Evaluation of Mathematical Models in Sustainable Supply Chain Management: Gap Analysis

The main purpose of this paper is to present a comprehensive view of the application mathematical models in the designing and implementing SSCM beside to solving problems and making decision. The research questions are: what kind of mathematical models are used for designing and implementing sustainable supply chain management, how to use them, which industries implemented in, what modules of SSCM depth in and finally finding the gaps between the goals of Sustainable development and current researches and suggestions for further researches. The methodology of the research is Systematic Literature review and evaluation peer review papers which are published in high ranking journals: First, we gather all papers through scientific data bases like Scopus, science direct, MDPI, Springer, Google Scholar. Then, screening papers based on the criteria such as object of paper, subject of paper, journals impact factor, peer review paper, and relative content of the papers. Finally, we selected 245 papers through three steps screening from 2806 papers that they have enough quality and relative to our research goals for context analysis. For context analysis: First we categorize the information of the papers and draw the current situation of researches in the framework of our topic. Then, we evaluate and compare the goals of sustainability and current situation and find the gapes, then, offer suggestions required researches for pollutant industries such as Casting Industry, Heavy Industry, Coal Industry and so on. On the other hand, there are gaps in researches in some modules of SSCM such as packaging, designing products, etc.


Introduction
SSCM refers to implementing all sustainable goals via Triple Bottom Line which are economic, environmental and social dimensions. In parallel, SSCM define as management of information, capital, and materials through cooperation and collaboration of Supply chain partners, stakeholders, customers, and people (Seuring and Müller 2008). In two last decades the numbers of scholars and academic researchers made different conceptual and mathematical models for SSCM and used a several of tools for decision makings. Some papers evaluated sustainability in the wide range of supply chain referred by the area of research like development and developing countries and made some mathematical models, rules or new suggestions for developing countries (Sá nchez-Flores, et al. 2020); (Ali, Yufeng and Glyn, Sustainable supply chain management in emerging economies: Trade-offs between environmental and cost performance 2016); (Köksal and Müller 2018); (Jia, et al. 2018). Because of rapid changing in environmental conditions and a number of alarming for warming world and environment protection, recently, the scholars and researchers take more attention on environment dimension of sustainability and green sustainable supply chain management (Kannan, Jabbour and Jabbour 2014); (Fang, Wang and Song 2020); (Rinib 2015); (Agi and Hazır 2020). Unfortunately, the social aspect in majority of papers underrepresented in comparison with economic and environmental factors (Martins and Pato 2019). In addition, Governments and new policies set some rules for carbon cap and emission carbon for factories, suppliers and In this paper, we evaluate different mathematical models which are used in SSCM in order to decision support system, design and modeling, implementing, development, Environmental protection and social responsibility. First we define the sources of recently researches from 2008 to now, then we find proper papers and analysis the current researches which are related to our subjects. After that, we define a target for achievement to an ideal SSCM structure with use of 2021 Sustainable Development Goals (United Nation 2015). Finally, we compare the current situation and Target, the results of comparison are shown the gaps.

Materials and Methods
In this paper, we use different researches, papers, protocoles and manifests which are related to Sustainability, SSCM and future plan of the world. As it shows in Figure (1), we use a systematically paper review and gap analysis in our research. Second: searching and gathering papers through the key words which are -SSCM‖ + -Mathematic‖, -Sustainability Supply Chain Management‖ + -math‖, -SSCM‖ + -Model‖, -Sustainability‖ + -Supply chain‖ + -math‖. In this step, the number of papers with mentioned key words are 2806. Also, Only papers written in English considered and, The range of data was the year from 2008 to May 2021.  Vol. 14, No. 10;2021 Third: Screening papers in three steps;  Step one of screening is to evaluation the valid journals with criterias like peer review, ranking and index; After finishing first screening, the number of papers are 791. These papers are published in peer review, high index journals.

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Step two of screening is to evaluation the topic and abstract of journals; After finishing the second screening, the number of papers are 382. These papers are selected based on the relevant topic and abstract to the objectives of paper and research questions.

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Step Three of Screening is to use the systematically content analysis for selecting relevant papers. After final selection and content analysis, the number of papers are 245 which are published in international, peer review and high index journals, have relevant topic, abstract, keyword and content with the research objectives and questions.
Forth: definning the target for SSCM according to 2021 Sustainabile Development Goals (United Nation 2015). Based on Sustainable Development Goals, Goals numbers 9 and 12 is related to our topic. For every module of SSCM and partners we define the Target for research.
Fifth: with using gap analysis, find the gaps in several categories like Industries, module of SCM and responsibilities of different partners.

Review and Results
For review and analysis selected papers, we categorized selected papers in four categories. Every categories, first the existing situation of papers and researches are presented, then evaluate and analysis the gaps.
 Category one: overall information like as Year of published, Journals, Country of first author, Industrial, Dimension of SSCM;  Category two: SSCM modules that the papers depth in;  Category Three: Mathematical models and methods which are used for SSCM;  Category Four: The roles of parties in SSCM modeling.
After reviewing and analysis the papers and categorizing in four main categories, the existing situation of recently researches is recognized. These categories present the current situation of researches of mathematical models which are used for SSCM. For gap analysis and propose new idea, the depth of information in this step is very important. Then, we analysis the papers in different point of view.

Category One: Overal Information
This Category analysis the overal information of the papers like year, journals, country, Industrial and dimension of SSCM. The figure 2 shows the distribution of papers between 2008-End of March 2021 and presents the numbers of papers which are published in every year.  Research Vol. 14, No. 10;2021 mathematical methods and using different tools and methods for modeling and solving problems in the field of sustainability and SCM.
The Figure 3 shows the distribution of journals which published more than two relative papers.

Figure 3. Number of papers by Journal
As clearly seen in the figure 3, the cleaner production Journal has the most quantity of papers in the territory of our research by 85 papers. After that the sustainability Journal is the second journal which published relative papers by 27. The 51 journals published only one paper related to the research scope.
The Figure 4 shows the numbers of published papers per country of author. The papers which have several authors from several countries, only the country of first authors are considered. International Business Research Vol. 14, No. 10; 2021 Figure 5 presents the mathematical models which are implement in industries as case study. This statistics help us to find gaps in the industries that there is no research for them. Although, we can use the existing research for development.

Figure 5. The number of papers for each Industry
The researches had more attention on food industry and maximum papers and case studies are related to Food industry by 24 papers. Then the papers in the field of Textile, Services, Logistics, Electrical, Chemical and oil and Gas industries are 16, 15, 15, 11, 9, and 9 respectively. The different is refer to the other papers which are concentrated in several industry or case study or services.   Figure 6 illustrate the number of papers for dimensions of sustainability which are social, environmental and economic in SCM modeling. The most striking feature of the picture seems to the environmental dimension is more interesting in the researches. However, the social dimension is needed to be research more.

Category Two: Modules of SSC and Papers for Every Category
First of all, the modules of SSCM are defined. For definning SSCM Modules, we defined level one of process of SSCM in two kind of process: Main Process and Supporting process. The main process are the process to involve for producing the products and delivery to customers and recycling the products for protecting environment. The supporting process are the process which are needed for the best services to customers and social responsibility or needed for better performance in main process. The main and supporting process devided to modules. The figure 7 shows the modules of SSCM modeling that it presents level two of process.  The figure 9 represents the mathematical tools and models which are used for making SSCM modeling. As a general overview, it can be said that the Fuzzy theory is a usefule mathematical method for making models and solving problems in SSCM models. Fuzziy theory is used as a single method for solving problem or combine with other mathematical models for making SSCM models. After that, the multi objective programming is the second mathematical model which is used for SSCM. One of the main reason of used multi objective programming is thriple bottom line in SSCM and need to offer the optimum solutions for supporting decision making. Table 1 shows the authors who have more researchs and papers for using mathematical models and methods in SSCM modeling and problem solving. As it can clearly seen, they also used fuzzy theory with combination of other methods, Multi-Objective Programming as a mathematical methods and models in their papers more than other methods. Although, Supplier Selection module and Framework of Sustainable SCM are more intresting for authors and they focused on these two modules more than others. Table 1 shows the authors who have more than one research in the fireld of application mathematical models for SSCM modeling, solving problems and decision suport system. Prof. Kannan Govindan, Prof. Devika Kannan, and Prof. Stefan Seuring have the more researches in this field.   (Marcus, et al. 2014); (Sunil, et al. 2017); (Zeinab, Mina and Kannan 2018)  As it is clearly seen in Table 1, the modules that the authors intrested in are SS and FS, which are supplier selection and Framework Structure for SSCM. Table 2 presents the mathematical models, methods and tools which are used for SSCM, the number of papers and refrences of them.  14 DEMATEL 11 (Anil, et al. 2020);(Chong, Yi, et al. 2020); (Erfan, et al. 2020); (Fuli, et al. 2018); (Fang, Wang and Song 2020); (Jing, Marco and Miguel 2016) (Erfan, et al. 2020); (Fuli, et al. 2018); (Harpreet, et al. 2020); (John and Sheila 2020); (Rashidi, et al. 2020); (Govindan, Madan and Devika, Supplier selection based on corporate social responsibility practices 2018); (Amiri, et al. 2020); (Majid, et al. 2015); (Md Maruf, et al. 2020); (Ming-Lang, et al. 2020); (Izadikhah, Reza and Kourosh, How to assess sustainability of suppliers in volume discount context? A new data envelopment analysis approach 2017); (Izadikhah, et al. 2020); (Nejah 2021); (Ozden, et al. 2017); (Patchara and Chunqiao 2019); (Pezhman, Ahmad and Cathal 2017); (Phommaly, et al. 2019); (Pratibha, et al. 2020); (Ravi, Divya and Sanjay 2018); (Sumit and Neeraj 2020); (Tat-Dat, et al. 2021); (Xiaoyang, et al. 2016); (Xin, et al. 2019); (Yan, et al. (Morteza, et al. 2017); (Renato, et al. 2020); (Rohmer, Gerdessen and Claassen 2019); (Rohmer, Gerdessen and Claassen 2018); (Vafaeenezhada, Tavakkoli-Moghaddama and Cheikhrouhoud 2019); (Xiaoyang, et al. 2016); (Xin, et al. 2019); (Yadong, et al. 2020); (Zeinab, Mina and Kannan 2018) (Fuli, et al. 2018); (Patchara and Chunqiao 2019); (Phommaly, et al. 2019); (Sunil, et al. 2017) The most notable feather of the table 2 concerns some papers and authors used several mathematical models and methods together for making a model or solving problems in SSCM. For example , majority of papers used the fuzzy logic method for normalizing variables, or balancing parameters and enablers in the mathematical models as primary method, then used another model such as Goal programming for finding the optimum solution (Zainab, Syed and Shakeel 2019); (Renato, et al. 2020); (Erfan, et al. 2020) or Multi Object Program (Hatami-Marbini, Ali andSebastián 2017); (Azadeh, et al. 2017); (Xiaoyang, et al. 2016) for best solution. Also, AHP method is used for weighting variables, priorities as an auxilary methods for definning variabled and normalizing them for using in the mathematical models, beside to AHP, authors offer another mathematical model for completed SSCM model like AHP-VIKOR (Awasthi, Govindan and Gold 2018); AHP -MCDM and Gray Theory (Mathivathanan, Govindan and Haq 2017); AHP-Multi Objective program (Hamid, et al. 2018); and etc.

Category four: The Roles of Parties in SSCM Modeling
For SSCM modeling, there are different parties which are involving and have roles who are Stakeholders, Governments, People, Social, Environmet, Factories, Logistics Companies and resources. Figure 10 represents the different parties and the relative effects. . The limitation of carbon cap and carbon credit is a constraint for controlling carbon caps and protecting environment. Every country can define their own limitations for factories, companies, transportation and so on, and control the pollutions. The different researches are investigate how to control carbon cap through different partners and rules which are set by governments (Esfahbodi, et al. 2017); (Huiyun, et al. 2018); (Köksal and Müller 2018). On the other hand, customer's demands are an important cause for producing the environmental unfriendly products (EUFP). For controlling the carbon cap and green environment, the training people for choosing the environmental friendly product (EFP) (Kannan, A.Jafarian, et al. 2014); (Huiyun, et al. 2018).

Conculation and Sugesstions
Although gainning increased attention on SSCM, the using mathematical methods and models for solving problems and designning new models relative to SSCM frames and modules are increased. In this paper, we conducted a systematic litrature review to identify the current situation of using mathematical models and methods for SSCM and finding the gaps. The Gaps between the Current situation which are discussed in section three, and the ideal are divided in modules of SSCM, Partners who are involved in SSCM, Countries and area for SSCM and industries.

SSCM Modules
We divided the SSCM in eleven modules which are shown in Figure 7, then defined these modules with using different papers conclusions and contents and finally categorised them in eleven core of research in SSCM and named as modules of SSCM. The resulte of analysis papers and research contents showed that there is no balance for research in different modules. Some modules like SS (Supplier Selection) or FS (Frame work Structure) are evaluated in different papers and there are different mathematical models and methods for modeling these modules. However some modules like SR (Sustainable Recycling) and SPK (Sustainable Packaging) are needed more research. The new research is needed for evaluation the weight of every modules according to environmental impacts and social attention and how to optimum the current situation and gainning goals of sustainability in different modules.

Involved Partners in SSCM Mathematical Models
After analysis the paper contents, we offer a model of different partners who have an important role in SSCM ( Figure 10). With content analysis of papers, we found that the changing approach for customer's demand is needed. We suggest that the role of demand in designning products and EFP should be investigated. In the researches, the role of stakeholders and governments are more highlight. However other roles should be considered and need to add in the roles of SSCM models.

Countries or Area of Research
As it is clearly seen in the Figure 4, the research in some countries are a few. According to united nation definition for sustainability (United Nation 2015), different countries have different goals for sustainability. There is a gap between modeling SSCM in different countries and the defined goals. Some countries need more research which are clear in figure 4.

Industries as Case Study or Implementing Models
In the figure 5 ahows the industries which are investigated as case study or implementing SSCM models in them.
As it is clearly seen, the heavy industries which have more weight on the sustainability (United Nation 2015) like casting, steel, and so on, need more research.
After analysis the gap between current situations and goals of sustainability, we found to need more research on different modules of SSCM, different industries, different countries no matter developed or undevelopped and differend involved partners in SSCM. The analysis presented in this paper enabled the authors to define SSCM models in different modules and categorised in different mathematical models. These categorizes and gap analysis can be helped future researches and designning new models.