A country-level multi-objective optimization model for a sustainable steel supply chain

: Steel supply chains have been pushed to consider environmental and social aspects, other than financial, however, in the context of Operational Research, the few papers proposing mathematical formulations and algorithms tackle only few dimensions of the problem. This study proposes a solution for sustainable steel production by formulating a multi-objective, multi-level, multi-modal, multi-product, and multi-period model and also devising an evolutionary algorithm for the problem. The results provide a Pareto front mapping the conflicting nature of economic, environmental and social objectives; show how changes in the production technology and transportation mode impact the objectives, and how locations with social vulnerability influence the decision of where and when to locate facilities. This paper provides a broad-ranging formulation and the results show its potential to help decision makers of the steel supply chain to make decisions considering not only economic factors.


Introduction
Despite the critical role played in several sectors of the economy, steel supply chains (SSC) are the largest energy consumers of the industrial sector and massive greenhouse gas (GHG) generators.Steel production and distribution deploy lots of renewable and non-renewable natural resources causing environmental issues (Conejo et al., 2020).According to United Nations (2015), the steel industry should consider its social and ecosystem impact, going beyond the financial aspects and devising a green supply chain management (GSCM) with focus on a careful process for supplier selection, process integration, and reverse logistics activities (Tseng et al., 2019;Mc Loughlin et al., 2021).
Beyond environmental preservation, industries have been encouraged for decades to review the need for considering social development (Mota et al., 2018;Tseng et al., 2019).Despite some progress, the incorporation of social and sustainability factors while building a steel supply chain is slow (Elkington, 2013;Eskandarpour et al., 2015;Arampantzi & Minis, 2017) and this is partially explained by the lack of studies proposing practical formulations that can indeed help the organizations to include such factors in their process decision making (Nielsen, 2017;Zhang et al., 2019).
There are optimization models tackling these issues, but they mostly consider few dimensions of the supply chain in terms of layers, periods, products, technological routes and the number of objectives to be optimized, limiting their practical application (Barbosa-Póvoa et al., 2018; CHAIN Moreno-Camacho et al., 2019).In this context, the focus of this study is to provide a countrylevel sustainable steel production solution by formulating a multi-level, multi-modal, multiproduct, multi-period and multi-objective model that is able to suggest where and when to build new plants and distributions centers or modify the capacity of the existent ones; also devising an evolutionary algorithm to solve the proposed model.The provided data enabled the investigation of the Brazilian steel industry, and the proposed solution can be generalized to other countries to extend the supply chain simultaneously improving the economic, environmental, and social indicators.

Literature Review
In SSCM, traditional indicators are economical, environmental and social, coining the term Triple Bottom Line (TBL) as a foundation of the SSCM (Elkington, 2013).Common examples of economic indicators refer to minimizing total costs, maximizing total profit or minimizing the net present value (Barbosa-Póvoa et al., 2018).The environmental indicators include the Life Cycle Assessment (LCA) or CO2 measures (Macowski et al., 2020).The social dimension of TBL is still the least discussed in the literature (Brandenburg et al., 2014), most assessments use the number of jobs generated (Arampantzi & Minis, 2017;Zhang et al., 2019).Other metrics tend to prioritize less developed areas to locate facilities (Arampantzi & Minis, 2017), increase community services, and even donations to non-governmental organizations.
In this context involving different goals, multi-criteria decision-making methods are adequate.
Studies on SCND approaching TBL are scarce, especially in South America, which has received little attention so far (Moreno-Camacho et al., 2019;Tseng et al., 2019).The published literature has little explored the problem of planning sustainable steel chains from a broader and strategic point of view, that is, on the country level.The few studies on country-level steel CHAIN planning concentrate on a single objective, such as energy efficiency (Ates ,2015) or production efficiency (Nielsen, 2017) focusing on state planning versus market-based comparisons, which is different in scope from this study.
Table 1 and Table 2 summarize a literature review of relevant papers published in the last 10 years formulating optimization models for the SSCM, also including information of the present work to better situate it in the literature.The columns of Table 1 refer to different features presented by the formulations, as follows: 1) Multi-objective optimization (MO): methods able to create a Pareto front of nondominated solutions.In a priori methods, preference information is first asked from the decision makers and then a solution is found.In a posteriori method, a set of nondominated solutions is first found and then the decision makers must choose one of them.All models of the table have multiple objectives but some formulations use weighted sum of objectives to crate a single objective function, not being considered multi-objective in the present context.
2) Multi-level (ML): multi-level, multi-layers or multi-echelon models refers to a logistic network having multiple entities such as: suppliers, plants, distribution centers, retailers, customer zones, collection/inspection centers, among others.
Table 1 shows that most of the formulations that are able to create nondominated solutions have implemented "a priori" methods.The majority of the models are multi-layers and multiproducts but a minority are multi-period and multi-modal.All models have economical objectives with most having also an environmental objective, but few of them also have a social objective.(Khorasani &Almasifard, 2018 andKhoshfarman et al., 2023) apply "a priori" multi-objective methods while the proposed work has applied "a posteriori" method.
Table 1 and 2 shows this work provides a formulation with a broader set of relevant features when compared with others from the related literature.A Genetic Algorithm (GA) is devised to solve the proposed multi-objective SCND model using "a posteriori" method that is more efficient to explore the objective space solution when compared with "a priori" methods.The proposed model is also multi-level, multi-modal, multi-product, multi-period and multiobjective.The model provides several managerial insights for the government's top management team responsible for industry policy-making and regulation helping to build a sustainable supply chain.The following section describes the proposed mathematical formulation and metaheuristic.
Section 4 presents results for experiments analyzing trade-off scenarios considering real data from the Brazilian steel sector and managerial implications to the global steel industry.Finally, Section 5 concludes and presents future directions for this study.

Method
This is an applied, quantitative and explanatory research.In the context of Operational Research, the literature review showed there is a lack of papers proposing optimization models  7 presents its variables.Production p produced at industrial plant j in period t by route r t The sustainable steel SCND model comprises economic, environmental, and social objectives.
In doing so, the model is aligned with the Triple Bottom Line of sustainable supply chain The environment-related objective function (Equation 2) consists of (a) minimizing carbon The social-related objective function (Equation 3) comprises (a) the SVI of the city in which the industrial plant can be located, multiplied by the production in the period; (b) the SVI of the city of the DC location multiplied by the number of products it received in the period.The multiplication of SVI by production discourages industrial plants that are not producing, as these would not be positive for the city's development.
The multiple objective functions are subject to several constraints.Equation 4 The problem is NP-Hard; therefore, we adopted a metaheuristic to solve it in non-prohibitive time, modifying the popular NSGA-II support decision-making in the search for a more sustainable steel industry.

Representation and decoding
In this study, the individuals are represented by a modification of priority-based encoding (Gen et al., 2006) in which a solution consists of a chromosome of length |  +  |, where I is the set of sources and J is the set of destinations.The position of a gene represents a facility, while its value corresponds to the priority of that facility.A chromosome represented only by destinations has been used to solve supply chain problems (Kadziński et al., 2017).
This work adopted a chromosome comprised of a  * (3 + 3 + ) matrix, where J is the number of plants, K is the number of DCs, L is the number of local retailers, and T is the number  Mutation operators are used to introducing diversity into the population through the utilization of an insertion operator where a sequence of random size is removed and inserted into another position, also selected at random.Four sequences are selected: two from the facilities establishment section and two from the capacities and priorities sections.
Although mutation is important to introduce diversity into the population, it can also result in low-quality random solutions if poorly designed.In this study, the mutation probability parameter is defined dynamically, starting with a value of 0.4 and updated along the generations as the number of generations without improvement divided by the number of of the stopping criteria.Therefore, as the number of generations without improvement gets closer to the stopping criteria, the mutation probability increases, hopefully helping the algorithm to escape from a local optimum.

The multi-objective GA framework
The GA is carried out as follows: firstly, an initial population () is generated at random, where each individual in the population must be decoded and their objective function values are calculated.Secondly, the fitness of each individual is measured in terms of dominance and crowding distance.Then, a binary tournament operator is used to select parents where two individuals are randomly selected from the population and the one with the best fitness value is chosen as a parent.Every two parents generate two children by crossover and, with a given probability, the offspring is submitted to mutation.Once another  individuals have been generated, they are inserted into the parent population forming a new population of size 2 * .
This new population is then classified by non-dominance, as only the  fittest individuals survive to the next generation.Initially, individuals from the first non-dominated front are added to the next population, as long as the number of individuals on the front is smaller than .The last front to be added in the new generation is classified by crowding distance, and the best individuals are selected until the remaining spots are filled, completing the new population.
As long as the maximum number of generations without improvement is not reached, this procedure is repeated, and the new population becomes the parent population.
After preliminary experiments,  was set to 100 and the algorithm is stopped when reaching 20 generations without improvement in any of the three objectives.

CHAIN
The experiments have focused its attention on scenarios from Brazil but the proposed solution can be extended to other cases.

Brazilian Case Study
Brazil is the sixth-largest greenhouse gas generator (IABr, 2018, Climate Watch, 2020), where pig iron and steel production are responsible for about 44% of the CO2 emissions of Brazilian industries (Climate Observatory, 2020).Brazil has the largest steel industrial park in South America, represented by 15 companies that operate 31 industrial plants distributed over ten states.It has 51 million tons of annual capacity and is the world's sixth-largest net steel exporter (IABr, 2021).
The Brazilian steel industry has the particularity using charcoal as a reducer in some blast furnaces.About 20% of Brazilian pig iron production uses charcoal (SINDIFER, 2019), which is an eco-efficient renewable fuel, therefore a more advantageous environmental alternative, since part of the carbon emitted in production would be captured during the growth stage of forests.Furthermore, there may be socio-environmental barriers because in some countries, like Brazil, part of the charcoal used by independent pig iron producers comes from native forests and is produced in precarious working conditions.These facts motivated this work to perform experimentations based on Brazilian data.
The experiments adopted the SVI, a social index ranging between zero and one, with zero corresponding to the ideal situation and one corresponding to the worst-case situation (IPEA, 2020) with a region having a higher level of social vulnerability in terms of urban infrastructure, human capital, income, and labor.The SVI is a comprehensive indicator and readily available for all Brazilian municipalities.To better understand the properties of the solutions returned by the algorithm, test instances with different complexity levels (small-size, a medium-size, largesize) were created and solved (Table 8).These test instances (I1, I2, I3) have different size for each one of its eight sets, comprising typical cases of the Brazilian steel industry.A link with more details of the instances is provided after Section 6.The GA was implemented in Python 3.7 and solved on an Intel Core i7-3537U processor, CPU @ 2.0 GHz, and 8GB RAM.Due to the random nature of a GA, the experiments executed the algorithm 10 times with different random seeds.Preliminary experiments trained the model to select the best parameters for population size, selections and crossover rates.

Trade-off analysis of the objective functions
Considering the conflicts among the three objectives, it is a challenge to improve one objective without deteriorating the others, therefore it is important to discuss the trade-offs.Figure 2 presents the GA results of an experiment solving the instance I3.Because there are three objectives, and two-dimension projections are more intuitive than three-dimensions, the figure shows the three combinations of 2 by 2 objectives.In Figure 2(a), the Pareto front shows that the SVI values increase with the raised CO2 emissions.The social indicator increases when more facilities are open; however, the emission level also grows.In Figure 2(b), one may note that the costs tend to be higher for lower emission scenarios.An investigation showed that the algorithm tried to improve the environmental objective (influenced by greenhouse gas emissions) by reducing the production of the plants, but the side effect was to increase the costs due to penalty payments for back-ordered demand.Figure 3 shows that the environmental OF is mostly impacted by the change from coke to planted charcoal, where the average emissions are reduced by 66.9%.The EAF route also helps to improve environmental performance, reducing average emissions by 46.6%.The results also show that the economical dimension is not severely impacted by the alternative production routes, obtaining reductions from 11.6% to 14.6%, evidencing that integrated industrial plants that adopt coke have higher production yields, contributing to higher production scenarios.
Therefore, a higher production index based on coke also contributes to a higher social index, as described in the problem definition.The three alternative routes reduced the social impact when compared to the coke production route' scenario.Adopting the native charcoal production route reduces the social index by 28.3%, the highest negative variation for the social dimension.It is useful to notice form the results that a change from coke to any of the other technologies has approximately the same economic impact, opening possibilities to find a solution benefiting the environmental and social objectives.

CHAIN
In the Brazilian steel industry, the typical transportation modes are: highways and railroads.To compare the effects in the objective functions when using one mode or the other, an experiment has been performed.The results show that when switching from railroads to roads, the economic and social values of the OFs remain virtually the same, however, it severely impacts the environment index.The resulting environmental costs increase by 526.7% (see Figure 4).
This result makes clear that the environmental objective is much more sensitive to the change of the transportation mode than the other two objectives.

Effect of changing candidate locations to open facilities
In real problems, it is common to select a set of candidate locations before running the optimization that will select the best ones.Here, an experiment is proposed to learn about how different sets of candidate locations influence the result of the optimization.In this experiment, a data base of 28 locations (municipalities) is sorted by their social vulnerability index (SVI) and then separated into four groups comprised of seven locations each.Ranging from the lowest to the highest SVI, the first group refers to locations with the lowest SVI, while the fourth group refers to locations with the highest SVI.For each group, the problem was optimized using only the locations of the respective group.Figure 5 shows the changes in the mean of the objective functions values (OF) when changing from the first group (with lowest SVI), to the other three groups, with higher SVI.The first group is used as a baseline and Figure 5 reports relative percentages.
The solution returned from the algorithm when using Group 4 as a set of candidate locations increases the social objective by 91.6% when compared to the baseline group (Group 1), as presented in Figure 5. Therefore, the result shows that the social index improves with the SVI CHAIN increase.It is also seen that the values for the economic index do not vary significantly, ranging from -1.6 to 2.6%.This study presents some delimitations concerning data and methods.We adopted only one option for the production route in steel plants, while there may be plants with more than one or a combination of different technological processes.The parameters used to quantify the environmental impact are limited to a few indicators, while a product life cycle assessment could be employed.Concerning the social index, the assumptions for selecting locations are comprised of several metrics that also incorporate qualitative aspects.In order to make the proposed model even more complete in terms of practical applications, future research may consider the inclusion of uncertainties in the model, specially regarding the product demand per time period, using Fuzzy Logic, for example.
to design sustainable supply chains, particularly about the steel industry.The existents models tackle few dimensions of the supply chain; therefore, this research developed a broader formulation (Section 3.1) comprising factories, distribution centers, local retailers, products, raw materials, transportation modes, technological routes and time-periods.The designed formulation allows the decision maker to decide where and when to open new plants and DCs, and also to change the capacity of the existent facilities; considering simultaneously the three TBL objectives.Following the creation of this formulation, it was necessary to devise a mean to solve the mathematical model; and the authors have chosen a genetic algorithm, more specifically, an algorithm based on NSGA-II, for several reasons: a metaheuristic is more suitable to solve NP-Hard problems (which is the case of the proposed formulation); it is a "posteriori" multi-objective method; it is suitable to explore non-convex search space and multi-modal equations.The next step consisted in modifying the well know NSGA-II algorithm (Sections 3.2-3.4)to incorporate the features of the studied problem, devising a representation, data structure, decoding, crossover and mutation.Finally, the mathematical model and algorithm were tested (Section 4) in instances using data from several Brazilian institutional reports; firstly, with preliminary tests to adjust the parameters of the algorithm; and then, performing specific experiments to test the algorithm and learn from the results how the CHAIN solutions found by the optimization managed simultaneously three objectives that have completely different nature.3.1 Mathematical formulationThis section describes the proposed mathematical formulation for sustainable steel network design problem.The multi-objective optimization model aims at minimizing the network operations costs, the CO2 emissions, and maximizing social well-being.Social well-being is established by setting facilities in locations with a high social vulnerability index (SVI), supporting the local community, and promoting its development.The steel production equations incorporate a cradle-to-cradle approach by considering steel production by Electric Arc Furnace (EAF) using steel scrap.The network consists of industrial plants, distribution centers (DCs), and local retailers.The steel logistics supply chain includes available transport links between the network elements, and the industrial plants acquire raw materials, like coal and charcoal, and process the products to satisfy the local retailers' demand.The finished products are sent to DCs, and then from DCs to local retailers.The entrant steel networks must consider the pre-existing competing chain and candidates' facilities locations.The candidate municipalities are set in advance considering a wide range of characteristics, such as (i) the availability of minimal infrastructure of transport; (ii) the transport modes; (iii) the distance to local retailers; (iv) the access to ports for exportation; and (v) additional qualitative characteristics which are out of scope of this work, as the presence of universities for technical support and training, and the availability of raw materials nearby.The model shows whether a facility along with its steel production route (technological process) should be established or not in the candidate location.Possible steel production routes for industrial plants comprise integrated production with coke, native charcoal, planted charcoal, and semi-integrated EAF.Unmet local retailers' demands are back-ordered and subject to a penalty.The notation and definitions of the model are given next.The steel network elements are set by  = 1, … , factories,  = 1, … ,  distribution centres,  = 1, … ,  local retailers,  = 1, … ,  finished products,  = 1, … ,  raw materials,  = 1, … ,  transportation modes,  = 1, … ,  production routes, and  = 1, … ,  time periods.Each long term trade-off scenario presents strategic planning decisions comprising the location to set industrial plants and DCs; the total capacity of each facility in each period, considering the possibility of expansion or retraction; the activation of DCs in each period; the steel production route in established industrial plants; the production volume per period for each type of finished product to be processed in each CHAIN plant; the amount of finished product transported between industrial plants, DCs, and local retailers, for each mode of transport and each period; and the amount of back-ordered demand for each finished product and each local retailer, in each period.Tables 3 to 6 describe the model parameters, and Table management.The economic indicator concerns the minimization of total network production and logistics costs.The models' environmental bottom line minimizes carbon dioxide emissions during transport and production.The social indicator maximizes social well-being by establishing facilities in areas with higher SVI.The model economic objective function (Equation 1) consists of: (a) penalty for back-ordered demand; (b) the purchase costs of raw materials; (c) the variable costs of processing the products; (d) the fixed costs of facilities operations; (e) the transport costs from DCs to local retailers and from industrial plants to DCs; (f) the fixed costs of establishing industrial plants and DCs and (g) the facilities capacity variation costs.
dioxide emissions during transportation and (b) minimizing carbon dioxide emissions in production.A COUNTRY-LEVEL MULTI-OBJECTIVE OPTIMIZATION MODEL FOR A SUSTAINABLE STEEL SUPPLY CHAIN 2 = : of periods.The J + K first genes indicate whether a facility is set, or not.DCs are set to zero if they are not established, and to one otherwise.Industrial plants also receive zero, in case they are not established, otherwise, they receive an integer between 1 and R, where R is the set of possible production routes.The J + K following chromosomes define the facilities' capacities, where the capacity in any given period is equal to the minimum capacity if the gene value is A COUNTRY-LEVEL MULTI-OBJECTIVE OPTIMIZATION MODEL FOR A SUSTAINABLE STEEL SUPPLY CHAIN zero and equal to the maximum if its value is one.For intermediate values, the capacity is obtained by multiplying the gene's value by the difference between the maximum and minimum capacities and adding the result to the minimum capacity.The remainder part of the chromosome is a priority-based representation to determine product flow, and each row represents one period.Figure 1 shows an example of the representation for an instance of two plants, three production routes, three DCs, 4 local retailers, and 2 periods.

Figure 2 :
Figure 2: Two-dimension projections for the GA results.(a) Environmental vs. Social; (b) Environmental vs. Economic and (c) Economic vs. Social decisions dimensions

Figure 3 :
Figure 3: Effects in each OF when production route switches from the coke route to each of the other three production route.

Figure 4 :
Figure 4: Effects in each OF when transport mode switches from railroad to roads.

Figure 5 :
Figure 5: Effects in each OF when candidate municipalities are changed.Still, in Figure5, it is seen that Groups 3 and 4 show an increase in the environmental dimension.Group 3 contains a city that is not accessible by rail, resulting in an increase in CO2 emissions due to the use of roads.Additionally, the separation of groups by SVI rank creates a concentration of municipalities in a single region, for instance, the most vulnerable cities are in the North and Northeast regions of Brazil.Nevertheless, local retailers remain scattered throughout the national territory, which results in greater travel distances, increasing CO2 emissions.Therefore, we carried out an additional analysis considering two groups of four municipalities.The first group contains the municipalities with the lowest SVI and the second group with the highest SVI municipalities for each of the four regions considered (Figure6).

Figure 6 :
Figure 6: OF variation when municipalities group switches from groups.The second analysis (Figure6) shows that switching from the location of facilities on the low to locating steel plants in the high SVI group results in a social index increase, with a lower variation in the other dimensions, favoring the establishment of facilities in the most vulnerable municipalities.

Table 1 :
Literature classification based on problem features for the SSCM PaperMO ML MP MPR MM Ec.En .SProd.

LEVEL MULTI-OBJECTIVE OPTIMIZATION MODEL FOR A SUSTAINABLE STEEL SUPPLY CHAIN
integer linear programming (MILP) and then applying ε-constraint multi-objective method to generate a Pareto Front.Because this method creates linear combinations of the objective functions it is considered a "a priori" method; and these combinations have the limitation of building a set of nondominated solution only in a convex objective function space.It seen that

Table 3 :
Market, production, and logistics parameters

Table 4 :
Environmental parameters

Table 5 :
Social parameters

Table 6 :
Economic parameters

Table 7 :
Model variables Decision whether a plant j is established with route r or not --  Decision indicating whether DC k is established or not - ensures that local retailer demand in period t must be met or back-ordered.to19 are constraints to model the flow of products over the distribution elements of the steel supply chain.Equation 20 states that the back-ordered demand in period zero is null, i.e., at the beginning of the planning horizon, there is no back-ordered demand.

Table 8 :
Set size for each instance.A