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A mix integer programming model and solution approach to determine the optimum machine number in the unrelated parallel machine scheduling problem

JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GA...

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JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GAZI UNIVERSITY 2022年第1期37卷 329-345页

作者： Sarac, Tugba Tutumlu, Busra Eskisehir Osmangazi Univ Ind Engn Dept TR-26480 Eskisehir Turkey Kutahya Dumlupinar Univ Ind Engn Dept TR-43100 Kutahya Turkey

It is assumed that all machines will be used in studies dealing with parallel machine scheduling problems. However, for some businesses having special processes, where large furnaces with very intense energy consumption are used during commissioning, it can be very critical to complete jobs using the least number of furnaces. In addition, for many businesses, doing their jobs with fewer machines creates opportunities for unused machines to be rented to another company or to accept additional jobs as much as the capacity of idle machines. For this reason, in this study, the assumption that all machines will be used has been removed and a mathematical model has been proposed that will decide both which machines will be used and which jobs will be produced in which order on these machines, for the unrelated parallel machine scheduling problem with sequence and machine dependent setup times and machine eligibility restriction. The objectives of the considered problem are minimizing the number of machines to be used and the completion time of the last job. The objective functions of the proposed multi-objective mathematical model are scalarized using the weighted sum method. In order to show the solution performance of the mathematical model, randomly generated test problems were solved with GAMS / CPLEX. To solve the large problems, a local search algorithm and a genetic algorithm have been proposed due to the lack of feasible solutions with GAMS / CPLEX. In the large-scale problem, when all weight pairs are taken into account, genetic algorithm is more successful than local search algorithm an average of 25.64% in terms of solution quality and 50.31% in terms of time.

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Synergistic CO₂ and Air Pollution Reduction Based on multi-objective programming

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2nd International Conference on Energy, Environment and Sustainable Development (EESD 2012)

作者： Chang, Wentao Wen, Juan Bao, Jingling Li, Ran Tianjin Acad Environm Planning Tianjin Peoples R China Hebei Univ Technol Tianjin Peoples R China Nankai Univ Tianjin Peoples R China Tianjin Environm Protect Bur Tianjin Peoples R China

ISBN: (纸本)9783037855522

With increasing frequency of hazards caused by global climate change, the importance of regulating carbon dioxide emission and coping with climate change has been recognized by the entire society. This paper utilized an Energy Flow Diagram to incorporate the energy supplies, conversion and final consumption for analyses. A multi-objective programming model was established to reduce the economic investment on the reduction of air pollution and carbon emission, and applied in a case study of Tianjin, one of the economic hubs of North China. This study can be potentially useful for making decisions on the synergistic CO2 and air pollution reduction and solving conflicts between economic development and environmental protection in China.

关键词： multi-objective programming Air Pollutants CO2 Synergistic Carbon Emission Reduction

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On solving multi-objective fully quadratic fractional optimisation model with interactive FGP approach

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INTERNATIONAL JOURNAL OF QUALITY & RELIABILITY MANAGEMENT 2022年第10期39卷 2286-2301页

作者： Rani, Namrata Goyal, Vandana Gupta, Deepak Maharishi Markandeshwar Deemed Univ Dept Math Ambala India

Purpose - The main motive behind framing this paper is to provide a compromised solution for trapezoidal fuzzy number-multi-objective fully quadratic fractional optimisation model (TrFN-MOFQFOM) by avoiding ambiguities and confusion of decision-makers (DMs). Many researchers have used Taylor's series and parametric approach to transform fractional objective function into non-fractional ones, but Taylor's series expansion is valid only up to a neighbourhood. To avoid these extra efforts, this article suggests a methodology in which numerator of objective function is optimised under the condition of optimising denominator. Design/methodology/approach - This paper suggests an efficient procedure to search for compromised solution of MOFQFOM with fuzzy coefficients using alpha-level set and FGP approach. Incomplete data in model is dealt with alpha-level set. Then after defuzzification, non-fractional models are built from fractional model to get optimal solution of every objective. Finally, the linear weighted sum of negative deviational variables is minimised to satisfy all objective functions up to maximum possible extent. Findings - On applying suggested approach to the example given in end, the authors arrived at compromised solution having mu(O1) (O-1(x)) =1 and mu(O2) (O-2(x)) = 0.71. The applied procedure requires less computational efforts and provides the preferred compromised solution. Originality/value - This work has not been done previously by anyone. The idea being developed here of constructing non-fractional model by dealing numerators and denominators separately is completely new. 10;In the end, an algorithm, flowchart and numerical are also given to clarify the applicability of the suggested approach.

关键词： alpha-Cut method Non-fractional models multi-objective programming Trapezoidal fuzzy number (TrFN) Fuzzy goal programming (FGP)

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Towards multi-objective Optimization of Sustainable Insect Production Chains 22

Towards Multi-Objective Optimization of Sustainable Insect P...

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Genetic and Evolutionary Computation Conference (GECCO)

作者： Mouhrim, Nisrine Smetana, Sergiy Bhatia, Anita Mathys, Alexander Green, Ashley Peguero, Daniela Tonda, Alberto INRAE MIA Paris UMR 518 Paris France German Inst Food Technol Quakenbruck Quakenbruck Germany Swiss Fed Inst Technol Sustainable Food Proc Lab Zurich Switzerland

ISBN: (纸本)9781450392686

Due to the relatively recent history of industrial insect farming, there are still no extensive studies on the optimization of insect production chains. In this context, the present work aims to be a first step in filling this gap. A tentative set of mathematical models is proposed to take into account three different, conflicting objectives: maximizing economic viability, minimizing environmental impacts, and maximizing societal benefits. The state-of-the-art multi-objective algorithm NSGA-II is used to obtain an approximate Pareto fronts of solutions, that are later analyzed to identify suitable trade-offs. While preliminary, the results are encouraging enough for the computer-assisted design and development of sustainable insect production chains. Future works will take into account more extensive models, able to simulate scenarios in different European countries, and include parts of the chain such as transportation of goods to and from the production facilities.

关键词： life cycle assessment sustainability insects decision making genetic algorithm multi-objective programming NSGA-II

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Portfolio optimization using higher moments in an uncertain random environment

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INFORMATION SCIENCES 2021年 567卷 348-374页

作者： Mehlawat, Mukesh Kumar Gupta, Pankaj Khan, Ahmad Zaman Univ Delhi Dept Operat Res Delhi 110007 India

In this paper, a multi-objective portfolio optimization problem is studied in an uncertain random environment using higher moments. We consider a scenario involving an asset universe wherein some assets have sufficient historical return data for modelling as random variables, and others, listed relatively recently, lack historical data. The asset returns of such assets are modelled as uncertain variables. Thus, a hybrid environment involving both uncertain and random variables is considered. We use mean absolute semi deviation as a risk measure and employ skewness (i.e., third moment) in the portfolio optimization model. The expressions for the mean absolute semi-deviation and skewness of an uncertain random variable have been derived. We show that the derivation of mean absolute semi-deviation is not based on any stipulation and thus is an accurate measure of risk (unlike the variance of an uncertain random variable, which uses stipulation). We propose a hybrid genetic algorithm as a solution methodology and provide empirical proofs to illustrate its advantages. The proposed methodology has been applied to a case study involving 100 assets listed in the NASDAQ-100 index of the U.S. stock market. We do an ex-post analysis to track the performance of our model out-of-sample and illustrate its advantages. (c) 2021 Elsevier Inc. All rights reserved.

关键词： Uncertain random variable Chance distribution multi-objective programming Uncertain measure Portfolio optimization Real-coded genetic algorithm

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ORDER ALLOCATION MODEL IN LOGISTICS SERVICE SUPPLY CHAIN WITH DEMAND UPDATING AND INEQUITY AVERSION: A PERSPECTIVE OF TWO OPTION CONTRACTS COMPARISON

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2021年第6期17卷 3269-3295页

作者： Liu, Weihua Shen, Xinran Wang, Di Wang, Jingkun Tianjin Univ Coll Management & Econ 92 Weijin Rd Tianjin 300072 Peoples R China

This paper considers an logistics service supply chain consisting of a logistics service integrator (LSI) and a number of functional logistics ser-vice providers (FLSPs). In the environment of demand updating, we focus on the inequity aversion among the FLSPs and introduce two option contracts (the reservation option contract and the option guarantee contract), build the multi-objective programming models, to explore effects of the inequity aver-sion behavior on the order allocation, and whether the two option contracts can mitigate the impact of inequity aversion on order allocation. Three im-portant conclusions are obtained after two option contracts comparisons: first, there is an optimal update time, at which point, the order allocation results reach the optimal value and tend to be stable. Second, two option contracts both can not only increase the total performance of the supply chain, but also mitigate the impact of inequity aversion on the allocation under certain condi-tions. Third, when demand decreases, the reservation option contract is better than option guarantee contract, in contrast, when demand increases, option guarantee contract is better.

关键词： Order allocation model demand updating option contract inequity aversion multi-objective programming

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multi-objective infinite horizon optimal control problems: characterization of the Pareto fronts and Pareto solutions

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COMPUTATIONAL & APPLIED MATHEMATICS 2021年第8期40卷 1-24页

作者： Chorobura, Ana Paula Univ Fed Parana Postgrad Program Math CP 19081 BR-81531980 Curitiba Parana Brazil

In this paper, multi-objective infinite horizon optimal control problems with state constraints are investigated. First, a mono-objective auxiliary optimal control problem, free of state constraints, is introduced. The weak Pareto front of the multi-objective optimal problem is related to a set contained in the boundary of the zero level set of the value function of the auxiliary control problem. Moreover, a more detailed characterization of the Pareto front for the multi-objective problem is presented. In the infinite horizon context, the value function of the auxiliary optimal control problem satisfies a Hamilton-Jacobi-Bellman equation;however, it is not the unique solution. A semi-Lagrangian scheme, based on the Dynamic programming Principle, is considered to compute the value function of the auxiliary optimal control problem. Furthermore, optimal Pareto trajectory reconstruction is analyzed.

关键词： multi-objective programming Infinite horizon optimal control problem Trajectory reconstruction Semi-Lagrangian scheme

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Toward a robust optimal point selection: a multiple-criteria decision-making process applied to multi-objective optimization using response surface methodology

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ENGINEERING WITH COMPUTERS 2021年第4期37卷 2735-2761页

作者： Souza Rocha, Luiz Cello Rotela Junior, Paulo Aquila, Giancarlo de Paiva, Anderson Paulo Balestrassi, Pedro Paulo Fed Inst Educ Sci & Technol North Minas Gerais Management Dept Almenara MG Brazil Univ Fed Paraiba Prod Engn Dept Cidade Univ S-N BR-58051900 Joao Pessoa Paraiba Brazil Univ Fed Itajuba Inst Prod Engn & Management Itajuba MG Brazil

During the multi-objective optimization process, numerous efficient solutions may be generated to form the Pareto frontier. Due to the complexity of formulating and solving mathematical problems, choosing the best point to be implemented becomes a non-trivial task. Thus, this paper introduces a weighting strategy named robust optimal point selection, based on ratio diversification/error, to choose the most preferred Pareto optimal point in multi-objective optimization problems using response surface methodology. Furthermore, this paper proposes to explore a theoretical gap-the prediction variance behavior related to the weighting. The ratios Shannon's entropy/error and diversity/error and the unscaled prediction variance are experimentally modeled using mixture design and the optimal weights for the multi-objective optimization process are defined by the maximization of the proposed measures. The study could demonstrate that the weights used in the multi-objective optimization process influence the prediction variance. Furthermore, the use of diversification measures, such as entropy and diversity, associated with measures of error, such as mean absolute percent error, was determined to be useful in mapping regions of minimum variance within the Pareto optimal responses obtained in the optimization process.

关键词： multi-objective programming multi-criteria analysis Robust optimal point selection (ROPS) Diversification measures Error measures

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A TWO-STAGE SOLUTION APPROACH FOR PLASTIC INJECTION MACHINES SCHEDULING PROBLEM

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2021年第3期17卷 1289-1314页

作者： Sarac, Tugba Sipahioglu, Aydin Ozer, Emine Akyol Eskisehir Osmangazi Univ Dept Ind Engn Meselik Campus TR-26040 Eskisehir Turkey Eskisehir Tech Univ Dept Ind Engn Iki Eylul Campus TR-26555 Eskisehir Turkey

One of the most common plastic manufacturing methods is injection molding. In injection molding process, scheduling of plastic injection machines is very difficult because of the complex nature of the problem. For example, similar plastic parts should be produced sequentially to prevent long setup times. On the other hand, to produce a plastic part, its mold should be fixed on an injection machine. Machine eligibility restrictions should be considered because a mold can be usually fixed on a subset of the injection machines. Some plastic parts which have same shapes but different colors are used same mold so these parts can only be scheduled simultaneously if their mold has copies, otherwise resource constraints should be considered. In this study, a multi-objective mathematical model is proposed for parallel machine scheduling problem to minimize makespan, total tardiness, and total waiting time. Since NP-hard nature of problem, this paper presents a two-stage mathematical model and a two-stage solution approach. In the first stage of mathematical model, jobs are assigned to the machines and each machine is scheduled separately in the second stage. The integrated model and two-stage mathematical model are scalarized by using goal programming, compromise programming and Lexicographic Weighted Tchebycheff programming methods. To solve large-scale problems in a short time, a two-stage solution approach is also proposed. In the first stage of this approach, jobs are assigned to machines and scheduled by using proposed simulated annealing algorithm. In the second stage of the approach, starting time, completion time and waiting time of the jobs are calculated by using a mathematical model. The performance of the methods is demonstrated on randomly generated test problems.

关键词： Plastic injection identical parallel machine scheduling multi-objective programming integer programming

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An Overview of the Cash Transportation Problem

An Overview of the Cash Transportation Problem

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International Conference on Decision Aid Sciences and Applications (DASA)

作者： Alaya, Houda Univ Tunis Tunis Business Sch Business Analyt & Decis Making Lab Tunis Tunisia IHE Paris Logist & Innovat Technol Res Ctr Paris France

ISBN: (纸本)9781665495011

One of the relatively new study topics in Vehicle Routing is the Cash Transportation Problem. This problem takes into consideration the security in planning vehicle routes. Few papers have focused on the cash transportation problem. Minimizing the travel cost and/or minimizing the transportation risk are the objective functions considered in these problems. This paper is the first overview of the cash transportation problem addressed in the literature. We classify these problems into two categories, mono-objective and multi-objective problems.

关键词： Vehicle Routing Problem multi-objective programming Cash transportation Cash-in-Transit

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