A Sustainable Location Model of Transshipment Terminals Applied to the Expansion Strategies of the Soybean Intermodal Transport Network in the State of Mato Grosso, Brazil

Abstract

The transport system is one of the main bottlenecks of the world’s largest producer and exporter of soybeans, Brazil. Long-distance truck transportation of grains increases costs, food waste, and CO${}_2$ emissions. To handle these problems, the Brazilian government seeks to expand the transportation system through the national transport logistics plan (PNLT), promoting efficient operations. Collaborating on the environmental aspect, this paper proposes sustainable logistic infrastructure for soybean transportation. Investigating the largest grain-producing state in the world, Mato Grosso (Brazil), we show the optimal location for capacitated transshipment terminals untangling the relationship between logistics and sustainability. Besides handling cargo truck costs and CO${}_2$ emission, the optimization model considers cities, road distances, transshipment terminals existents, terminals capacities, implementing costs, and locations near waterways and railways. In five scenarios with different combinations of waterways and railways, we contrast the cost of installing terminals and the total road distance traveled under different weights for the environmental components. The results indicate that it is possible to simultaneously obtain the minimum cost of installing transshipment terminals and to reduce emissions by 20% in all analyzed scenarios. We conclude that obtaining strategic solutions at lower costs can be combined with proper environmental responsibility. As contributions, the results allow for advances in the area of sustainable logistics, encouraging the development of new research in Brazil involving the dimensions of sustainability. In addition, the study supports the government’s strategic decisions regarding ongoing discussions on expanding the intermodal soy transport network in the country.

1. Introduction

Agribusiness is one of the quickest emerging markets today. Commonly known as the granary of the world, Brazil has stood out as the leader of exports of agricultural products [1]. Soybean is one of the crops with the greatest impact on agribusiness [2]. Kamali et al. [3] emphasized that soybean production plays a crucial role in the development of agriculture, making it the most important commodity of Brazilian agribusiness.

In terms of the expansion of soybean, Reenberg and Fenger [4] noticed that the global area of land devoted to soybean production has been increasing significantly for decades. This view is also reinforced by Schaffer-Smith et al. [5], which confirm that this increase is due to global demand. Consequently, these authors emphasize that the main reason for the increase is exponential population growth. Thus, both soybean and its derivatives have become the strategic target for agribusiness.

According to the National Supply Company (CONAB) [6], Brazil has emerged as one of the largest soybean exporters in the world. As stated by the Food and Agriculture Organization (FAO) [7] and Statistics Division of Food and Agriculture Organization of the United Nations (FAOSTAT) data, in 2016, Brazil was the second largest producer of soybeans in the world, the third largest producer of maize, and ninth in world production of rice. The Organisation for Economic Co-operation and Development OECD and FAO [8] report indicates that soybean production will continue to grow in the next decade, and further expansion of land use for soybean is projected at the expense of pastures. Coradi et al. [2] attested that, until 2019, Brazil ranked second in the world for soybean production. Therefore, it was already a potential supplier for global sourcing. As reported by the authors, soybean has an expanding and demanding market due to population growth.

Although the United States of America (USA) assumed this position as the main producer of soybeans, at world levels, Brazilian soybeans also stood out in exports. In general, the impact is more than 40% of the world market, together with the USA and Argentina [9]. In the 2020 scenario, referring to the 2019/2020 harvest, which reached levels above 123 million tons of harvested soybeans, Brazil once again led the ranking of soybean-producing countries as the world’s largest producer due to the American drop during the period, as stated in a survey by the United States Department of Agriculture [10]. From there, in 2020, Brazil assumed global leadership. Although China was the birthplace of soybeans thousands of years ago and is historically an exporter of grain, as Sun et al. [11] claims, this country was surpassed by the USA. Reenberg and Fenger [4] reported that the US has overtaken China with a dominant export system. China, in this context, started to import soybeans. According to Schaffer-Smith et al. [5], imports from China, during that period, already corresponded to 50% of global exports.

Amaral et al. [12] showed that Brazil has been facing diversities in terms of transporting increasing volumes of production each year, from within the country to the port terminals located on the coast. Soybean production is concentrated in the state of Mato Grosso. About 46% of Brazilian grain production, including corn, is concentrated in the Midwest region, in the states of Mato Grosso, Mato Grosso do Sul, and Goiás [13]. Only with an efficient infrastructure of transport services was it possible to guarantee a better operationalization of logistics, in the movement of products from the soybean complex, from the production site to the customs facilities (spaces delimited by the customs authority: ports, airports, and border points, whose purpose is to control the movement, storage and customs clearance of goods destined or coming from abroad [14]) [15].

It is worth remembering that the biggest obstacle in Brazil to the advancement of the agribusiness sector is included in the infrastructure for the movement and flow of agricultural products. Fearnside [16] addressed this same aspect when dealing with long-term plans for Brazilian infrastructure. Added to this, the lack of public investment policies in the sector and the few optimization studies in the area that allowed for exploring strategic decisions contribute negatively to this scenario. It should be noted the agribusiness sector plays a major role in the Brazilian economy, either due to its significant contribution to the trade balance or the budget surplus index for the country [17]. For this reason, the relevance of the article is highlighted. After all, it is understood that aspects related to infrastructure and logistics generate great impacts on the efficiency and economy of a developing country. The studies by Crainic et al. [18] Manerba et al. [19] deal with the new concept of synchromodal logistics, bringing suggestions for modeling logistical problems with an emphasis on sustainable efficiency. These environmental concerns are pointed out in [20,21,22]. Proposals such as Manerba et al. [23] and Rentschler et al. [24] are viable for directing medium and long-term applications in the case of Brazilian soybean logistics.

Given the logistical difficulties faced by Brazil in its logistics systems pointed out in Wanke and Fleury [25], Branco et al. [26], Fajardo [27], the objective of this article is to propose an optimization model directed to the expansion strategies of the intermodal soybean transport network in the state of Mato Grosso to promote better product flow to exportation. The mathematical model allows for the location and dimensional analysis of transshipment terminals in the state, taking into account aspects of prioritization of modal implementation, costs, and emission of CO${}_2$. This investigation uses approximate real-world data to contrast the cost of installing the terminals, the total road distance traveled, and the environmental component under five scenarios. This paper presents new evidence regarding the trade-off between emissions and economic efficiency in logistic agribusiness settings. It is believed that, with the georeferencing of the data and the understanding of the dynamics of the geographic system of soybean export together with governmental structuring projects, the mathematical model is capable of providing subsidies to aid in strategic decision-making. The results obtained from the proposed model make it possible to improve studies on the best routes for the transport of soybeans from the location of transshipment terminals, such as those proposed by [28,29,30,31,32]. Additionally, the proposed mathematical model can be used in similar situations in other countries, with due adjustments in the input data.

To better address the topic under study, we have organized the paper as follows: Section 2 presents a literature review with a brief discussion about the importance of soybean in Brazilian logistic systems and summarizes the location approaches and environmental emissions assessment in logistic systems. Section 3 describes the case study, assumptions considered, and mathematical model proposed for the location of transshipment terminals. Section 4 presents the results of the case study with different scenarios. These solutions created show the trade-off between the economic and environmental criteria, presents in Section 5. Lastly, Section 6 highlights the conclusions and presents some recommendations for future works.

2. Literature Review

Brazil is one of the leading food suppliers in the world [1]. The country’s agribusiness sector accounts for 27% of the national GDP [33]. Moreover, soybean champions production value [34] and exports (40% of Brazilian agribusiness) [35], being the most prominent crop in the country. Calil and Ribera [1] argued that expansion to the Midwest helps explain Brazil’s agricultural success, especially the country’s leadership in world soybean production and exports.

Mato Grosso tops soybean production with 32% of the national output, with 41.5K tons in 2022 [36]. However, the state in the Midwest suffers logistical challenges in addition to being far from urban centers and ports [12]. Long-distances truck transportation of grains increases costs, food waste, and CO${}_2$ emissions. To handle these problems, the Brazilian government seeks to expand the transportation system through the National Logistic Plan [37]. Nonetheless, there is a relative paucity of empirical research focusing on green logistics for agri-food systems to support such policy decisions. Even fewer investigations explore the role of transshipment terminals in developing countries where agriculture is the main economic activity.

According to Confederação Nacional do Transporte [38], the main role of the transport service is to promote the mobility of people, inputs, and goods and to allow access to markets. Therefore, it is an essential part of a country’s economy. When there are efficiency problems due to limitations and a lack of infrastructure, the country’s socioeconomic development is compromised. In this context, an efficient transport network is necessary. Confederação Nacional do Transporte [38] also claims that there are several advantages to having an adequate transport system: lower operating costs; accident reduction; shorter travel time; access options to destinations; reduction in environmental impacts; and lower fuel costs.

Wanke and Fleury [25] explain that the Brazilian transport sector has structural problems, largely due to the lack of integrated development planning, which substantially compromises the country’s economic and social development. This points to a need for investments in infrastructure, whether in expansion, implementation, or even optimization of operations, aiming at multimodality and intermodality. Multimodality, as mentioned by Martins [39], is a possible way to reduce logistics costs.

According to Confederação Nacional do Transporte [38], the drop in the number of federal public investments in transport infrastructure is remarkable, as seen in Figure 1. The direction of the investment budget is unstable and ends up harming the transport system, especially for long-term planning.

According to Coradi et al. [2] (p. 2), Brazil has faced problems in the agricultural sector concerning soybeans. “The production in the country is greater than the static storage capacity”. In this sense, Chen et al. [40] already stated that the lack of storage units aggravates the problem since the producers were forced to reduce the price of their products after the harvest.

In addition, Jesus and Pereira [15] (p. 324) argue that “because agro-industrial products have low added value, freight prices have a direct impact on the final price of agrifood products”. Pontes et al. [41] characterized the logistical problems of Brazilian exports of one of the most important national commodities, soybeans. The authors carried out extensive bibliographic research with a detailed survey of the main problems, causes, costs, and solutions for the flow of Brazilian soybeans for export. From the study, it is clear that the challenges of soybean logistics are diverse. If it is possible to achieve the resolution of the problems mentioned, Brazil will increase its international competitiveness, with reliability in delivery times and a reduction in the costs of inefficiencies in the export process.

Plaza et al. [42] (p. 750) reminded us that it is necessary to implement logistics integration centers (LIC), “both to balance the transport matrix, reducing the logistics costs involved and to increase its long-term economic efficiency”. Branco et al. [26] emphasized that infrastructure bottlenecks and low transport productivity have increased freight costs, as well as $C{O}_2$ emissions. In this sense, it is essential to implement logistics integration centers to balance the transport matrix and to increase economic efficiency. Guimarães et al. [43] showed that, for the integration structures to enable optimization of logistics costs, it is necessary to locate them in strategic points of the national territory.

According to the Food and Agriculture Organization of the United Nations (FAO) recommendations, static storage capacity should be at least 1.2 times annual production. However, the Brazilian storage capacity is 162,317.5 million tons, with a deficit of approximately 70 million tons in relation to its production ([2] (p. 2)).

The units responsible for receiving and storing the raw material play an important role in agribusiness, especially in terms of grain flow and supply policy [44]. Caixeta-Filho [45] argues that, in the commodities sector, storage is crucial not only to reduce losses and conserve products but also to be a strategic resource during off-season periods, when prices fluctuate for products.

Plaza et al. [42] stated that Brazilian efficiency in the transport sector is low, which has an impact on trade relations. The logistics cost is equivalent to 10.6 to 15.4% of the value of the product, while that of the United States is 8.5%. In this regard, the hypothesis that inefficient transport management is one of the obstacles that hinder the development of Brazilian agribusiness is confirmed [46,47].

Caixeta-Filho and Pera [48] pointed out that Brazil’s competitive advantages and productive gains tend to be lost as its agricultural products go through the various post-harvest stages, mainly due to bottlenecks and logistical deficiencies. The research proposed by the authors aims to adapt indicators and mitigation strategies derived from research in the USA to reduce post-harvest losses, mainly in grain transport, and to make this information available in Brazil.

Pontes et al. [41] characterized the logistical problems of the brazilian exports of one of the most important national commodities, soybeans. The authors carried out extensive bibliographic research with a detailed survey of the main problems, causes, costs, and solutions for the flow of the Brazilian soybeans for export. From the study, it is clear that the challenges of soybean logistics are diverse. If it is possible to achieve the resolution of the problems mentioned, Brazil will increase its international competitiveness, with reliability in delivery times and a reduction in the costs of inefficiencies in the export process.

The Brazilian Infrastructure Department [49] emphasizes that “the state of Mato Grosso, the largest producer of soybeans, deserves top-quality logistics to meet the needs of agribusiness and take account of the region’s production potential”. Fajardo [27] attested that the Midwest region is promising in terms of possibilities for expanding the plantation area and productivity per hectare. The author reported the need to improve the logistical structure of flow given the expected growth of the soybean production sector since that time. In addition, there is also a highlight of growth facing the interior of the country, which makes it difficult to flow to the ports.

Several facility location problems are available in the literature since this approach is essential for both the public and private sectors. As far as the public sector is concerned, the problems with this approach are effective, for example, to find the best places to install health centers, hospitals, and police stations [50,51,52]. In the private sector, however, a facility location approach can be created to find the best locations for warehouse or factory facilities [53,54]. Additionally, in the literature, there are approaches to facility location problems that take into account environmental criteria, such as the works of Mohammadi et al. [55], who proposed a mathematical model for locating sustainable hubs; Sedehzadeh et al. [56], who provided a multi-objective model to design a tree-hub network, which allows for the calculation of the total cost and energy consumption; and Tang et al. [57], which presented a multi-objective model for the location of facilities applied to the planning of the private sector, with an analysis of the trade-off between cost, CO${}_2$ emission, and level of service in decisions.

A model that minimizes total transport costs using logistical integrator terminals is presented in [58]. The proposal makes it possible to combine different demands for the same product but does not address the particular requirements between the regions of production and consumption. In Guimarães et al. [43], facility location models were applied to determine the ideal location of logistical integrator centers, explicitly imposing peer demands, with an approximation to economic reality. In Almeida et al. [59], the application of a mathematical model of linear programming was observed to assist in the decisions of soybean flow and location of intermodal terminals. Based on a secondary database and considering the main soybean-producing and moving states, they proposed three drainage networks, with different coverage areas. In each one of them, there is the possibility of using railroads still under construction or in the project. The results of the computational experiments indicate flows and locations of terminals compatible with reality. In addition, other network scenarios were also investigated, demonstrating the analysis capability of the developed optimization tool.

Guimarães [46] and Plaza et al. [42] proposed mathematical modeling for the location allocation of logistics integration centers (LICs) in which economic and environmental criteria are considered. Through the weighted sum technique, the author dealt with the problem of minimizing logistical costs in the export of soybeans, soybean meal, corn, and sugar. As a result, she stated that the model developed is useful as a tool to support governmental strategic planning, as it is capable of indicating the ideal locations for the implementation of LICs, mitigating logistical costs, and CO${}_2$ emissions in the decision-making process.

A review of articles on the facility location problem can be found in [60,61,62,63,64]. In the study by Guimarães et al. [60], the authors highlight the few approaches to the subject and an opportunity for publications that include the environmental dimension to mathematical models and for expansion in company–university–government collaboration. Zanjirani Farahani et al. [61] provided a collection of papers on multicriteria facility location problems that are organized into three categories: bi-objective, multi-objective, and multi-attribute. Melo et al. [62] also addressed a literature review of facility location models in situations where supply chain management is known. Studies and applied models have discussed the integration of location decisions in conjunction with other decisions relevant to the design of a supply chain network. Alumur Alev and Kara [63] reviewed more than 100 studies that deal with or are related to the problem of locating network hubs. In Owen and Daskin [64], the stochastic or dynamic characteristics of facility location problems were explored in works that make up a literature review. From the review studies noted here, it appears that the economic approach is far more common in modeling facility location problems than an environmental and economic approach.

The model presented in Section 3 fits into the opportunity gap highlighted by Guimarães et al. [60] and the literature reviews studies by Zanjirani Farahani et al. [61], Melo et al. [62], Alumur Alev and Kara [63], and Owen and Daskin [64], in the trade-off of economic and environmental sustainability, as it has characteristics that can be easily applied in strategic decision making. The paper also fits into other opportunity gaps, such as the lack of works in the literature with the application of georeferenced optimization in the largest soy-producing state in the world, the absence of a statistical model to designate costs of implantation of grain terminals in Brazil, and few studies that present models directed to Brazilian logistic problems. Furthermore, the results obtained from the proposed model allow for directing the studies of alternative routes for grain flow from a sustainable transshipment terminal location to terminals such as those in [28,29,30,31,32]. The proposed mathematical modeling differs from those of Costa et al. [58], Guimarães [46], Plaza et al. [42], Oliveira and Caixeta-Filho [65], Dwivedi et al. [66], Mogale et al. [67], and Oliveira et al. [68] as it aims to minimize the costs of implementing transshipment terminals, including the treatment of strategic cities according to their potential for implementing waterway and railway modal, in addition to being able to mitigate possible costs related to the emission of CO${}_2$, thus reducing the total road distance traveled. It should be noted that the main objective of the strategic location of transshipment terminals in the state of Mato Grosso corroborates the Brazilian government’s transport expansion strategies, in the sense of promoting efficiency in intermodality with a cost reduction. This measure allows for directing the most efficient use of modal capacity, helping logistical planning, and contributing to the environment, with possible reductions in carbon emissions.

3. Case Study and Mathematical Model

The following subsections present the case study details, the hypotheses, and the mathematical model developed to address the problem.

3.1. Case Study and Assumptions

The case study begins with analyzing the soybean production scenario involving all 141 cities in the state of Mato Grosso, the largest soybean producer in Brazil. Of all the municipalities, 121 locations produced soybeans in 2020, with around 65% of all production destined for export [69]. Therefore, without loss of generality, each of the 121 cities in Mato Grosso that produced soybeans will have an equal contribution to the amount destined for export. Therefore, the amount of soybean that each city in Mato Grosso is destined for export is proportional to its production. Figure 2 below, created using Google Maps, shows a map with the geographic location of each soybean-producing and non-producing city in the state for the year 2020.

We used Microsoft API Bing Maps (Bing Maps, which is a Microsoft tool that allows you to search for road distances between cities automatically [70]) to find the road distance between the 141 cities, validating the data with Google Maps. These tools allow us to automatically find the distance between two cities, using the positional information of municipalities’ latitudes and longitudes. The consolidated results yield a matrix of dimension $141\times 141$ with road distances between each city. This information is essential for the optimization model because we adopt the maximum distance $Dmax$ from the origin to the transshipment terminal.

The Brazilian Association of Technical Standards (ABNT) NBR 14.653 provides the framework to estimate the terminals’ implementation costs. Specifically, the guidelines come from three components of NBR 14.653: general procedures (part 1 [71]), assessment of urban properties (part 2 [72]), and assessment of facilities and industries (part 5 [73]). Therefore, with market data for similar assets, we evaluated our object of study with comparative statistics.

We selected our sample to build the statistical model with data from Brazilian logistics companies that invested in constructing transshipment terminals, branches of activity, and grain storage capacity. Thus, we extracted prices and attributes to estimate the asset with real values using SisDEA software. This study is unique in the literature that works with real-world data modeling of transshipment terminal infrastructure costs in Brazil, and Equation (1) provides subsidies for future works that use this type of data.

Three attributes are independent variables (Capacity, Year, and Other) and one is a dependent variable (Unit Value). First, ‘Capacity’ represents the terminal’s grain storage capacity. Second, ‘Year’ corresponds to the transshipment terminal implementation year. Third, ‘Other’ assigns the terminals, if only for storage grains or if it includes fertilizers, sugar, and others products. Finally, the ‘Unit Value’ captures the cost of implementing a terminal per ton of soybean.

Equation (1) presents the linear regression model outcome. All variables are statistically significant (p-value below 10%) and meet the criteria for homoscedasticity and non-collinearity. Furthermore, the results align with NBR 14.653-2:2011 [72], displaying a grounding degree II.

$$\begin{array}{cc}\hfill UnitValu{e}_{Unit/Ton}=& -857031.1943+\frac{274478.0851}{\sqrt{Capacity}}\hfill \\ & +112679.5806\times ln\left(Year\right)+536.5991\times Other\hfill \end{array}$$

(1)

Equation (1) captures the inverse relationship between the cost per ton of deploying the terminal and its size, as shown in

Table 1. Terminals types (with an approximation of cost and storage capacity according to the real world).

Terminal Types	Storage Capacity (ton)	Unit Value Unit/ton. (BRL)	Total Cost (BRL Million)
T1	50,000	1839.78	92
T2	60,000	1732.83	104
T3	70,000	1649.70	116
T4	80,000	1582.70	127
T5	90,000	1527.20	138
T6	100,000	1480.25	148
T7	125,000	1388.62	174
T8	150,000	1320.97	198
T9	175,000	1268.40	222
T10	200,000	1226.03	245
T11	250,000	1161.23	290
T12	300,000	1113.40	334
T13	350,000	1076.23	377
T14	400,000	1046.26	419
T15	450,000	1021.44	460
T16	500,000	1000.44	500
T17	550,000	982.38	541
T18	600,000	966.62	580
T19	650,000	952.72	620
T20	700,000	940.34	658
T21	750,000	929.21	697
T22	800,000	919.15	735

. In other words, it indicates an economy of scale.

The Brazilian National Logistic plan [37] documents the strategic situation of cities regarding railroad development (in operation, planned, or under study) and the navigability of rivers in the region. Consequently, a table of values can translate this information into terminal installation potential for each location. The values fit the following criteria:

Waterway

• 1000—cities with no potential to install an intermodal terminal due to the absence of a river;
• 1—cities with the potential to install an intermodal terminal due to the presence of a navigable river.

Railway

• 1000—cities with no potential for installing an intermodal terminal due to the lack of planning or study of the railway route;
• 1 to 3—cities with the medium potential for installing an intermodal terminal due to the presence of studies for implementing a railway route;
• 0.3 to 1—cities with high potential for installing an intermodal terminal due to the presence of planning for implementing a railway;
• less than 0.3—cities with extreme potential for installing an intermodal terminal due to a rail route. This scale includes municipalities with terminals already in place.

The operation of a road-railway or road-waterway transshipment terminal consists of receiving trucks from the production centers, unloading them into dumpers or hoppers, storing the goods, forming batches, and loading them onto trains or barges bound for the ports of export. This process is very common in agribusiness logistics, especially in the transport of soybeans. Given these characteristics, the service provided by transshipment terminals is essential for sustainability and the reduction in logistical costs in agribusiness. In this study, we considered a refusal rate of 10% due to possible excess soy stored in the terminals. Each transshipment terminal can refuse up to 10% of the annual demand requests. Another factor that we evaluate is the storage capacity of the possible terminals implemented in the state, which will be given in tons. To represent unloading, storage, and shipment operations at the transshipment terminal, we consider the average permanence time ($TMP$) of 6 days for the product in the terminals. This information was obtained from the operational research sector of a large logistics company that operates with intermodal transshipment terminals. This value was used as a standard in all analyzed units. In addition, we adopted an average value of 77.6 g/t·km for carbon emissions on roads generated by road transport, as highlighted in [42]. This value served as a reference for the composition of the tables presented in the sensitivity analysis of the weight variation $\theta$. Finally, based on the aspects mentioned, we developed a mathematical model to deal with candidate positions for the installation of intermodal terminals. These facilities located in candidate positions and the possible flow of rail and waterway operations were also analyzed under the strategic and sustainable lens of the flow of this soy production destined for export. After understanding all the data and assumptions, we built the model, the objective function, and the restrictions, as presented in the following subsection.

3.2. Mathematical Model

This section presents the model, relying on essential data for the problem, such as distance matrix, costs related to the types of transshipment terminals, and criteria for cities with the potential to implement intermodal terminals.

Table 2. Sets and indexes of model.

Notation	Description
I	Set of soybean producing cities in the state of Mato Grosso, where $i\in I$
J	Set of candidate locations for the installation of a transshipment terminal (which may be each city in the state), where $j\in J$
S	Set of the types of transshipment terminals, according to their storage capacity, where $s\in S$

shows the sets and indexes used in the mathematical model.

Table 3. Decision variables.

Notation	Description
$x_{ij}$	1, if the production of the city $i\in I$ is directed to the terminal in $j\in J$
	0, otherwise
$y_{js}$	1, if the location $j\in J$ receives a terminal of type $s\in S$
	0, otherwise

presents the decision variables, and

Table 4. Parameters of model.

Notation	Description
$c_s$	Cost of implementing a $s\in S$ type terminal, according to its storage capacity
$\rho$	Terminal occupancy rate
$Dis{t}_{ij}$	Distance matrix between each of the cities $i\in I$ and candidate positions $j\in J$
$Dmax$	Maximum road distance traveled by producers in the city $i\in I$ to the terminal installed in the candidate position $j\in J$
$Hi{d}_j$	Vector of weights associated with preferred locations (cities) for the implementation of intermodal terminals (road to waterway), where $j\in J$
$Fe{r}_j$	Vector of weights associated with preferred locations (cities) for implementing intermodal terminals (road to railway), where $j\in J$
$PDe{m}_i$	Soybean production of the city $i\in I$ destined for export
$DemT$	Total amount of soybean exported by cities in the state of Mato Grosso in the year
$Ca{p}_s$	Terminal capacity of type $s\in S$
$TMP$	Average length in days of stay of soybeans in the terminal
$Tsaf$	Time (in days) for the duration of the soybean crop in the year
$T{E}_{js}$	Terminal already existing in a given location $j\in J$, of type $s\in S$
$\alpha$	Weight associated with the terminal installation cost component in the objective function
$\beta$	Weight associated with the waterway modal component in the objective function
$\gamma$	Weight associated with the railway modal component in the objective function
$\theta$	Weight associated with the environmental component in the objective function

describes all parameters. The following mathematical model represents the trade-offs that the decision-maker faces to solve the proposed problem.

Objective Function:

Minimize

$$\begin{array}{cc}\hfill & \alpha ·\left[UT\left(cost\right)=\left(\sum _{j\in J}\sum _{s\in S}{y}_{js}·c_s-T{E}_{js}·c_s\right)\right]\hfill \\ & +\beta ·\left[UT\left(waterway\right)=\sum _{j\in J}\sum _{s\in S}{y}_{js}·Hi{d}_j\right]\hfill \\ \hfill & +\gamma ·\left[UT\left(railway\right)=\sum _{j\in J}\sum _{s\in S}{y}_{js}·Fe{r}_j\right]\hfill \\ & +\theta ·\left[UT\left(environmental\right)=\sum _{j\in J}\sum _{i\in I}{x}_{ij}·Dis{t}_{ij}\right]\hfill \end{array}$$

(2)

Subject to:

$$\sum _{s\in S}{y}_{js}\le 1,\forall j\in J$$

(3)

$$\sum _{j\in J}{x}_{ij}\le 1,\forall i\in I$$

(4)

$$x_{ij}·Dis{t}_{ij}\le Dmax,\forall i\in I,\forall j\in J$$

(5)

$$x_{ij}\le \sum _{s\in S}{y}_{js},\forall i\in I,\forall j\in J$$

(6)

$$x_{jj}=\sum _{s\in S}{y}_{js},\forall j\in J$$

(7)

$$\sum _{i\in I}\sum _{j\in J}{x}_{ij}·PDe{m}_i=DemT$$

(8)

$$\sum _{s\in S}Ca{p}_s·y_{js}·\rho \ge \sum _{i\in I}\frac{x_{ij}·PDe{m}_i·TMP}{Tsaf},\forall j\in J$$

(9)

$$x_{ij},y_{js}\in \{0,1\}\forall i\in I,j\in J,s\in S$$

(10)

Equation (2) represents the objective utility function, which provides, according to weights associated with $\alpha$, $\beta$, $\gamma$, and $\theta$, the priority control of the target dimension to be minimized. Thus, the objective function represents several functions to be minimized, each with its dimension analysis.

• $UT\left(cost\right)$: Preference in reducing the cost of terminal deployment;
• $UT\left(waterway\right)$: Preference for implantation of terminals in locations with waterway potential;
• $UT\left(railway\right)$: Preference for implantation of terminals in locations with railway potential;
• $UT\left(environmental\right)$: Lower CO${}_2$ emission preference due to reduction in road distance traveled by trucks.

Constraint (3) represents that, for each location, there can be at most 1 terminal of a specific size. Constraint (4) says that each soybean-producing municipality can only direct its production to a single terminal. Constraint (5) establishes a maximum distance that a soybean producer in the municipality i can travel to a terminal. In Constraint (6), the municipality i only sends its soybean production to a terminal at destination j if a terminal is installed in that location. Constraint (7) deals with the condition that every municipality must direct its production to a terminal installed in the same location. In Constraint (8), we have that the sum of production (storage demand for export) of the municipalities i equal to the total demand for dispatch for export. Finally, Constraint (9) says that each terminal must have enough storage capacity to meet the soybean demand directed to it.

4. Results

In the following subsections, we describe the computational experiments and the results obtained and present the implications of $\theta$ weight for each investigated scenario under economic and environmental criteria.

4.1. Computational Experiments

The computational resource was used with the following configurations: Windows 10 Home 64 bits, Intel(R) Core(TM) i7-10510U processor, 8 GB of RAM, and 256Gb SSD. First, the mathematical, optimization model was developed in Python(Open-source) version 3.8.5 using the Gurobi solver (academic license) to point out which would be the candidate positions for the installation of the intermodal terminals, according to the demand of loads throughout the state. Then, in SisDea (own license), the data were processed to obtain the linear regression equation that supports the table of values of terminals’ implantation costs in line with their storage capacity.

4.2. Scenarios Results

We calculate the results regarding the location of transshipment terminals for the Mato Grosso state in five scenarios, following the mathematical model of Section 3.2. The scenarios primarily analyze the decision-making scope, involving financial costs related to implementing terminals and to reducing the total road distance traveled, focusing on CO${}_2$ emissions reductions.

For each scenario, we show the location position of each transshipment terminal on the map and to report the results for three assumptions: no environmental concern (initial result, $\theta =0$), moderate environmental concern (intermediate result, $\theta =0.4$), and high environmental concern (Final result, $\theta =0.8$). Additionally, below the maps, the chart displays the static storage capacity of the terminals and the annual soybean demand destined for it. Cities are represented in numbers (full names in

Table A1. Cities names, production, and share of soybean exports—Mato Grosso.

#	City	Prod. (ton.)	Prod. (%)	Exported Total (ton.)
1	Água Boa	528,000	1.64%	331,258
2	Alta Floresta	92,156	0.29%	57,817
3	Alto Araguaia	122,696	0.38%	76,977
4	Alto Boa Vista	87,180	0.27%	54,695
5	Alto Garças	287,299	0.89%	180,247
6	Alto Paraguai	21,000	0.07%	13,175
7	Alto Taquari	162,464	0.50%	101,927
8	Araguaiana	8201	0.03%	5145
9	Araguainha	2244	0.01%	1408
10	Arenápolis	7500	0.02%	4705
11	Aripuanã	4680	0.01%	2936
12	Barra do Bugres	4040	0.01%	2535
13	Barra do Garças	83,267	0.26%	52,240
14	Bom Jesus do Araguaia	367,948	1.14%	230,844
15	Brasnorte	772,800	2.40%	484,842
16	Cáceres	39,287	0.12%	24,648
17	Campinápolis	104,400	0.32%	65,499
18	Campo Novo do Parecis	1,276,800	3.96%	801,043
19	Campo Verde	673,920	2.09%	422,806
20	Campos de Júlio	667,590	2.07%	418,835
21	Canabrava do Norte	91,942	0.29%	57,683
22	Canarana	874,500	2.71%	548,647
23	Carlinda	37,768	0.12%	23,695
24	Chapada dos Guimarães	104,000	0.32%	65,248
25	Cláudia	355,736	1.10%	223,183
26	Cocalinho	33,482	0.10%	21,006
27	Colíder	50,644	0.16%	31,773
28	Comodoro	254,400	0.79%	159,606
29	Confresa	145,080	0.45%	91,021
30	Conquista D’Oeste	21,103	0.07%	13,240
31	Cotriguaçu	936	0.00%	587
32	Denise	10,156	0.03%	6372
33	Diamantino	1,138,500	3.53%	714,276
34	Dom Aquino	112,320	0.35%	70,468
35	Feliz Natal	471,960	1.46%	296,100
36	Gaúcha do Norte	666,600	2.07%	418,214
37	General Carneiro	179,860	0.56%	112,841
38	Guarantã do Norte	41,580	0.13%	26,087
39	Guiratinga	227,700	0.71%	142,855
40	Ipiranga do Norte	686,400	2.13%	430,636
41	Itanhangá	279,000	0.87%	175,040
42	Itaúba	149,424	0.46%	93,746
43	Itiquira	594,000	1.84%	372,666
44	Jaciara	141,000	0.44%	88,461
45	Jangada	2636	0.01%	1654
46	Juara	140,800	0.44%	88,336
47	Juína	27,360	0.08%	17,165
48	Juruena	1650	0.01%	1035
49	Juscimeira	85,860	0.27%	53,867
50	Lambari D’Oeste	3402	0.01%	2134
51	Lucas do Rio Verde	789,600	2.45%	495,382
52	Luciara	1908	0.01%	1197
53	Marcelândia	201,500	0.62%	126,418
54	Matupá	135,300	0.42%	84,885
55	Mirassol d’Oeste	13,748	0.04%	8625
56	Nobres	132,217	0.41%	82,951
57	Nortelândia	81,120	0.25%	50,893
58	Nossa S, do Livramento	1896	0.01%	1190
59	Nova Bandeirantes	192	0.00%	120
60	Nova Brasilândia	35,476	0.11%	22,257
61	Nova Canaã do Norte	146,267	0.45%	91,765
62	Nova Guarita	41,400	0.13%	25,974
63	Nova Lacerda	66,040	0.20%	41,432
64	Nova Marilândia	56,760	0.18%	35,610
65	Nova Maringá	648,000	2.01%	406,544
66	Nova Monte Verde	4527	0.01%	2840
67	Nova Mutum	1,322,580	4.10%	829,765
68	Nova Nazaré	49,500	0.15%	31,055
69	Nova Santa Helena	79,464	0.25%	49,854
70	Nova Ubiratã	1,275,357	3.96%	800,138
71	Nova Xavantina	195,000	0.60%	122,340
72	Novo Horizonte do Norte	13,440	0.04%	8432
73	Novo Mundo	138,600	0.43%	86,955
74	Novo Santo Antônio	5406	0.02%	3392
75	Novo São Joaquim	196,638	0.61%	123,367
76	Paranaíta	28,451	0.09%	17,850
77	Paranatinga	795,600	2.47%	499,146
78	Pedra Preta	224,278	0.70%	140,708
79	Peixoto de Azevedo	92,800	0.29%	58,221
80	Planalto da Serra	81,589	0.25%	51,188
81	Poconé	26,669	0.08%	16,732
82	Pontal do Araguaia	2940	0.01%	1845
83	Ponte Branca	353	0.00%	221
84	Pontes e Lacerda	72,376	0.22%	45,407
85	Porto Alegre do Norte	112,530	0.35%	70,599
86	Porto dos Gaúchos	589,380	1.83%	369,767
87	Porto Esperidião	7965	0.02%	4997
88	Poxoréu	207,360	0.64%	130,094
89	Primavera do Leste	842,400	2.61%	528,508
90	Querência	1,101,600	3.42%	691,125
91	Ribeirão Cascalheira	297,000	0.92%	186,333
92	Ribeirãozinho	67,106	0.21%	42,101
93	Rondonópolis	272,000	0.84%	170,648
94	Rosário Oeste	87,524	0.27%	54,911
95	Salto do Céu	6732	0.02%	4224
96	Santa Carmem	400,200	1.24%	251,079
97	Santa Cruz do Xingu	127,530	0.40%	80,010
98	Santa Rita do Trivelato	499,200	1.55%	313,190
99	Santa Terezinha	74,357	0.23%	46,650
100	Santo Afonso	46,200	0.14%	28,985
101	Santo Antônio do Leste	299,880	0.93%	188,140
102	Santo Antônio do Leverger	77,490	0.24%	48,616
103	São Félix do Araguaia	830,141	2.57%	520,817
104	São José do Rio Claro	381,600	1.18%	239,409
105	São José do Xingu	306,720	0.95%	192,431
106	São José dos Q, Marcos	7722	0.02%	4845
107	São Pedro da Cipa	7200	0.02%	4517
108	Sapezal	1,192,800	3.70%	748,343
109	Serra Nova Dourada	19,398	0.06%	12,170
110	Sinop	526,949	1.63%	330,599
111	Sorriso	2,141,700	6.64%	1,343,667
112	Tabaporã	499,388	1.55%	313,308
113	Tangará da Serra	349,800	1.08%	219,459
114	Tapurah	583,200	1.81%	365,890
115	Terra Nova do Norte	57,040	0.18%	35,786
116	Tesouro	89,900	0.28%	56,402
117	Torixoréu	51,979	0.16%	32,611
118	União do Sul	195,840	0.61%	122,867
119	Vera	451,440	1.40%	283,226
120	Vila Bela da S, Trindade	91,179	0.28%	57,204
121	Vila Rica	141,750	0.44%	88,932
122	Acorizal	0	0%	0
123	Apiacás	0	0%	0
124	Araputanga	0	0%	0
125	Barão de Melgaço	0	0%	0
126	Castanheira	0	0%	0
127	Colniza	0	0%	0
128	Cuiabá	0	0%	0
129	Curvelândia	0	0%	0
130	Figueirópolis D’Oeste	0	0%	0
131	Glória D’Oeste	0	0%	0
132	Indiavaí	0	0%	0
133	Jauru	0	0%	0
134	Nova Olímpia	0	0%	0
135	Porto Estrela	0	0%	0
136	Reserva do Cabaçal	0	0%	0
137	Rio Branco	0	0%	0
138	Rondolândia	0	0%	0
139	São José do Povo	0	0%	0
140	Vale de São Domingos	0	0%	0
141	Várzea Grande	0	0%	0
TOTAL		32,242,463	10,000%	20,228,381

, Appendix A), and the configurations adopted for the weights $\alpha$, $\beta$, $\gamma$, and $\theta$ are described below.

Scenario 1: Figure 3 summarizes the results of the preference for the railway modal. The weights adopted are decreasing cost component $\alpha$, ranging from 0.8 to 0; waterway modal component $\beta$ = 0, not considering the use of this modal; waterway modal component $\gamma$ assumes a fixed value of 0.2; and increasing $\theta$ environmental component, ranging from 0 to 0.8.

Scenario 2: Figure 4 summarizes the results of the preference for the waterway modal. The weights are decreasing cost component $\alpha$, ranging from 0.8 to 0; waterway modal component $\beta$ assumes a fixed value of 0.2; railway modal component $\gamma$ = 0, not considering the use of this modal; and increasing $\theta$ environmental component, ranging from 0 to 0.8.

Scenario 3: Figure 5 summarizes the results of the preference for the modal with 50% waterway use and 50% railway use. The weights are decreasing cost component $\alpha$, ranging from 0.8 to 0; waterway modal component $\beta$ assumes a fixed value of 0.1; railway modal component $\gamma$ assumes a fixed value of 0.1; and increasing $\theta$ environmental component, ranging from 0 to 0.8.

Scenario 4: Figure 6 summarizes the results of the preference for the modal with 75% waterway use and 25% railway use. The weights are decreasing cost component $\alpha$, ranging from 0.8 to 0; waterway modal component $\beta$ assumes a fixed value of 0.15; railway modal component $\gamma$ assumes a fixed value of 0.05; and increasing $\theta$ environmental component, ranging from 0 to 0.8.

Scenario 5: Figure 7 summarizes the results of the preference for the modal with 25% waterway use and 75% railway use. The weights are decreasing cost component $\alpha$, ranging from 0.8 to 0; waterway modal component $\beta$ assumes a fixed value of 0.05; railway modal component $\gamma$ assumes a fixed value of 0.15; and increasing $\theta$ environmental component, ranging from 0 to 0.8.

The results indicate that the proposed mathematical model that works with the aspects of implementation costs of transshipment terminals, cities with the potential for waterway/railway intermodality, and the reduction in road distance traveled with environmental repercussions allows decision-makers to develop better strategic transport plans. Furthermore, intermodal transport allows for improvements in the operation of grain logistics systems, improving their efficiency in both economic and environmental aspects. The following section discusses the variation in $\theta$ weight concerning cost and environmental criteria for each scenario.

5. Discussion of Variation of $\mathbf{\theta }$ Weight in Relation to Cost and Environmental Criteria

In this section, the effects of the variation in the weight of the environmental component $\theta$ on the cost of implementing the terminals and on the total road distance traveled are analyzed. A three-axis graph is presented to compare the economic (of the implementation cost) and the environmental commitment (with a focus on carbon emission reduction).

In Figure 8, Figure 9 and Figure 10, the variation in the weight of the environmental component $\theta$ from 0 to 0.8 for each scenario is shown on the x-axis. The left y-axis shows the cost associated with the new transshipment terminals implemented. The y-axis on the right shows the total road distance traveled to the candidate positions of the transshipment terminals in Mato do Grosso. The total distance makes it possible to obtain the amount of CO${}_2$ emitted per year from all road logistics from soybeans to the transshipment terminals.

By analyzing Figure 8, Figure 9 and Figure 10, it is possible to notice that the increase in the weight of the environmental component $\theta$ causes an increase in the total cost of implementing transshipment terminals. This effect is related to an increase in the number of terminals that must be installed, which reduces the total road distance traveled.

To analyze situations that combine the bi-criteria economic and environmental commitment, Figure 8, Figure 9 and Figure 10 have highlighted the region in light blue. This region presents solutions that can be adopted at a minimum cost and a significative reduction in the emission of CO${}_2$. The yellow line highlighted in the figures indicates the point of joint efficiency between the economic and environmental criteria. The results for each analyzed scenario are presented below.

In Figure 8, on the left, which represents scenario 1, the analysis of the highlighted light blue region allows for keeping the cost of installing new transshipment terminals at a minimum value of BRL 616 million with a reduction in emissions of CO${}_2$ by 20.7%, through the reduction of approximately 10,000 km of road traffic. To reach the yellow line, the increase in cost by BRL 134 million would lead to a further 16% reduction in the emission of CO${}_2$, according to the data in

Table 5. Scenario 1 result of the $\theta$ weight variation in relation to economic, environmental, and static storage capacity aspects.

$\mathit{\theta }$ Weight Variation	Total Cost (mi BRL)	Total Road Distance (km)	CO${}_2$ Total Emission (mi ton)	CO${}_2$ Emission Reduce (%)	Installed Static Capacited (ton)
0	616	49,189.0	77.2	0%	1,270,000
0.05	616	39,002.5	61.2	−20.71%	1,270,000
0.1	616	39,002.5	61.2	−20.71%	1,270,000
0.15	616	39,002.5	61.2	−20.71%	1,270,000
0.2	683	34,312.0	53.9	−30.24%	1,270,000
0.25	735	31,524.0	49.5	−35.91%	1,275,000
0.3	771	30,144.0	47.3	−38.72%	1,310,000
0.35	851	27,694.5	43.5	−43.70%	1,350,000
0.4	875	27,040.5	42.4	−45.03%	1,375,000
0.45	875	27,040.5	42.4	−45.03%	1,375,000
0.5	875	27,040.5	42.4	−45.03%	1,375,000
0.55	921	26,060.5	40.9	−47.02%	1,415,000
0.6	944	25,616.0	40.2	−47.92%	1,440,000
0.65	944	25,616.0	40.2	−47.92%	1,440,000
0.7	1055	23,862.5	37.5	−51.49%	1,560,000
0.75	1055	23,862.5	37.5	−51.49%	1,560,000
0.8	1102	23,249.5	36.5	−52.73%	1,560,000

. In this region of the chart, between the light blue hatch and the yellow line, each 0.01 variation in $\theta$ weight represents a 1.20% reduction in CO${}_2$ emissions and an increase of BRL 10.3 million in implementation costs of the transshipment terminals.

In Figure 8, on the right, which represents scenario 2, the analysis of the highlighted light blue region allows for a slight variation in the cost of installing new transshipment terminals at a value of BRL 685 million with a reduced emission of CO${}_2$ by 28.4%, through the reduction of approximately 12,700 km of road traffic. To reach the yellow line, a cost increase of BRL 175 million would lead to a further 17% reduction in the emission of CO${}_2$, according to the data in

Table 6. Scenario 2 result of the $\theta$ weight variation in relation to economic, environmental, and static storage capacity aspects.

$\mathit{\theta }$ Weight Variation	Total Cost (mi BRL)	Total Road Distance (km)	CO${}_2$ Total Emission (mi ton)	CO${}_2$ Emission Reduce (%)	Installed Static Capacited (ton)
0	668	44,763.0	70.3	0%	1,270,000
0.05	668	33,773.5	53.0	−24.55%	1,270,000
0.1	668	33,773.5	53.0	−24.55%	1,270,000
0.15	685	32,058.5	50.3	−28.38%	1,275,000
0.2	685	32,058.5	50.3	−28.38%	1,275,000
0.25	747	29,055.0	45.6	−35.09%	1,285,000
0.3	771	28,176.0	44.2	−37.06%	1,310,000
0.35	839	26,039.0	40.9	−41.83%	1,335,000
0.4	969	22,662.5	35.6	−49.37%	1,360,000
0.45	995	22,065.5	34.6	−50.71%	1,390,000
0.5	995	22,065.5	34.6	−50.71%	1,390,000
0.55	1064	20,771.0	32.6	−53.60%	1,420,000
0.6	1064	20,771.0	32.6	−53.60%	1,420,000
0.65	1108	20,059.5	31.5	−55.19%	1,420,000
0.7	1108	20,059.5	31.5	−55.19%	1,420,000
0.75	1233	18,302.5	28.7	−59.11%	1,500,000
0.8	1400	16,160.5	25.4	−63.90%	1,640,000

. In this region of the chart, between the light blue hatch and the yellow line, each 0.01 variation in $\theta$ weight represents a 1.05% reduction in CO${}_2$ emissions and an increase of BRL 14.2 million in implementation costs of the transshipment terminals.

In Figure 9, on the left, which represents scenario 3, the analysis of the highlighted light blue region allows for keeping the cost of installing new transshipment terminals at a minimum value of BRL 668 million with a reduction in emissions of CO${}_2$ by 23.5%, through the reduction of approximately 10,000 km of road traffic. To reach the yellow line, a cost increase of BRL 109 million would lead to a further 12% reduction in the emission of CO${}_2$, according to the data in

Table 7. Scenario 3 result of the $\theta$ weight variation in relation to economic, environmental, and static storage capacity aspects.

$\mathit{\theta }$ Weight Variation	Total Cost (mi BRL)	Total Road Distance (km)	CO${}_2$ Total Emission (mi ton)	CO${}_2$ Emission Reduce (%)	Installed Static Capacited (ton)
0	668	45,424.5	71.3	0%	1,270,000
0.05	668	34,687.0	54.4	−23.64%	1,270,000
0.1	668	34,687.0	54.4	−23.64%	1,270,000
0.15	668	34,745.5	54.5	−23.51%	1,270,000
0.2	685	33,375.5	52.4	−26.53%	1,275,000
0.25	685	33,366.5	52.4	−26.55%	1,275,000
0.3	735	30,807.0	48.4	−32.18%	1,275,000
0.35	777	29,269.5	45.9	−35.56%	1,325,000
0.4	777	29,289.0	46.0	−35.52%	1,325,000
0.45	777	29,269.5	45.9	−35.56%	1,325,000
0.5	875	26,734.0	42.0	−41.15%	1,375,000
0.55	875	26,734.0	42.0	−41.15%	1,375,000
0.6	914	26,113.5	41.0	−42.51%	1,400,000
0.65	911	25,995.0	40.8	−42.77%	1,405,000
0.7	934	25,550.5	40.1	−43.75%	1,430,000
0.75	934	25,550.5	40.1	−43.75%	1,430,000
0.8	1068	23,535.5	36.9	−48.19%	1,530,000

. In this region of the chart, between the light blue hatch and the yellow line, each 0.01 variation in $\theta$ weight represents a 0.48% reduction in CO${}_2$ emissions and an increase of BRL 4.4 million in implementation costs of the transshipment terminals.

In Figure 9, on the right, which represents scenario 4, the analysis of the highlighted light blue region allows for keeping the cost of installing new transshipment terminals at a minimum value of BRL 668 million with a reduction in emissions of CO${}_2$ by 22.4%, through the reduction of approximately 10,000 km of road traffic. To reach the yellow line, a cost increase of BRL 112 million would result in a further 12% reduction in the emission of CO${}_2$, according to data in

Table 8. Scenario 4 result of the $\theta$ weight variation in relation to economic, environmental, and static storage capacity aspects.

$\mathit{\theta }$ Weight Variation	Total Cost (mi BRL)	Total Road Distance (km)	CO${}_2$ Total Emission (mi ton)	CO${}_2$ Emission Reduce (%)	Installed Static Capacited (ton)
0	668	44,701.0	70.2	0%	1,270,000
0.05	668	34,687.0	54.4	−22.40%	1,270,000
0.1	668	34,687.0	54.4	−22.40%	1,270,000
0.15	685	33,366.5	52.4	−25.36%	1,275,000
0.2	685	33,375.5	52.4	−25.34%	1,275,000
0.25	735	30,807.0	48.4	−31.08%	1,275,000
0.3	759	29,825.0	46.8	−33.28%	1,300,000
0.35	771	29,416.5	46.2	−34.19%	1,310,000
0.4	783	29,056.0	45.6	−35.00%	1,320,000
0.45	822	27,965.5	43.9	−37.44%	1,350,000
0.5	875	26,734.0	42.0	−40.19%	1,375,000
0.55	911	25,995.0	40.8	−41.85%	1,405,000
0.6	934	25,550.5	40.1	−42.84%	1,430,000
0.65	934	25,550.5	40.1	−42.84%	1,430,000
0.7	934	25,550.5	40.1	−42.84%	1,430,000
0.75	1056	23,674.0	37.2	−47.04%	1,520,000
0.8	1068	23,535.5	36.9	−47.35%	1,530,000

. In this region of the chart, between the light blue hatch and the yellow line, each 0.01 variation in $\theta$ weight represents a 0.42% reduction in CO${}_2$ emissions and an increase of BRL 3.8 million in implementation costs of the transshipment terminals.

In Figure 10, which represents scenario 5, the analysis of the highlighted light blue region allows for keeping the cost of installing new transshipment terminals at a minimum value of BRL 668 million with an emission reduction in CO${}_2$ by 20.5%, through the reduction of approximately 10,000 km of road traffic. To reach the yellow line, a cost increase of BRL 103 million would lead to a further 13% reduction in the emission of CO${}_2$, according to the data in

Table 9. Scenario 5 result of the $\theta$ weight variation in relation to economic, environmental and static storage capacity aspects.

$\mathit{\theta }$ Weight Variation	Total Cost (mi BRL)	Total Road Distance (km)	CO${}_2$ Total Emission (mi ton)	CO${}_2$ Emission Reduce (%)	Installed Static Capacited (ton)
0	668	45,287.0	71.1	0%	1,270,000
0.05	668	35,982.0	56.5	−20.55%	1,270,000
0.1	668	35,982.0	56.5	−20.55%	1,270,000
0.15	668	35,982.0	56.5	−20.55%	1,270,000
0.2	685	34,555.5	54.2	−23.70%	1,275,000
0.25	735	31,647.0	49.7	−30.12%	1,275,000
0.3	759	30,616.0	48.1	−32.40%	1,300,000
0.35	777	30,040.0	47.2	−33.67%	1,325,000
0.4	789	29,692.5	46.6	−34.43%	1,335,000
0.45	875	27,391.0	43.0	−39.52%	1,375,000
0.5	875	27,391.0	43.0	−39.52%	1,375,000
0.55	911	26,611.0	41.8	−41.24%	1,405,000
0.6	934	26,166.5	41.1	−42.22%	1,430,000
0.65	934	26,166.5	41.1	−42.22%	1,430,000
0.7	988	25,302.5	39.7	−44.13%	1,490,000
0.75	1068	24,115.5	37.9	−46.75%	1,530,000
0.8	1068	24,115.5	37.9	−46.75%	1,530,000

. In this region of the chart, between the light blue hatch and the yellow line, each 0.01 variation in $\theta$ weight represents a 0.66% reduction in CO${}_2$ emissions and an increase of BRL 5.5 million in implementation costs of the transshipment terminals.

The sensibility analysis of $\theta$ weight variation in each scenario indicates regions of economic efficiency combined with better CO${}_2$ emission rates. The percentages obtained in the reduction in CO${}_2$ emissions are close to the results by [26,54]. Thus, as it is strategically positioned close to the regions with the greatest potential for intermodality according to [37], the installation of transshipment terminals considerably reduces truck traffic, generating the lowest cost per operational kilometer of road transport. From a managerial point of view, these results allow decision-makers to implement actions that combine economic and environmental sustainability. In addition, it fills gaps in the studies of Garcia et al. [28], Melo et al. [29], Lopes et al. [30], Oliveira and Cicolin [31], and Zucchi et al. [32], as it allows for a search for more efficient routes for the export of soy from the state of Mato Grosso from strategically positioned transshipment terminals.

6. Conclusions

The article presented a model for the localization of capacitated transshipment terminals that can be applied to the expansion strategies of the intermodal soybean transport network in Mato Grosso, the largest grain-producing state in Brazil. The mathematical model considers a possible multi-modal transport network [37], treating several variables of interest, such as all soybean-producing cities in the state, the actual road distances between cities, the existing transshipment terminals and their capacities, the terminal implementation costs, candidate locations near waterways, and railways that benefit intermodality. Furthermore, all location data were treated in a georeferenced way. The results obtained by the model can help in decision-making that reduces costs of implementing logistic structures and environmental concerns since it allows for working with weights that benefit conditions predetermined by the decision maker. The solutions show that in all scenarios, it is possible to reduce at least 20% of the emission of CO${}_2$ while maintaining the lens of a minimum cost of infrastructure deployment.

The sensibility analysis of $\theta$ weight variation made it possible to obtain boundaries comparing the cost of installing transshipment terminals and the total road distance traveled to reach them. The charts illustrate that, after a particular value of the $\theta$ environmental component, the implementation costs are very high, to the detriment of the gain of reducing the total road distance traveled and reducing the emission of CO${}_2$. In these graphs, regions whose variations in the costs of implementing the infrastructure and the total distance traveled for each analyzed scenario can be promising for an economic and environmental decision are highlighted.

The results presented here make it possible to generate advances in sustainable logistics in the largest soy-producing state in the world, encouraging the development of more research involving the dimensions of sustainability, according to the challenges pointed out in [74,75]. Thus, we can conclude that it is possible to obtain strategic solutions with lower costs in the logistics system with due environmental responsibility.

This study is limited to the problem of locating and allocating capacity for transshipment terminals in the state of Mato Grosso, using actual government data and the 2020 soybean crop. Studies on the navigability of certain rivers are recommended to refine and improve the possible location of transshipment terminals in the localities.

As possible advances, we propose to evaluate the behavior of each transshipment terminal over a harvest period, assessing the need for possible expansions of its capacity. Such studies can be conducted using stochastic simulation models. We also indicate the study of the flow of soybeans from the proposed new transshipment terminals to the exporting maritime terminals, dealing with the transport capacities and particularities of each modal to the exporting seaport. Finally, applications of the proposed model in evaluations of Brazilian macro-regions and in similar situations in other countries can be elaborated from expansion or adjustments in the input data.