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Bi-Objective Mixed Integer Nonlinear Programming Model for Low Carbon Location-Inventory-Routing Problem with Time Windows and Customer Satisfaction
by
Lihua Liu
Lihua Liu
Lihua LIU is a lecturer in the School of Science at Guangxi University of Science and Technology. is [...]
Lihua LIU is a lecturer in the School of Science at Guangxi University of Science and Technology. She is now studying for her PhD in Applied Mathematics at Universiti Putra Malaysia. She received her master's
degree in applied mathematics from Guilin University of Electronic Technology. Her main research interests are operations research and optimization. She has published several papers in peer-reviewed journals and conferences.
1,2,
Aneng He
Aneng He
Aneng He is a graduate student in Mathematical Sciences at Universiti Putra Malaysia (UPM). His is [...]
Aneng He is a graduate student in Mathematical Sciences at Universiti Putra Malaysia (UPM). His research is dedicated to using mathematics to solve problems related to the social sciences. His areas of
interest are operations research, the application of operations research in education and comprehensive sexuality education.
1,
Tian Tian
Tian Tian
Tian Tian, currently a PhD student at the Institute for Mathematical Research, Universiti Putra her [...]
Tian Tian, currently a PhD student at the Institute for Mathematical Research, Universiti Putra Malaysia (UPM), dedicates her research to harnessing mathematical frameworks to tackle complex challenges across various applications. Her academic interests center on operations research, with a specific focus on its implementation in revenue management and supply chain management. Tian's work aspires to bridge the divide between theoretical mathematics and practical solutions, fostering innovation in these vital fields.
3,
Lai Soon Lee
Lai Soon Lee
Lai Soon Lee is a Professor of Operations Research in the Department of Mathematics and Statistics 5 [...]
Lai Soon Lee is a Professor of Operations Research in the Department of Mathematics and Statistics in the Faculty of Science, Universiti Putra Malaysia. He is also the President of the Management Science/Operations Research Society of Malaysia. His recent research concentrates on heuristics and metaheuristics for transportation, humanitarian logistics, supply chain management, credit scoring, and revenue management. He has copyrighted 5 intellectual properties and published over 125 publications. He is also the project leader for 14 research grants. Currently, Prof. Lee is the editor/guest editor of more than 10 international journals. He is also serving as a reviewer for more than 100 national and international journals.
1,3,* and
Hsin-Vonn Seow
Hsin-Vonn Seow
Hsin-Vonn Seow is a Professor of Operations Research and is currently the Associate Dean of Exchange [...]
Hsin-Vonn Seow is a Professor of Operations Research and is currently the Associate Dean of Research
and Knowledge Exchange for the Faculty of Arts and Social Sciences at the University of Nottingham Malaysia. She received her doctorate from the University of Southampton, UK in 2006. Her current research interests include looking at applications of operations research in the many areas of management and multi-disciplinary research. Prof. Seow was part of the international team of researchers (Germany, Belgium, and the UK) that won the Best Paper (Theory and Methodology) in the European Journal of Operational Research (EJORS) in 2017. This prestigious award was presented by the Association of European Operational Research Societies.
4
1
Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia
2
Faculty of Science, Guangxi University of Technology and Science, Liuzhou 545000, China
3
Laboratory of Computational Statistics and Operations Research, Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia
4
Faculty of Arts and Social Sciences, Nottingham University Business School, University of Nottingham Malaysia, Semenyih 43500, Selangor, Malaysia
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(15), 2367; https://doi.org/10.3390/math12152367 (registering DOI)
Submission received: 20 June 2024
/
Revised: 23 July 2024
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Accepted: 27 July 2024
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Published: 29 July 2024
Abstract
In order to support a low-carbon economy and manage market competition, location–inventory–routing logistics management must play a crucial role to minimize carbon emissions while maximizing customer satisfaction. This paper proposes a bi-objective mixed-integer nonlinear programming model with time window constraints that satisfies the normal distribution of stochastic customer demand. The proposed model aims to find Pareto optimal solutions for total cost minimization and customer satisfaction maximization. An improved non-dominated sorting genetic algorithm II (IMNSGA-II) with an elite strategy is developed to solve the model. The model considers cost factors, ensuring that out-of-stock inventory is not allowed. Factors such as a carbon trading mechanism and random variables to address customer needs are also included. An entropy weight method is used to derive the total cost, which is comprised of fixed costs, transportation costs, inventory costs, punishment costs, and the weight of carbon emissions costs. The IMNSGA-II produces the Pareto optimal solution set, and an entropy–TOPSIS method is used to generate an objective ranking of the solution set for decision-makers. Additionally, a sensitivity analysis is performed to evaluate the influence of carbon pricing on carbon emissions and customer satisfaction.
Share and Cite
MDPI and ACS Style
Liu, L.; He, A.; Tian, T.; Lee, L.S.; Seow, H.-V.
Bi-Objective Mixed Integer Nonlinear Programming Model for Low Carbon Location-Inventory-Routing Problem with Time Windows and Customer Satisfaction. Mathematics 2024, 12, 2367.
https://doi.org/10.3390/math12152367
AMA Style
Liu L, He A, Tian T, Lee LS, Seow H-V.
Bi-Objective Mixed Integer Nonlinear Programming Model for Low Carbon Location-Inventory-Routing Problem with Time Windows and Customer Satisfaction. Mathematics. 2024; 12(15):2367.
https://doi.org/10.3390/math12152367
Chicago/Turabian Style
Liu, Lihua, Aneng He, Tian Tian, Lai Soon Lee, and Hsin-Vonn Seow.
2024. "Bi-Objective Mixed Integer Nonlinear Programming Model for Low Carbon Location-Inventory-Routing Problem with Time Windows and Customer Satisfaction" Mathematics 12, no. 15: 2367.
https://doi.org/10.3390/math12152367
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