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Operational Research Tools for Solving Sustainable Engineering Problems
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Operational Research Tools for Solving Sustainable Engineering Problems

A special issue of Sustainability (ISSN 2071-1050).

Deadline for manuscript submissions: closed (30 June 2021) | Viewed by 85065

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

Dr. Dragan Pamucar

grade E-Mail Website
Guest Editor
Department of logistics, University of Defence, Belgrade, Pavla Jurišića Šturma 33, 11000 Belgrade, Serbia
Interests: multi-criteria decision making problems; computational intelligence; sustainability neuro-fuzzy systems; fuzzy; rough and intuitionistic fuzzy set theory; neutrosophic theory
Special Issues, Collections and Topics in MDPI journals
Dr. Željko Stević

E-Mail Website
Guest Editor
Faculty of Transport and Traffic Engineering, University of East Sarajevo, Doboj, Bosnia and Herzegovina
Interests: logistics; transport; supply chain; multi-criteria decision making; sustainable engineering; fuzzy set; rough set
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The need for operations research (OR) tools and techniques is manifested in its ability to balance conflicting objectives (goals or interests) where there are many alternative courses of action available to the decision-makers when resources, time, and funds are limited. Therefore, beyond the domain of theoretical knowledge and model building activities, OR is having all pervasive applications in decision making about the problems in sustainable engineering, sustainable society, and business. OR tools and techniques find applications in all aspects of sustainability operations, like sustainable supply chain planning, sustainable distribution, sustainable traffic flow optimization, industrial waste reduction, energy conservation, sustainable city planning, etc. Over the years, applications of OR have been extended to solve the problems of communication of information and socio-economic fields. In this context, the academic community needs to take the lead in the design, development, and demonstration of sustainable operational research models, endowed and supported by organizations.

Engineering is the application of scientific principles for practical objectives such as the processes, manufacture, design, and operation of products, while accounting for constraints invoked by sustainable factors. There are various factors that need to be considered in order to address engineering sustainability, which is critical for the overall sustainability of human development and activity.

This Special Issue seeks high-quality papers that develop OR optimization models in the field of sustainable engineering. Submitted papers should not have been previously published or be currently under consideration for publication elsewhere.

We invite authors to submit an original research article that proposes novel OR optimization models for sustainable engineering.

Dr. Dragan Pamučar
Dr. Željko Stević
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Sustainability is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Environmental sustainability in engineering processes
  • Uncertainty and mathematical programming for sustainable engineering
  • Hybrid decision analysis for sustainable engineering
  • OR tools in sustainable logistics scheduling
  • Multi-criteria decision making (MCDM) optimization in sustainable engineering
  • Network optimization
  • Risk analysis/modeling for sustainable engineering
  • Innovative applications of OR tools

Published Papers (25 papers)

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Research

20 pages, 7394 KiB  
Article
Predicting the Degree of Dissolved Oxygen Using Three Types of Multi-Layer Perceptron-Based Artificial Neural Networks
by Fen Yang, Hossein Moayedi and Amir Mosavi
Sustainability 2021, 13(17), 9898; https://doi.org/10.3390/su13179898 - 03 Sep 2021
Cited by 37 | Viewed by 3109
Abstract
Predicting the level of dissolved oxygen (DO) is an important issue ensuring the sustainability of the inhabitants of a river. A prediction model can predict the DO level using a historical dataset with regard to water temperature, pH, and specific conductance for a [...] Read more.
Predicting the level of dissolved oxygen (DO) is an important issue ensuring the sustainability of the inhabitants of a river. A prediction model can predict the DO level using a historical dataset with regard to water temperature, pH, and specific conductance for a given river. The model can be built using sophisticated computational procedures such as multi-layer perceptron-based artificial neural networks. Different types of networks can be constructed for this purpose. In this study, the authors constructed three networks, namely, multi-verse optimizer (MVO), black hole algorithm (BHA), and shuffled complex evolution (SCE). The networks were trained using the datasets collected from the Klamath River Station, Oregon, USA, for the period 2015–2018. We found that the trained networks could predict the DO level of 2019. We also found that both BHA- and SCE-based networks could predict the level of DO using a relatively simple configuration compared to that of MVO. From the viewpoints of absolute errors and Pearson’s correlation coefficient, MVO- and SCE-based networks performed better than BHA-based networks. In synopsis, the authors recommend MVO- and MLP-based artificial neural networks for predicting the DO level of a river. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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23 pages, 21825 KiB  
Article
Extended Maximal Covering Location and Vehicle Routing Problems in Designing Smartphone Waste Collection Channels: A Case Study of Yogyakarta Province, Indonesia
by Diana Puspita Sari, Nur Aini Masruroh and Anna Maria Sri Asih
Sustainability 2021, 13(16), 8896; https://doi.org/10.3390/su13168896 - 09 Aug 2021
Cited by 8 | Viewed by 2306
Abstract
Most people will store smartphone waste or give it to others; this is due to inadequate waste collection facilities in all cities/regencies in Indonesia. In Yogyakarta Province, there is no electronic waste collection facility. Therefore, an e-waste collection network is needed to cover [...] Read more.
Most people will store smartphone waste or give it to others; this is due to inadequate waste collection facilities in all cities/regencies in Indonesia. In Yogyakarta Province, there is no electronic waste collection facility. Therefore, an e-waste collection network is needed to cover all potential e-waste in the province of Yogyakarta. This study aims to design a collection network to provide easy access to facilities for smartphone users, which includes the number and location of each collection center and the route of transporting smartphone waste to the final disposal site. We proposed an extended maximal covering location problem to determine the number and location of collection centers. Nearest neighbor and tabu search are used in forming transportation routes. The nearest neighbor is used for initial solution search, and tabu search is used for final solution search. The study results indicate that to facilitate all potential smartphone waste with a maximum distance of 11.2 km, the number of collection centers that must be established is 30 units with three pick-up routes. This research is the starting point of the smartphone waste management process, with further study needed for sorting, recycling, repairing, or remanufacturing after the waste has been collected. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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27 pages, 3260 KiB  
Article
SmartISM: Implementation and Assessment of Interpretive Structural Modeling
by Naim Ahmad and Ayman Qahmash
Sustainability 2021, 13(16), 8801; https://doi.org/10.3390/su13168801 - 06 Aug 2021
Cited by 37 | Viewed by 7665
Abstract
Interpretive Structural Modeling (ISM) is a technique to establish the interrelationships between elements of interest in a specific domain through experts’ knowledge of the context of the elements. This technique has been applied in numerous domains and the list continues to grow due [...] Read more.
Interpretive Structural Modeling (ISM) is a technique to establish the interrelationships between elements of interest in a specific domain through experts’ knowledge of the context of the elements. This technique has been applied in numerous domains and the list continues to grow due to its simplistic concept, while sustainability has taken the lead. The partially automated or manual application of this technique has been prone to errors as witnessed in the literature due to a series of mathematical steps of higher-order computing complexity. Therefore, this work proposes to develop an end-to-end graphical software, SmartISM, to implement ISM technique and MICMAC (Matrice d’Impacts Croisés Multiplication Appliquée á un Classement (cross-impact matrix multiplication applied to classification)), generally applied along with ISM to classify variables. Further, a scoping review has been conducted to study the applications of ISM in the previous studies using Denyer and Tranfield’s (2009) framework and newly developed SmartISM. For the development of SmartISM, Microsoft Excel software has been used, and relevant algorithms and VBA (Visual Basic for Applications) functions have been illustrated. For the transitivity calculation the Warshall algorithm has been used and a new algorithm reduced conical matrix has been introduced to remove edges while retaining the reachability of variables and structure of digraph in the final model. The scoping review results demonstrate 21 different domains such as sustainability, supply chain and logistics, information technology, energy, human resource, marketing, and operations among others; numerous types of constructs such as enablers, barriers, critical success factors, strategies, practices, among others, and their numbers varied from 5 to 32; number of decision makers ranged between 2 to 120 with a median value of 11, and belong to academia, industry, and/or government; and usage of multiple techniques of discourse and survey for decision making and data collection. Furthermore, the SmartISM reproduced results show that only 29 out of 77 studies selected have a correct application of ISM after discounting the generalized transitivity incorporation. The outcome of this work will help in more informed applications of this technique in newer domains and utilization of SmartISM to efficiently model the interrelationships among variables. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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17 pages, 702 KiB  
Article
Development of Modified SERVQUAL–MCDM Model for Quality Determination in Reverse Logistics
by Željko Stević, Ilija Tanackov, Adis Puška, Goran Jovanov, Jovica Vasiljević and Darko Lojaničić
Sustainability 2021, 13(10), 5734; https://doi.org/10.3390/su13105734 - 20 May 2021
Cited by 24 | Viewed by 3162
Abstract
To run a business successfully, quality determination and customer relations are very important factors. Therefore, it is necessary to measure quality and identify critical points of business. In this paper, an original integrated model for measuring the service quality of reverse logistics (RL) [...] Read more.
To run a business successfully, quality determination and customer relations are very important factors. Therefore, it is necessary to measure quality and identify critical points of business. In this paper, an original integrated model for measuring the service quality of reverse logistics (RL) was developed for the company Komunalac Teslić, which was used as an example. The Delphi and Full Consistency Method (FUCOM) was applied to determine the significance of the quality dimensions, while a modified SERVQUAL (SQ) model was used to measure the service quality of the logistics. An original SQ questionnaire was formed with a total of 21 statements that were arranged in five standard dimensions. Examining the reliability of the questionnaire for quality dimensions using the Cronbach Alpha coefficient, it was found that the measurement scales for dimensions are appropriate in terms of user expectations, while in terms of quality perception there is no measurement scale for the empathy dimension. An extensive statistical analysis was then performed to verify the results. A Signum test was applied to identify the relationship between the responses in terms of expectations and perceptions, i.e., to examine their differences. The findings obtained by this research show that the expectations were higher than the perceived quality of the services and that there was a significant statistical difference for 12 of the SQ statements. For two statements, there was a significant statistical difference in favor of perceived quality compared to expectations. Based on the results obtained, the company must improve its services in order for service quality to be at a satisfactory level. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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23 pages, 2993 KiB  
Article
A Study on Fiscal Risk of China’s Employees Basic Pension System under Longevity Risk
by Min Le, Xinrong Xiao, Dragan Pamučar and Qianling Liang
Sustainability 2021, 13(10), 5526; https://doi.org/10.3390/su13105526 - 15 May 2021
Cited by 1 | Viewed by 1899
Abstract
It is generally accepted that China’s Employees Basic Pension System (CEBPS) cannot cover its expenses. The government needs to fill the gap in income and expenditure with fiscal revenue to ensure sustainability of the system, which may cause it to take fiscal risk [...] Read more.
It is generally accepted that China’s Employees Basic Pension System (CEBPS) cannot cover its expenses. The government needs to fill the gap in income and expenditure with fiscal revenue to ensure sustainability of the system, which may cause it to take fiscal risk caused by the volatility of the fund gap. In this article, through the establishment of a prediction model for the income and expenditure of CEBPS with dynamic mortality, we aimed to measure the fiscal risk caused by longevity risk and provide policy basis for the government. We found that longevity risk leads to serious fiscal risk. The income and expenditure gap of CEBPS fluctuates greatly, and the 2.5% and 97.5% quantiles of fund balance in 2067 are 1.52 and 0.44 times the expected value, respectively. The knock-on effect of fiscal risk, measured by value-at-risk (VaR), is 1.15 times gross domestic product and 4.75 times state fiscal expenditure in 2020. In this article, we not only calculate the expected value like the other literatures but also discuss the volatility of the CEBPS fund gap. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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17 pages, 364 KiB  
Article
Robust Scheduling of Waste Wood Processing Plants with Uncertain Delivery Sources and Quality
by Balázs Dávid, Olivér Ősz and Máté Hegyháti
Sustainability 2021, 13(9), 5007; https://doi.org/10.3390/su13095007 - 29 Apr 2021
Cited by 2 | Viewed by 2760
Abstract
While the study of reverse wood value chains has become an important topic recently, optimization-focused studies usually consider network-level problems and decisions, and do not address the individual processes in the network. In the case of waste wood, one such important process is [...] Read more.
While the study of reverse wood value chains has become an important topic recently, optimization-focused studies usually consider network-level problems and decisions, and do not address the individual processes in the network. In the case of waste wood, one such important process is the scheduling of the various machines in a waste wood processing facility to treat incoming wood deliveries with multiple sources and varying quality. This paper proposes a robust multi-objective mixed-integer linear programming model for the optimization of this process that considers the uncertain origins and compositions of the incoming deliveries, while aiming to minimize both lateness and energy consumption. An exhaustive study is performed on instance sets of different sizes and structures to show the efficiency and the limits of the proposed model both in single- and multi-objective cases. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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37 pages, 3535 KiB  
Article
Novel Fuzzy Composite Indicators for Locating a Logistics Platform under Sustainability Perspectives
by Hana Ayadi, Nadia Hamani, Lyes Kermad and Mounir Benaissa
Sustainability 2021, 13(7), 3891; https://doi.org/10.3390/su13073891 - 01 Apr 2021
Cited by 20 | Viewed by 2691
Abstract
The purpose of this paper is to help decision-makers choose the location of a logistics platform with sustainability perspectives. This study presents a compensatory and partially compensatory approach to build composite indicators, using mainly fuzzy multi-criteria decision-making methods. In the first instance, the [...] Read more.
The purpose of this paper is to help decision-makers choose the location of a logistics platform with sustainability perspectives. This study presents a compensatory and partially compensatory approach to build composite indicators, using mainly fuzzy multi-criteria decision-making methods. In the first instance, the fuzzy full consistency method (F-FUCOM) was used to calculate the weight of the criteria and sub-criteria. In the second instance, two aggregation methods, namely the fuzzy multi-attribute ideal-real comparative analysis (F-MAIRCA) and the fuzzy preference ranking organization method for enrichment evaluation (F-PROMETHEE), were used to rank the location of a logistics platform. The novelty of the work lays in studying the impact of limited sustainability and weak sustainability on the location of a logistics platform. In this respect, the aggregation of various sustainability criterion in fuzzy compensatory and partially compensatory composite indicators is an innovative and interesting approach used to locate a logistics platform. The obtained results show that economic sustainability is the most important criterion for the selection of a logistics platform, followed by the environmental criterion. Obviously, the F-MAIRCA and F-PROMETHEE methods provided the same ranking orders. Finally, sensitivity analyses were performed to validate the robustness of the proposed approach. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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16 pages, 1709 KiB  
Article
Analytic Hierarchy Process-Based Airport Ground Handling Equipment Purchase Decision Model
by Yu-Jwo Tao, Hsuan-Shih Lee and Chang-Shu Tu
Sustainability 2021, 13(5), 2540; https://doi.org/10.3390/su13052540 - 26 Feb 2021
Cited by 3 | Viewed by 2029
Abstract
The Airport ground handling services (AGHS) equipment supplier provider selection requires a safety guarantee in terms of the daily operations AGHS provider. AGHS providers seek to avoid aircraft damage and airline delays and ensure the provision of reliable and high-quality services. The primary [...] Read more.
The Airport ground handling services (AGHS) equipment supplier provider selection requires a safety guarantee in terms of the daily operations AGHS provider. AGHS providers seek to avoid aircraft damage and airline delays and ensure the provision of reliable and high-quality services. The primary objective of this paper was to develop purchasing decision model of the analytic hierarchy process (AHP), AHP-fuzzy linear programming (FLP), and AHP-Taguchi loss function (TLF) multi-choice goal programming (MCGP) purchase decision models to help the AGHS purchasing managers in selecting the best AGHS equipment supplier provider. The constructed models were assessed, and results obtained for the AHP-FLP and AHP-TLF-MCGP models were compared. We conducted a real-world example of supplier selection by an AGHS company by using the proposed models. The proposed model provides useful information and has practical value for AGHS providers. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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25 pages, 2603 KiB  
Article
Application of Exact and Multi-Heuristic Approaches to a Sustainable Closed Loop Supply Chain Network Design
by Abdul Salam Khan, Qazi Salman Khalid, Khawar Naeem, Rafiq Ahmad, Razaullah Khan, Waqas Saleem and Catalin Iulian Pruncu
Sustainability 2021, 13(5), 2433; https://doi.org/10.3390/su13052433 - 24 Feb 2021
Cited by 7 | Viewed by 2127
Abstract
Closed-loop supply chains (CLSC) are gaining popularity due to their efficiency in addressing economic, environmental, and social concerns. An important point to ponder in the distribution of CLSC is that imperfect refrigeration and bad road conditions may result in product non-conformance during the [...] Read more.
Closed-loop supply chains (CLSC) are gaining popularity due to their efficiency in addressing economic, environmental, and social concerns. An important point to ponder in the distribution of CLSC is that imperfect refrigeration and bad road conditions may result in product non-conformance during the transit and thus such products are to be returned to the supply node. This may hinder the level of customer satisfaction. This paper presents a sustainable closed-loop supply chain framework coupled with cross-docking subject to product non-conformance. A cost model is proposed to investigate the economic and environmental aspects of such systems. The transportation cost is analyzed in terms of total carbon emissions. A set of metaheuristics are administered to solve the model and a novel lower bound is proposed to relax the complexity of the proposed model. The results of different size problems are compared with the branch and bound approach and the proposed lower bound. The results indicate that the proposed research framework, mathematical model, and heuristic schemes can aid the decision-makers in a closed-loop supply chain context. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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26 pages, 1842 KiB  
Article
An Analytic Hierarchy Process Approach for Prioritisation of Strategic Objectives of Sustainable Development
by Zsuzsanna Katalin Szabo, Zsombor Szádoczki, Sándor Bozóki, Gabriela C. Stănciulescu and Dalma Szabo
Sustainability 2021, 13(4), 2254; https://doi.org/10.3390/su13042254 - 19 Feb 2021
Cited by 17 | Viewed by 4280
Abstract
Sustainability is one of the world’s fundamental objectives, and a wide variety of information types, parameters, and uncertainties need to be appraised and managed to assess it. In the present paper, Multi-Criteria Decision Analysis (MCDA) is used to prioritise the criteria of sustainable [...] Read more.
Sustainability is one of the world’s fundamental objectives, and a wide variety of information types, parameters, and uncertainties need to be appraised and managed to assess it. In the present paper, Multi-Criteria Decision Analysis (MCDA) is used to prioritise the criteria of sustainable development based on regularly published indicators. In line with most approaches in the literature, the main criteria are Economy, Society and Environment. Complex criteria are decomposed into subcriteria until the performance with respect to them can be measured directly. Weights of importance are calculated by the Analytic Hierarchy Process (AHP), in decision support system PriEsT. The model is flexible to both the modification of criteria and re-weighting, and the PriEsT file is supplemented to the paper. Moreover, the results can also be applied in decisions on resource allocation. The proposed methodology has the potential of resulting in a new composite index to measure, compare or rank countries and regions regarding sustainable development or one of its subcriteria, as well as to track, year by year, the improvements or the impact of the policies introduced. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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24 pages, 1733 KiB  
Article
A Hesitant Fuzzy Combined Compromise Solution Framework-Based on Discrimination Measure for Ranking Sustainable Third-Party Reverse Logistic Providers
by Arunodaya Raj Mishra, Pratibha Rani, Raghunathan Krishankumar, Edmundas Kazimieras Zavadskas, Fausto Cavallaro and Kattur S. Ravichandran
Sustainability 2021, 13(4), 2064; https://doi.org/10.3390/su13042064 - 14 Feb 2021
Cited by 43 | Viewed by 2749
Abstract
Customers’ pressure, social responsibility, and government regulations have motivated the enterprises to consider the reverse logistics (RL) in their operations. Recently, companies frequently outsource their RL practices to third-party reverse logistics providers (3PRLPs) to concentrate on their primary concern and diminish costs. However, [...] Read more.
Customers’ pressure, social responsibility, and government regulations have motivated the enterprises to consider the reverse logistics (RL) in their operations. Recently, companies frequently outsource their RL practices to third-party reverse logistics providers (3PRLPs) to concentrate on their primary concern and diminish costs. However, to select the suitable 3PRLP candidate requires a multi-criteria decision making (MCDM) process involving uncertainty owing to the presence of many associated aspects. In order to choose the most appropriate sustainable 3PRLP (S3PRLP), we introduce a hybrid approach based on the classical Combined Compromise Solution (CoCoSo) method and propose a discrimination measure within the context of hesitant fuzzy sets (HFSs). This approach offers a new process based on the discrimination measure for evaluating the criteria weights. The efficiency and practicability of the present approach are numerically demonstrated by solving an illustrative case study of S3PRLPs selection under a hesitant fuzzy environment. Moreover, sensitivity and comparative studies are presented to highlight the robustness and strength of the introduced methodology. The result of this work concludes that the introduced methodology can recommend a more feasible performance when facing with determinate and inconsistent knowledge and qualitative data. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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19 pages, 1300 KiB  
Article
A New Sustainable Warehouse Management Approach for Workforce and Activities Scheduling
by Vlado Popović, Milorad Kilibarda, Milan Andrejić, Borut Jereb and Dejan Dragan
Sustainability 2021, 13(4), 2021; https://doi.org/10.3390/su13042021 - 13 Feb 2021
Cited by 19 | Viewed by 6555
Abstract
Sustainable engineering is very important for logistics systems. Nowadays, sustainable warehouse management is a key factor in market success. Workforce fluctuation and inverting the number of customers’ demands make a lot of problems in distribution warehouses. This study addresses a sustainable approach for [...] Read more.
Sustainable engineering is very important for logistics systems. Nowadays, sustainable warehouse management is a key factor in market success. Workforce fluctuation and inverting the number of customers’ demands make a lot of problems in distribution warehouses. This study addresses a sustainable approach for the workforce scheduling problem recognized in a real distribution warehouse. The problem arises from the high variability of demand for workers over one workday, which causes workforce surplus in some periods of the workday and shortages in others. Engineering managers of the distribution warehouse already use different full-time and part-time shifts, and schedule workers on different activities, but they still have significant workforce surpluses or shortages in some periods. This study proposes the scheduling of activities’ execution together with workers to face that variability and decrease the cost of the workforce. This idea comes from the fact that some activities in a distribution warehouse can be done in a specific time period after the need for them occurs. In this way, the variability of demand for workers can be decreased, and a lower workforce cost may be ensured. Based on this idea, the entire problem is modeled as integer linear programming. The real example of the problem is solved, and the proposed model is tested on randomly generated instances of the problem in Python by means of the PuLP linear programming package. The results indicate different positive effects in the manner of sustainable warehouse management: lower workforce costs, time savings, better utilization of all types of resources and equipment, increased employee satisfaction, and so on. For even 61% of instances of the introduced problem, the obtained cost of the workforce is lower by more than 20% if activities’ executions are scheduled together with employees. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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16 pages, 1292 KiB  
Article
Mathematical Analysis of Criteria for Maintenance of Technical Systems in the Function of Achieving Sustainability
by Goran Otić, Oliver Momčilović, Ljiljana Radovanović, Goran Jovanov, Dragica Radosav and Jasmina Pekez
Sustainability 2021, 13(4), 1680; https://doi.org/10.3390/su13041680 - 04 Feb 2021
Cited by 3 | Viewed by 1646
Abstract
Achieving sustainable development requires strategic efforts involving the entire organization. Maintenance efforts also play an important role. Company management needs to understand and develop an appropriate strategy to achieve sustainable development by applying maintenance performance measurements. The aim of this paper is to [...] Read more.
Achieving sustainable development requires strategic efforts involving the entire organization. Maintenance efforts also play an important role. Company management needs to understand and develop an appropriate strategy to achieve sustainable development by applying maintenance performance measurements. The aim of this paper is to present possible ways of analyzing and ranking the impact of certain criteria with respect to achieving sustainability. The paper uses the method of Structural Equation Modeling—SEM in order to determine the most influential variable on the sustainability of maintenance of technical systems. Based on the set theoretical system model, for all its variables in the model, statements were made that describe them, on which 136 respondents gave their views (from 1 to 5, Likert scale) in the territory of the Republic of Serbia. An intuitive F-DEMATEL method was also used to prioritize variables. A team of 10 experts in the field of maintenance of technical systems was compared the criteria A—Application of technical diagnostics, B—Management of maintenance resources, C—Maintenance process planning, and the dependent variable D—Sustainability of maintenance of technical systems. According to experts, the importance of the criteria coincides with the results obtained by a survey with 136 respondents. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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20 pages, 2921 KiB  
Article
Evaluation of Safety Degree at Railway Crossings in Order to Achieve Sustainable Traffic Management: A Novel Integrated Fuzzy MCDM Model
by Aleksandar Blagojević, Sandra Kasalica, Željko Stević, Goran Tričković and Vesna Pavelkić
Sustainability 2021, 13(2), 832; https://doi.org/10.3390/su13020832 - 15 Jan 2021
Cited by 36 | Viewed by 3421
Abstract
Sustainable traffic system management under conditions of uncertainty and inappropriate road infrastructure is a responsible and complex task. In Bosnia and Herzegovina (BiH), there is a large number of level crossings which represent potentially risky places in traffic. The current state of level [...] Read more.
Sustainable traffic system management under conditions of uncertainty and inappropriate road infrastructure is a responsible and complex task. In Bosnia and Herzegovina (BiH), there is a large number of level crossings which represent potentially risky places in traffic. The current state of level crossings in BiH is a problem of the greatest interest for the railway and a generator of accidents. Accordingly, it is necessary to identify the places that are currently a priority for the adoption of measures and traffic control in order to achieve sustainability of the whole system. In this paper, the Šamac–Doboj railway section and passive level crossings have been considered. Fifteen different criteria were formed and divided into three main groups: safety criteria, road exploitation characteristics, and railway exploitation characteristics. A novel integrated fuzzy FUCOM (full consistency method)—fuzzy PIPRECIA (pivot pairwise relative criteria importance assessment) model was formed to determine the significance of the criteria. When calculating the weight values of the main criteria, the fuzzy Heronian mean operator was used for their averaging. The evaluation of level crossings was performed using fuzzy MARCOS (measurement of alternatives and ranking according to compromise solution). An original integrated fuzzy FUCOM–Fuzzy PIPRECIA–Fuzzy MARCOS model was created as the main contribution of the paper. The results showed that level crossings 42 + 690 (LC4) and LC8 (82 + 291) are the safest considering all 15 criteria. The verification of the results was performed through four phases of sensitivity analysis: resizing of an initial fuzzy matrix, comparative analysis with other fuzzy approaches, simulations of criterion weight values, and calculation of Spearman’s correlation coefficient (SCC). Finally, measures for the sustainable performance of the railway system were proposed. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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20 pages, 4561 KiB  
Article
Research on Speeds at Roundabouts for the Needs of Sustainable Traffic Management
by Slavko Davidović, Vuk Bogdanović, Nemanja Garunović, Zoran Papić and Dragan Pamučar
Sustainability 2021, 13(1), 399; https://doi.org/10.3390/su13010399 - 04 Jan 2021
Cited by 7 | Viewed by 3838
Abstract
Knowledge of the characteristics of speed at roundabouts is very important in design procedures, simulation models, and determining the influence of these roundabouts on traffic conditions in a street network. Sustainable management in the street network means the influence of all its parts [...] Read more.
Knowledge of the characteristics of speed at roundabouts is very important in design procedures, simulation models, and determining the influence of these roundabouts on traffic conditions in a street network. Sustainable management in the street network means the influence of all its parts on traffic conditions and travel time. In order to reliably determine roundabouts parameters in the procedures of planning and the choice of sustainable method of traffic management, it is very important to know the values of the traffic flow parameters, particularly the speeds at the entry and exit leg, as well as in the circulatory zone. This article analyses the speed characteristics in traffic flow at urban roundabouts with different geometrical characteristics in the city of Banja Luka. The applied method for traffic data collecting in this research was the method of video recording processing, which excludes any influence on driver behavior. Furthermore, statistical analysis was conducted, which established the correlation between the achieved speeds and geometrical characteristics of the intersection. Due to roundabout characteristics, the research was focused on the access, that is, the entry leg, the segment of the circulatory zone and the exit leg. The research results showed there is a significant dependence between geometrical characteristics of certain elements of the roundabout on speeds. In the further course of the research, it was proved that the variation of speeds at the segments of roundabouts significantly affects the size of time losses and emission of pollutants, i.e., parameters based on which it is possible to objectively assess the possibility of sustainable implementation of the planned solution of roundabouts of similar geometry within the street network in cities similar to Banja Luka. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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17 pages, 692 KiB  
Article
Determining the Competitiveness of Spa-Centers in Order to Achieve Sustainability Using a Fuzzy Multi-Criteria Decision-Making Model
by Miroslav Mijajlović, Adis Puška, Željko Stević, Dragan Marinković, Dragan Doljanica, Saša Virijević Jovanović, Ilija Stojanović and Jasminka Beširović
Sustainability 2020, 12(20), 8584; https://doi.org/10.3390/su12208584 - 16 Oct 2020
Cited by 28 | Viewed by 2779
Abstract
Bosnia and Herzegovina (B&H) possess many natural resources that can be exploited for the development of medical tourism. The offer of medical tourism in B&H is focused on spa tourism. B&H has 16 registered spa-centers offering different types of services. This study provides [...] Read more.
Bosnia and Herzegovina (B&H) possess many natural resources that can be exploited for the development of medical tourism. The offer of medical tourism in B&H is focused on spa tourism. B&H has 16 registered spa-centers offering different types of services. This study provides a complete overview of the assessment of the current state of spa-centres using expert decision-making and methods of multi-criteria analysis. An innovative and novel MCDM model based on integration of the FUCOM (full consistency method) and fuzzy MARCOS (Measurement of Alternatives and Ranking according to COmpromise Solution) methods was used. The model consists of 16 alternatives and eight sustainable criteria. The results of this research have shown that the spa-centers of Ilidža near Sarajevo, Fojnica and Vrućica have the best assessments of the current situation and prerequisites for sustainable business. These spa-centers should be a benchmark to other spas providing direction on how to improve their business to be more sustainable and competitive in the market. These results were confirmed by a sensitivity analysis with two approaches used. The first approach was to compare the results obtained by the fuzzy MARCOS method with other fuzzy methods, and the second approach was to examine the influence of the application of different weights on the final ranking of the spa. The results of this study can serve spa-canter managers to understand the position of their spa-centers in order to exploit advantages they have and eliminate the shortcomings to improve their business. Full article
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20 pages, 3856 KiB  
Article
Will Ending the One-Child Policy and Raising the Retirement Age Enhance the Sustainability of China’s Basic Pension System?
by Pu Liao, Hui Su and Dragan Pamučar
Sustainability 2020, 12(19), 8172; https://doi.org/10.3390/su12198172 - 03 Oct 2020
Cited by 3 | Viewed by 2734
Abstract
The sustainability of China’s Basic Pension System (CBPS) has been challenged by the ageing of the population and the decline in economic growth. This article establishes a Markov model for CBPS to examine whether the reforms, including ending the one-child policy and raising [...] Read more.
The sustainability of China’s Basic Pension System (CBPS) has been challenged by the ageing of the population and the decline in economic growth. This article establishes a Markov model for CBPS to examine whether the reforms, including ending the one-child policy and raising retirement the age, will shrink the negative income–expenditure gap. We find that the negative income–expenditure gap will destroy CBPS in the future in the absence of fiscal transfer or reform. Ending the one-child policy will increase the number of contributors and then reduce the gap in the short term but will worsen the gap in the long term. Raising the retirement age will have several positive effects overall while increasing expenditures in certain periods. The contributions of this article are describing CBPS in detail and establishing a precise model to analyze the effectiveness of reforms. Full article
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29 pages, 1519 KiB  
Article
Sustainability of the Motivation Policy Model for Employees in State Administration
by Milan Kovačević, Srđan Blagojević and Bojan Kuzmanović
Sustainability 2020, 12(19), 7974; https://doi.org/10.3390/su12197974 - 26 Sep 2020
Cited by 9 | Viewed by 4451
Abstract
An important condition for the performance sustainability of organizations, in the public and state sector, is the maintenance and improvement of the employee motivation policy model. Motivation for work has a significant impact on the success of modern organizations; the impact is multidimensional [...] Read more.
An important condition for the performance sustainability of organizations, in the public and state sector, is the maintenance and improvement of the employee motivation policy model. Motivation for work has a significant impact on the success of modern organizations; the impact is multidimensional and complex, and it has been confirmed empirically. Motivation is influenced by numerous factors, of different influence and hierarchy, which depend on socio-economic conditions and cultural determinants, but also on the characteristics of employees, and it is necessary to constantly monitor them. The paper presents a sustainable model of employee motivation in public administration and the results of research on the hierarchy and the impact of motivation factors on employees of different demographic characteristics. The research was conducted by an anonymous survey of 2128 respondents (1576 employees in the state administration and 552 persons employed in the Republic of Serbia outside the state administration), in the period March–June 2020. The questionnaire developed for this research has 16 questions on motivating factors with a scale with a high level of internal consistency. Using one-factor analysis of variance (ANOVA), tests of subsequent comparisons, and t-test, statistically significant differences are determined for the influence of motivational factors on respondents of different levels of education, age, role in organization, gender, and family status—also, the magnitude of influence ranges from small to large. The influence of motivational factors is greater for older people, for people with a higher level of education, for managers in relation to workers, for women in relation to men, as well as for persons in marriage in relation to persons out of wedlock. By applying multi-criteria analysis, the factors are ranked: the amount of salary and good interpersonal relations are at the top, while criticism and information about work are in the last positions. As a factor that negatively affects motivation, low wages stands out. The difference in the motivation of state administration members was determined by comparing the results of motivational factors’ influence with the appropriate sample of employees outside the state administration. Differences were registered for 15 out of 16 factors (only for the factor high wages, there is no difference), and the magnitude of the impact is medium and small. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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25 pages, 1062 KiB  
Article
Development of a Multi-Criteria Model for Sustainable Reorganization of a Healthcare System in an Emergency Situation Caused by the COVID-19 Pandemic
by Dragan Pamučar, Mališa Žižović, Dragan Marinković, Dragan Doljanica, Saša Virijević Jovanović and Pavle Brzaković
Sustainability 2020, 12(18), 7504; https://doi.org/10.3390/su12187504 - 11 Sep 2020
Cited by 33 | Viewed by 3034
Abstract
Healthcare systems worldwide are facing problems in providing health care to patients in a pandemic caused by the SARS-CoV-2 virus (COVID-19). The pandemic causes an extreme disease to spread with fluctuating needs among patients, which significantly affect the capacity and overall performance of [...] Read more.
Healthcare systems worldwide are facing problems in providing health care to patients in a pandemic caused by the SARS-CoV-2 virus (COVID-19). The pandemic causes an extreme disease to spread with fluctuating needs among patients, which significantly affect the capacity and overall performance of healthcare systems. In addition, its impact on the sustainability of the entire economic and social system is enormous and certain sustainable management strategies need to be selected. To meet the challenges of the COVID-19 pandemic and ensure sustainable performance, national healthcare systems must adapt to new circumstances. This paper proposes an original multi-criteria methodology for the sustainable selection of strategic guidelines for the reorganization of a healthcare system under the conditions of the COVID-19 pandemic. The selection of an appropriate strategic guideline is made on the basis of defined criteria and depending on infection capacity and pandemic spread risk. The criteria for the evaluation of strategic guidelines were defined on the basis of a survey in which the medical personnel engaged in the crisis response team during the COVID-19 pandemic in the Republic of Serbia participated. The Level-Based Weight Assessment (LBWA) model and Measuring Attractiveness by a Categorical-Based Evaluation Technique (MACBETH) method were used to determine the weight coefficient criteria, while a novel fuzzy Ranking of Alternatives through Functional Mapping of Criterion Subintervals into a Single Interval (RAFSI) model was used to evaluate the strategic guidelines. The proposed multi-criteria methodology was tested in a case study in the Republic of Serbia. The validity of the proposed methodology is shown through the simulation of changes in input parameters of Bonferroni aggregation functions and through a comparison with other multi-criteria methodologies. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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22 pages, 906 KiB  
Article
Dry Port Terminal Location Selection by Applying the Hybrid Grey MCDM Model
by Snežana Tadić, Mladen Krstić, Violeta Roso and Nikolina Brnjac
Sustainability 2020, 12(17), 6983; https://doi.org/10.3390/su12176983 - 27 Aug 2020
Cited by 48 | Viewed by 3631
Abstract
Globalization and decentralization of production generate the intensive growth of goods and transport flows, mostly performed by the maritime transport. Ports, as the main nodes in the global logistics networks, are becoming congested, space for their expansion limited, and traffic in their hinterland [...] Read more.
Globalization and decentralization of production generate the intensive growth of goods and transport flows, mostly performed by the maritime transport. Ports, as the main nodes in the global logistics networks, are becoming congested, space for their expansion limited, and traffic in their hinterland congested. As a solution to these and many other hinterland-transport-related problems stands out the development of dry port (DP) terminals. Selection of their location is one of the most important strategic decisions on which depends their competitiveness in the market and the functionality of the logistics network. Accordingly, the evaluation and selection of locations for the development of the DP in accordance with the requirements of various stakeholders is performed in this paper, as a prerequisite for the establishment of an ecological, economic, and socially sustainable logistics network in the observed area. To solve this problem, a new hybrid model of multi-criteria decision-making (MCDM) that combines Delphi, AHP (Analytical Hierarchy Process), and CODAS (Combinative Distance-based Assessment) methods in a grey environment is developed. The main contributions of this paper are the defined model, the problem-solving approach based on finding a compromise solution, simultaneous consideration of the environmental, economic, and social sustainability of the DP concept and its implementation in the regional international markets. The applicability of the approach and the defined MCDM model is demonstrated by solving a real-life case study of ranking the potential DP locations in the Western Balkans region. Based on the obtained results, it is concluded that in the current market conditions, it would be most realistic to open three DP terminals, in Zagreb, Ljubljana, and Belgrade. Full article
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19 pages, 1312 KiB  
Article
Evaluation of Process Orientation Dimensions in the Apparel Industry
by Andrea Dobrosavljević, Snežana Urošević, Milovan Vuković, Miroslav Talijan and Dragan Marinković
Sustainability 2020, 12(10), 4145; https://doi.org/10.3390/su12104145 - 19 May 2020
Cited by 8 | Viewed by 3446
Abstract
The dimensions that influence the establishment of business process management (BPM) practices and the progression to higher levels of process maturity derive from exploring the dimensions of process orientation of organizations. Small and medium-sized clothing enterprises (SME’s) are characterized by various specifics that [...] Read more.
The dimensions that influence the establishment of business process management (BPM) practices and the progression to higher levels of process maturity derive from exploring the dimensions of process orientation of organizations. Small and medium-sized clothing enterprises (SME’s) are characterized by various specifics that can affect the degree of process orientation adoption and the pace of transition from lower to higher levels of process maturity. According to these specifics, the acceptance of the process approach may be differently affected. For the purpose of adequate evaluation and prioritization of the most influential dimensions, a new integrated multicriteria decision-making (MCDM) model that combines classical and fuzzy theory was developed. First, the full consistency method (FUCOM) method was applied, followed by the fuzzy pivot pairwise relative criteria importance assessment (fuzzy PIPRECIA) method to obtain more accurate criteria values. Prioritization of the most influential BPM dimension contributes to highlighting the area of business that needs to be primarily strengthened by appropriate actions for successful establishment of BPM in apparel industry SMEs. Within this research, the prioritized dimension refers to human resource management in accordance with the specific aspects of business within the apparel industry. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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16 pages, 1943 KiB  
Article
A New Comprehensive Approach for Efficient Road Vehicle Procurement Using Hybrid DANP-TOPSIS Method
by Marko Stokic, Davor Vujanovic and Dragan Sekulic
Sustainability 2020, 12(10), 4044; https://doi.org/10.3390/su12104044 - 14 May 2020
Cited by 7 | Viewed by 2568
Abstract
The efficient vehicle procurement is an important business segment of different companies with their own vehicle fleet. It has a significant influence on reducing transport and maintenance costs and on increasing the fleet’s energy efficiency. It is indispensable that managers consider various criteria [...] Read more.
The efficient vehicle procurement is an important business segment of different companies with their own vehicle fleet. It has a significant influence on reducing transport and maintenance costs and on increasing the fleet’s energy efficiency. It is indispensable that managers consider various criteria from several aspects when procuring a vehicle. In that sense, we defined 13 relevant criteria and divided them into four multidisciplinary aspects: Construction-technical, financial, operational, and environmental. Decision-Making Trial and Evaluation Laboratory-Based Analytic Network Process (DANP) method was applied to evaluate the significance of defined criteria and aspects and their interdependency. It is established that the three most important criteria for vehicle procurement are vehicle price, vehicle maintenance, and vehicle selling price. The most important aspect is construction technical aspect, while the aspect of the environment is the least important. The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method was used to rank eight different vehicles, which were considered by vehicle fleet manager at the observed company. This model assists fleet managers in the selection of the most suitable vehicle for procurement, while significantly reducing decision-making time and simultaneously observing all necessary criteria and their weights. Moreover, we have considered 10 different scenarios to establish whether and how the rank of the observed alternatives would change. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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18 pages, 2267 KiB  
Article
Evaluation of Criteria for the Implementation of High-Performance Computing (HPC) in Danube Region Countries Using Fuzzy PIPRECIA Method
by Milovan Tomašević, Lucija Lapuh, Željko Stević, Dragiša Stanujkić and Darjan Karabašević
Sustainability 2020, 12(7), 3017; https://doi.org/10.3390/su12073017 - 09 Apr 2020
Cited by 20 | Viewed by 4105
Abstract
The use of computers with outstanding performance has become a real necessity in order to achieve greater efficiency and sustainability for the accomplishment of various tasks. Therefore, with the development of information technology and increasing dynamism in the business environment, it is expected [...] Read more.
The use of computers with outstanding performance has become a real necessity in order to achieve greater efficiency and sustainability for the accomplishment of various tasks. Therefore, with the development of information technology and increasing dynamism in the business environment, it is expected that these computers will be more intensively deployed. In this paper, research was conducted in Danube region countries: Austria, Bosnia and Herzegovina, Bulgaria, Croatia, Czech Republic, Germany, Hungary, Moldova, Montenegro, Romania, Serbia, Slovakia, Slovenia, and Ukraine. The aim of the research was to determine what criteria are most significant for the introduction of high-performance computing and the real situation in each of the countries. In addition, the aim was to establish the infrastructure needed to implement such a system. In order to determine the partial significance of each criterion and thus the possibility of implementing high-performance computing, a multi-criteria model in a fuzzy environment was applied. The weights of criteria and their rankings were performed using the Fuzzy PIvot Pairwise RElative Criteria Importance Assessment—fuzzy PIPRECIA method. The results indicate different values depend on decision-makers (DMs) in the countries. Spearman’s and Pearson’s correlation coefficients were calculated to verify the results obtained. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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21 pages, 2257 KiB  
Article
Sustainability of the Optimum Pavement Model of Reclaimed Asphalt from a Used Pavement Structure
by Edis Softić, Veljko Radičević, Marko Subotić, Željko Stević, Zlatan Talić and Dragan Pamučar
Sustainability 2020, 12(5), 1912; https://doi.org/10.3390/su12051912 - 03 Mar 2020
Cited by 8 | Viewed by 2659
Abstract
This paper demonstrates and provides additional findings and instructions to produce new cold-recycled layers of pavement structures spatially and temporally sustainable. At the same time, recycled pavement structures have been enhanced with optimum amounts of new stone materials and binders made of cement [...] Read more.
This paper demonstrates and provides additional findings and instructions to produce new cold-recycled layers of pavement structures spatially and temporally sustainable. At the same time, recycled pavement structures have been enhanced with optimum amounts of new stone materials and binders made of cement and foamed bitumen. The subject of the research is based on the examination of recycled asphalt from surface and bituminous base courses of pavement structures for use on higher-type roads. The aim of the research is to model the process of producing recycled asphalt by cold recycling to optimize the process of influential parameters. In addition, one of the primary goals of the research is to demonstrate a sustainable way of producing new cold-recycled layers of pavement structures. The obtained results indicated the inevitability of the use of recycled material from pavement structures with the possibility of applying secondary and tertiary crushing of recycled mass, which depends on the type of layer for which the recycled material would be used. The research resulted in an optimum mixture variant of the stabilization layer of pavement structure that consists mainly of recycled material from a worn pavement structure improved with a relatively small amount of new aggregate with the addition of minimal stabilizers made of cement and foamed bitumen. The results showed that the optimum mixture variant of the stabilization layer is spatially and temporally stable. Additionally, the presented optimum variant of the stabilization layer enables sustainable development of road networks with minimum consumption of new natural resources. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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17 pages, 3053 KiB  
Article
Dynamic Gaming Case of the R-Interdiction Median Problem with Fortification and an MILP-Based Solution Approach
by Yiyong Xiao, Pei Yang, Siyue Zhang, Shenghan Zhou, Wenbing Chang and Yue Zhang
Sustainability 2020, 12(2), 581; https://doi.org/10.3390/su12020581 - 13 Jan 2020
Cited by 3 | Viewed by 2397
Abstract
This paper studies the cyclic dynamic gaming case of the r-interdiction median problem with fortification (CDGC-RIMF), which is important for strengthening a facility’s reliability and invulnerability under various possible attacks. We formulated the CDGC-RIMF as a bi-objective mixed-integer linear programming (MILP) model [...] Read more.
This paper studies the cyclic dynamic gaming case of the r-interdiction median problem with fortification (CDGC-RIMF), which is important for strengthening a facility’s reliability and invulnerability under various possible attacks. We formulated the CDGC-RIMF as a bi-objective mixed-integer linear programming (MILP) model with two opposing goals to minimize/maximize the loss from both the designer (leader) and attacker (follower) sides. The first goal was to identify the most cost-effective plan to build and fortify the facility considering minimum loss, whereas the attacker followed the designer to seek the most destructive way of attacking to cause maximum loss. We found that the two sides could not reach a static equilibrium with a single pair of confrontational plans in an ordinary case, but were able to reach a dynamically cyclic equilibrium when the plan involved multiple pairs. The proposed bi-objective model aimed to discover the optimal cyclic plans for both sides to reach a dynamic equilibrium. To solve this problem, we first started from the designer’s side with a design and fortification plan, and then the attacker was able to generate their worst attack plan based on that design. After that, the designer changed their plan again based on the attacker’s plan in order to minimize loss, and the attacker correspondingly modified their plan to achieve maximum loss. This game looped until, finally, a cyclic equilibrium was reached. This equilibrium was deemed to be optimal for both sides because there was always more loss for either side if they left the equilibrium first. This game falls into the subgame of a perfect Nash equilibrium—a kind of complete game. The proposed bi-objective model was directly solved by the CPLEX solver to achieve optimal solutions for small-sized problems and near-optimal feasible solutions for larger-sized problems. Furthermore, for large-scale problems, we developed a heuristic algorithm that implemented dynamic iterative partial optimization alongside MILP (DIPO-MILP), which showed better performance compared with the CPLEX solver when solving large-scale problems. Full article
(This article belongs to the Special Issue Operational Research Tools for Solving Sustainable Engineering Problems)
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