation and an air quality control system. The proposed model was applied in an integrated air and waste management system. It can solve the waste allocation plan and air quality control, and reflect the interaction between these two systems. The solutions from the proposed IFFMIP model indicate that a landfill would be the first choice in period 1, whereas an incinerator would become the main approach for waste disposal at the end of the planning horizon. This is because of the increasingly strict environmental standards and loading capacity of SO(2) for industries, upon which waste planning prefers less operation costs for waste disposal. The solutions reflected the tradeoff between the environment and system cost. To control air quality at a safe level, the system must be willing to pay more operating costs;however, a desire to reduce the costs will run into the risk of potentially violating the emissions and/or ambient air quality standards. DOI: 10.1061/(ASCE)UP.1943-5444.0000088. (C) 2011 American Society of Civil Engineers.

关键词： Full-infinite programming Regional waste management Air quality control interval programming Fuzzy flexible

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An inexact fractional multi-stage programming (IFMSP) method for planning renewable electric power system

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RENEWABLE & SUSTAINABLE ENERGY REVIEWS 2023年第1期187卷

作者： Lin, Xiajing Huang, Guohe Zhou, Xiong Zhai, Yuanyuan Univ Regina Fac Engn & Appl Sci Regina SK S4S 0A2 Canada Beijing Normal Univ Sch Environm China Canada Ctr Energy Environm & Ecol Res UR BNUState Key Joint Lab Environm Simulat & Poll Beijing 100875 Peoples R China

The growing levels of greenhouse gas (GHG) emissions have made renewable energy sources a crucial aspect of power generation, especially in developing countries. However, with more investment in additional renewable energy components and the mandatory decommissioning requirement of the thermal stations, the uncertainty of renewable energy availability and the changeable policy environment have brought great complexity to the electric power systems. Hence, an innovative approach, the inexact fractional multistage programming (IFMSP), has been proposed to address the challenges of electric power system planning in transitioning to clean energy, specifically in South Africa from 2021 to 2050. The IFMSP approach balances economic benefits and GHG emission mitigation, providing a more constrained optimum interval solution than binary integer programming. The results illustrated a decline in the expansion of conventional energy sources, with natural gas, wind energy and solar energy taking the place of thermal power generation. In terms of performance, solar power ranks second to wind. By assessing various expansion scenarios, it is demonstrated that zero nuclear energy growth would yield more competitive economic advantages and fewer GHG emissions than no geothermal expansion, whereas a 20% increase in gas expansion capacity would achieve the most optimal ratio at [304.2, 317.3] (Rand/ t CO2 eq). By utilizing the proposed approach, decision-makers in developing countries can generate multiple expansion scenarios for Belt and Road Initiative (BRI) investments. This enables them to identify generation modes, capacity expansion schemes, financial planning, and carbon tax regulations, even under complex uncertainties.

关键词： Developing country interval programming Linear fractional programming Stochastic multi-stage programming Non-coal-fired technology Greenhouse gas (GHG) emissions

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Sparrow search algorithm with adaptive t distribution for multi-objective low-carbon multimodal transportation planning problem with fuzzy demand and fuzzy time

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EXPERT SYSTEMS WITH APPLICATIONS 2024年第PartD期238卷

作者： Zhang, Huizhen Huang, Qin Ma, Liang Zhang, Ziying Univ Shanghai Sci & Technol Sch Management Mail Box 459516 Jungong Rd Shanghai 200093 Peoples R China Shanghai Univ Engn Sci Sch Mat Engn 333 Longteng Rd Shanghai 201620 Peoples R China

In this paper, we present a multi-objective low-carbon multimodal transportation planning problem with fuzzy demand and fuzzy time (MOLCMTPP-FDFT) that minimizes both cost and time while incorporating mandatory carbon emission, carbon tax, carbon trading, and carbon offset policies. Chance constrained programming and interval programming are introduced to formulate the fuzzy demand chance constrained programming model and the fuzzy time interval programming model, respectively. Then, the mathematical model of uncertain MOLCMTPP-FDFT is transformed into a deterministic model. Based on the sparrow search algorithm, t distribution and the concept of Pareto optimality for multi-objective optimization, we also propose a solution strategy for the proposed model. In this algorithm, the number of iterations is used as the degree of freedom of -to update the sparrow location, which strikes a balance between the capabilities of global search and local search. Finally, the proposed algorithm and MOLCMTPP-FDFT are applied to a real case, resulting in a minimum cost of 260730.48 and a time duration of 13.044, which outperform the minimum cost of 268874.88 and minimum time of 18.32 obtained using single-mode transportation. The carbon emissions resulting from the lowest-cost solution obtained using single-mode transportation are 3,198.48, which are significantly more than the allowed emissions. Therefore, the proposed algorithm and mathematical model of MOLCMTPP-FDFT are valuable tools for optimizing multimodal transportation route. Additionally, the experimental results not only validate the superior efficiency and energy-saving benefits of the proposed multimodal transportation routes in comparison to the actual single-modal transportation, but also demonstrate the applicability of different low-carbon policies.

关键词： Low-carbon multimodal transportation Sparrow search algorithm Adaptive t distribution Chance constrained programming interval programming

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Allocation of products to a heterogeneous fleet of trucks in a cross-docking center based on carbon emissions and costs in food and beverage industry: Novel uncertain solution approaches

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JOURNAL OF ENVIRONMENTAL MANAGEMENT 2023年第1期332卷 117071页

作者： Rajabzadeh, Mohsen Mousavi, Seyed Meysam Shahed Univ Dept Ind Engn Tehran Iran

The threat of climate change continues to grow, which calls for strategies to reduce emissions. Carbon emissions from transportation are among the highest in the world, so it is essential to improve its efficiency. Cross-docking is a smart way to improve the efficiency of transportation operations through the optimal use of truck capacity. This paper develops a novel bi-objective mixed integer linear programming (MILP) model to determine which products should be shipped together, select the most appropriate truck among the available ones, and schedule them. It reveals a new class of cross-dock truck scheduling problems, in which products are not interchangeable and are sent to different destinations. The first objective is to minimize overall system costs, while the second is to minimize total carbon emissions. To deal with uncertainties in factors, such as costs, time, and emission rate, these parameters are considered interval numbers. Furthermore, innovative uncertain approaches are introduced under interval uncertainty based on optimistic and pessimistic Pareto solutions for solving MILP problems via epsilon-constraint and weighting methods. The proposed model and solution procedures are used for planning an operational day at a regional distribution center (RDC) of a real food and beverage company, and results are compared. The results show that the proposed epsilon-constraint method outperforms the other implemented methods in terms of quantity and variety of optimistic and pessimistic Pareto solutions. Using the newly developed procedure, the amount of carbon produced by trucks could decrease by 18% under optimistic assumptions and 44% under pessimistic assumptions. As a result of the proposed solution approaches, managers can observe how their optimism level and the importance of objective functions influence their decisions.

关键词： Cross -docking Carbon emissions Multi -objective mixed integer programming interval programming Epsilon -constraint method Weighting method Food and beverage industry

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