An Approach to Selecting an E-Commerce Warehouse Location Based on Suitability Maps: The Case of Samara Region

Abstract

In the context of the rapid development of e-commerce, the selection of optimal land plots for the construction of warehouse complexes that meet environmental, technical, and political requirements has become increasingly relevant. This task requires a comprehensive approach that accounts for a wide range of factors, including transportation accessibility, environmental conditions, geographic features, legal constraints, and more. Such an approach enhances the efficiency and sustainability of decision-making processes. This article presents a solution to the aforementioned problem that employs the use of land suitability maps generated by aggregating multiple evaluation criteria. These criteria represent the degree to which each land plot satisfies the requirements of various stakeholders and are expressed as suitability functions based on attribute values. Attributes describe different characteristics of the land plots and are represented as layers on a digital terrain map. The criteria and their corresponding attributes are classified as either quantitative or binary. Binary criteria are aggregated using the minimum operator, which filters out plots that violate any constraints by assigning them a suitability score of zero. Quantitative criteria are aggregated using the second-order Choquet integral, a method that accounts for interdependencies among criteria while maintaining computational simplicity. The criteria were developed based on statistical and environmental data obtained from an analysis of the Samara region in Russia. The resulting suitability maps are visualized as gradient maps, where land plots are categorized according to their degree of suitability—from completely unsuitable to highly suitable. This visual representation facilitates intuitive interpretation and comparison of different location options. These maps serve as an effective tool for planners and stakeholders, providing comprehensive and objective insights into the potential of land plots while incorporating all relevant factors. The proposed approach supports spatial analysis and land use planning by integrating mathematical modeling with modern information technologies to address pressing challenges in sustainable development.

1. Introduction

The physical, environmental, and regulatory characteristics of areas of the Earth’s surface can vary significantly. Formally, the properties of any given area can be described using a set of attributes. Attributes to consider may include, for example, soil characteristics (such as erosion, waterlogging, salinity), groundwater levels, terrain slope, land utilization classification, legal constraints, the number of sunny days per year, and other relevant factors. Depending on the values of these attributes, a particular area may be well-suited for certain types of land use while being unsuitable or only marginally suitable for others. The alignment between the properties of land plots and their intended use, especially when limiting factors are taken into account, is a fundamental condition for sustainable territorial development [1,2].

Nowadays, attribute data describing the Earth’s surface—originally produced by specialized government agencies is widely disseminated through geographic information systems (GIS). Advances in information technology have led to the emergence of increasingly sophisticated GIS software solutions [3]. Notably, it has been observed that approximately 80% of the data that decision makers (DMs) rely on for making informed decisions across a wide range of domains and fields are spatial in nature [4,5].

The convergence of these factors has contributed to the widespread adoption of decision support systems (DSS) based on GIS. Decision-making problems involving spatial data are referred to as geographic or spatial decision-making tasks [6].

Concurrently, the COVID-19 pandemic and the imposition of economic sanctions have disrupted traditional economic relationships [7,8], contributing to the rapid growth of geographically distributed e-commerce enterprises [9]. However, one of the key limitations in the development of such enterprises is the lack of a comprehensive assessment of available spatial data [10]. The continued expansion of distributed e-commerce necessitates informed spatial decisions that account for a complex and dynamic legal framework, as well as land plot characteristics such as population density, transportation access, and energy infrastructure.

One of the pivotal facilities within such enterprises is the warehouse, which serves as the dispatch point for goods destined for customer service locations. The decision regarding the placement of the warehouse, whether it involves construction or lease, requires the reconciliation of multiple, often conflicting objectives. For instance, one objective may be to minimize environmental impact, while another may aim to reduce transportation costs. The extent to which one goal is achieved is frequently contingent upon the degree to which other goals are compromised. Therefore, a careful and comprehensive evaluation of land plot characteristics is essential in selecting warehouse locations for e-commerce operations.

Traditionally, such decisions were made by the decision maker without the aid of a DSS. This approach presents several challenges. Firstly, the vast number of possible alternatives, combined with the limitations of human working memory, makes it difficult for the decision maker to evaluate all options simultaneously. Consequently, optimal solutions may be overlooked. Secondly, decision-making is often influenced by subjective judgment, which can hinder objective evaluation of alternatives [11]. As a result, decisions made without systematic analysis may lead to suboptimal outcomes with potentially significant environmental, legal, financial, or social consequences.

Moreover, warehouse location decisions must take into account the order assembly model used by the e-commerce enterprise [12], as this determines the configuration of transport flows. Since operational models may evolve over time, the logic of warehouse siting must be adaptable to such changes.

Many GIS-based DSS assume that land suitability attributes are independent. However, in practice, these attributes are often interdependent, which necessitates approaches that account for such dependencies. One such approach involves the use of the Choquet integral with respect to a fuzzy measure [13,14]. This approach accommodates interdependencies between attributes, but identifying an appropriate fuzzy measure can be challenging. Consequently, simplified procedures for estimating fuzzy measure coefficients are commonly used, which do not rely on the decision maker’s full understanding of attribute dependencies.

An alternative approach is based on Dujmovic’s graded logic [15], in which the decision maker explicitly defines the interdependencies and the relative importance of attributes. However, this method may be limited by the incompleteness or inconsistency of the decision maker’s knowledge.

Given these considerations, this study proposes an approach to constructing a spatial DSS for the selection of warehouse locations for distributed e-commerce enterprises based on land suitability maps. The proposed approach utilizes a set of land plot attributes to assess their suitability and aggregates these attributes using the Choquet integral over a fuzzy measure. The fuzzy measure is identified based on the decision maker’s explicit, though potentially incomplete, knowledge of attribute dependencies and their relative importance.

The remainder of this article is organized as follows:

Section 2 reviews relevant literature on warehouse location selection, suitability mapping, and aggregation operators, and identifies suitable components for the proposed approach.

Section 3 outlines the proposed approach as applied to the warehouse siting problem for a spatially distributed e-commerce enterprise in the Samara region of Russia.

Section 4 describes the implementation of the proposed approach.

Section 5 presents the results and discusses their application in spatial decision-making.

Finally, Section 6 provides a comprehensive discussion of the findings and concludes the study.

2. Related Works

Spatial decision support systems (SDSS) have largely developed independently of general decision support systems (DSS) and have since gained significant traction across various domains [3]. In particular, SDSS are now widely used in areas such as forest management [16], risk assessment in mining regions [17], urban development planning [18], route optimization for forest fire response [19], spatial vulnerability analysis to landslides [20], evaluation of land suitability for beekeeping [21], and many other applications [22,23,24].

In recent years, machine learning (ML) techniques have been increasingly applied in spatial planning and decision systems, reducing the need for extensive and detailed expert input [25]. However, the effective use of ML in this context requires reliable, domain-specific datasets. In certain applications, such as landslide risk prediction [26], disease risk forecasting [27], crop yield estimation [28], violence prediction [29], and siting of wind and solar power plants [30]—long-term observational data are available that objectively reflect site suitability with respect to specific indicators. These data can be used to train predictive ML models for estimating suitability across other sites based on known attribute values.

Conversely, in other domains, collecting objective suitability data is either impractical or impossible. One such domain is e-commerce warehouse siting, where suitability is typically assessed based on expert judgment rather than observable outcomes. Selecting a site for an e-commerce warehouse using machine learning requires extensive and reliable data on existing warehouse locations and their operational performance. However, such data have not been accumulated either in Russia or internationally, due to the relatively recent emergence of the e-commerce sector. Because of this, ML approaches are not considered further in this study as a suitable means for modeling warehouse site suitability.

Non-ML-based spatial DSS rely on various decision-making methodologies [3], which utilize both spatial GIS data and the domain knowledge of decision makers. While the implementation of such spatial DSS requires qualified expert knowledge, ML-based spatial DSS requires reliable data. Spatial GIS data is typically represented as layered maps, each containing numerical attribute values describing various characteristics of the land. In the context of warehouse site selection, these attributes often relate to cost considerations [31]. Additionally, legal restrictions, transportation access, environmental impacts, consumer proximity, and political factors are also critical to the decision-making process [32,33,34,35].

Numerous studies [31,32,33,34,35,36,37,38] have identified key land area attributes for evaluating warehouse suitability. These attributes are commonly classified into four main categories:

• Natural Area Characteristics:
  This category includes attributes such as soil type, elevation, vegetation, and terrain slope [32,35,36]. Among these, slope is particularly important, as it directly affects both construction costs and the risk of natural disasters [32].
• Transportation Accessibility:
  Key indicators here include proximity to major highways and average travel time from key cities within the region [39,40]. Accessibility plays a crucial role in optimizing logistics operations.
• Legal and Policy Constraints:
  This includes regulatory restrictions and the alignment of the warehouse location with national or regional policy goals [41,42]. For example, activities unrelated to the conservation of natural ecosystems are prohibited on lands designated as state natural reserves [43]. It is also forbidden to change the intended use of land or repurpose it for incompatible objectives. On federally protected lands, the construction of industrial, commercial, or residential facilities is generally banned unless directly tied to the protected area’s functioning. Water protection areas, whose width is defined by the Water Code, also impose strict construction restrictions [44,45]. These areas must be excluded from warehouse site consideration. Moreover, from a policy perspective, warehouse sites should be situated as far as possible from such protected areas. Consequently, attributes in this category include distance to heritage sites [46], reserves, sanctuaries, and national parks [47,48].
• Economic Viability Factors:
  These include the distance from the proposed warehouse site to key pick-up points and local population size [31,49]. Proximity to pick-up points reduces transportation costs, while population size serves as a proxy for both potential customer base and local labor availability, which are important factors when selecting a warehouse location [50].

The knowledge of DMs in this context can be classified into two categories:

• Knowledge of Specific Alternatives:
  This involves the identification of particular candidate areas for warehouse construction. Such knowledge can be directly elicited from DMs when the number of alternatives is small. For instance, Cetinkaya et al. considered three alternative areas for locating an emergency warehouse [51]. However, in scenarios with a large spatial area and numerous alternatives, it becomes difficult for DMs to evaluate each option. In such cases, decision makers are presented with a limited number of attribute-based alternative profiles, usually no more than seven, given the limitations of human working memory [52,53], and are asked to express preference relations among them.
• Knowledge of Attribute Aggregation:
  This refers to how individual land attributes are combined to assess overall suitability for a specific purpose. Such knowledge is formalized through the construction of criteria and an aggregation operator. The criteria construction process transforms each attribute into a normalized scale, typically within the [0, 1] interval, making it compatible with standard aggregation techniques [54].

There is no universally accepted method for constructing criteria based on attributes. The chosen method should be appropriate to the specific application and provide satisfactory empirical performance [55]. Each transformation is designed so that a higher criterion value reflects greater suitability. For example, transportation costs, which are a significant factor, can be transformed using a monotonically decreasing linear function to ensure that lower costs correspond to higher suitability values [13,56].

According to [54], the aggregation operator $AGG$ is a function ${\left[0, 1\right]}^H\to \left[0, 1\right]$, where $H$ is the number of criteria. This function has the following properties:

• $AGG\left(g_H\right) = g_H$, if $H = 1$;
• $AGG\left(0, \dots , 0\right) = 0$ and $AGG\left(1, \dots , 1\right) = 1$
• $g_1 \le g_1^{\prime }, \dots , g_H \le g_H^{\prime } \Rightarrow AGG\left(g_1, \dots , g_H\right) \le AGG\left(g_1^{\prime },\dots , g_H^{\prime }\right)$

SDSS employ various aggregation operators. In most cases, the weighted arithmetic mean serves as the primary aggregation method [5,16,51,57,58]. In other cases, alternative operators are utilized—for instance, the geometric mean is applied in [18], the Choquet integral in [13], and the ordered weighted averaging (OWA) operator by Jaeger in [59].

However, the use of many aggregation operators poses certain challenges. These challenges primarily stem from the fact that many operators are either overly simplistic, thus failing to capture the nuances of the decision maker’s (DM’s) knowledge, or they do not align well with the logic of human reasoning. This often leads to a simplification and distortion of formalized expert knowledge, and may result in uncertainty or mistrust in the SDSS output, as the decision-making mechanism may appear to the user as a “black box”. Moreover, many operators, such as the Choquet integral or the Jaeger OWA operator, can be difficult to interpret or apply for domain experts without a strong mathematical background. A particular limitation of the OWA operator is its inability to explicitly capture interdependencies between individual attributes.

To address these challenges, Dujmovic [60] studied the properties required of aggregation operators in order to create mathematical models consistent with observed patterns of human reasoning. The most common of these operators, the weighted arithmetic mean, does not account for possible dependencies among attributes. An alternative that reflects both dependencies and human reasoning patterns is the weighted power mean [61]. Based on this operator, a DSS was developed for assessing land suitability for growing various crops [15], producing suitability maps as its output.

However, to apply such a system, complete expert information is needed in the form of a hierarchically structured attribute tree that identifies both the type and strength of interactions between attributes. As previously noted, such comprehensive knowledge is often unavailable from the DM, who may possess incomplete or uncertain information about attribute interactions.

An alternative to power-based operators is the Choquet integral [62]. A range of visualization techniques has been developed to make the Choquet integral more accessible to decision makers [63,64], supporting intuitive interaction. The key challenge in using the Choquet integral lies in the identification of a fuzzy measure, which assigns weights to all subsets of the set of attributes. This process is complex, as the number of subsets grows exponentially with the number of attributes, making direct specification by the expert infeasible. To reduce complexity, Grabisch introduced the concept of k-order fuzzy measures [65], which assume that dependencies between subsets of more than $k$ attributes can be neglected. In practice, 2-additive fuzzy measures are most commonly used, striking a balance between simplicity and expressiveness [66]. These measures enable the modeling of pairwise interactions between attributes, allowing for a more nuanced representation of decision logic while reducing the burden on the decision maker.

Moreover, to identify such fuzzy measures without introducing unintended subjectivity, the entropy maximization method [67] can be employed. This method enables the incorporation of only the available expert knowledge, avoiding arbitrary assumptions about unknown attribute dependencies.

Given these advantages, our SDSS approach for selecting warehouse locations is based on constructing suitability maps using the 2-additive Choquet integral as the aggregation operator. Attribute values, covering natural conditions, transport accessibility, legal restrictions, and economic factors, are aggregated using a fuzzy measure identified through entropy maximization, ensuring both interpretability and alignment with human reasoning, while respecting interdependencies among attributes.

3. Materials and Methodology

3.1. Field of Study

This study was conducted in the Samara region of Russia, which is situated within the Volga River basin (Figure 1). The region is strategically located near major transport corridors, including the M5 Ural highway and an extensive railway network, providing significant logistical advantages for the movement of goods. Covering an area of 53.6 thousand square kilometers, the proximity to the Volga River further enhances the region’s capacity for handling large-sized cargo shipments.

As of 2024, the Samara region ranks 20th in e-commerce development within the Russian Federation [68]. This rapid growth of the e-commerce sector makes the task of selecting optimal warehouse locations particularly relevant for enterprises operating in the region.

The region’s topography is predominantly flat, characterized by low hills interspersed by small swamps and marshy areas. These landscape features must be considered when evaluating potential sites for warehouse development.

3.2. Warehouse Site Attributes and Corresponding GIS Layers

To develop an SDSS for selecting a warehouse location, attributes corresponding to the types listed above were chosen based on both the DM’s knowledge and the availability of relevant data in the form of GIS layers. These attributes can be represented on both continuous and discrete scales. Attributes defined on continuous scales will be referred to as quantitative attributes, while those defined on binary scales will be referred to as binary attributes.

3.2.1. Quantitative Attribute a₁ “Terrain Slope”

This attribute reflects the elevation difference in the site and is defined on a continuous percentage scale. A significant slope increases the costs of construction due to the need for extensive vertical planning. According to “SP 42.13330.2016 Urban Development. Planning and Development of Urban and Rural Settlements” [69], design elevations should be assigned based on minimizing excavation work, while also considering the use of displaced soils at the construction site. To create the slope map (Figure 2), data from the OpenTopography project [70] were utilized.

OpenTopography provides high-resolution topographic data gathered through LIDAR (Light Detection and Ranging) remote sensing technology [71].

3.2.2. Quantitative Attribute a₂ “Distance to Highways”

This attribute reflects the distance from the warehouse site to the nearest roads and is defined on a continuous spatial scale. The costs associated with building and operating the warehouse are directly influenced by this attribute. Specifically, the shorter the distance to highways, the lower the cost of constructing access roads to the site and the easier the delivery of construction materials. The relevant spatial data were sourced from a publicly available road map of the Samara region, Russia [70]. Data obtained from OpenStreetMap (OSM) provides spatially detailed, targeted, flexible, and reproducible information [72]. The term “Highways” here refers to roads suitable for freight transportation classified by OpenStreetMap as “primary,” “secondary,” “tertiary,” and “trunk.” The highway map of the Samara region is shown in Figure 3.

3.2.3. Quantitative Attribute a₃ “Average Travel Time”

This attribute reflects the average travel time from a given city in the area to the warehouse. Travel time is a crucial factor in geospatial decision-making, such as in choosing locations for fire departments [73], selecting waste transportation routes [74], and determining the fastest routes for fresh vegetable delivery [75]. Spatial information on average travel time can be obtained using QGIS 3.34.13 [76].

Average travel time was calculated for cities with a population exceeding 100,000 people in the study area [34]. A map of these cities is shown in Figure 4.

The selection of cities with populations over 100,000 is based on their role as key transport and logistics hubs.

3.2.4. Quantitative Attribute a₄ “Distance to Protected Areas”

This attribute reflects the suitability of the site in terms of its compliance with state policy regarding protected sites. The data from the “Public Cadastral Map” [77] served as the initial data source for determining the distance from the warehouse to historical heritage sites, reserves, and sanctuaries. Information about the location of these protected territories in the research area is presented in Figure 5.

3.2.5. Quantitative Attribute a₅ “Average Distance to Pick-Up Points”

The average distance from the warehouse to the pick-up point is calculated using spatial data on the location of highways and the coordinates of the pick-up points. The distance is determined as the arithmetic mean of the distances from the warehouse site to the various pick-up points. The map showing the locations of the order pick-up points is presented in Figure 6. These data were also sourced from OpenStreetMap [78].

3.2.6. Binary Attributes Corresponding to the Constraints Imposed on the Site

The following attributes were selected: $z_1$—the site belongs to the territory of a nature reserve; $z_2$—the site belongs to the territory of a wildlife sanctuary; $z_3$—the site belongs to the territory of a national park.; $z_4$—the site belongs to the territory of an arboretum; $z_5$—the site belongs to the territory of historical heritage; $z_6$—the site is located in the protected area of a water body. These attributes are defined on a binary scale {0, 1}, where 0 means that the corresponding restriction is not imposed, and 1 means that the restriction is imposed on the site.

Spatial data on water bodies was taken from OpenStreetMap. The map of water bodies in the Samara region is presented in Figure 7.

OpenStreetMap (OSM) contains a wealth of open geographic spatial data, including data on protected areas [78]. The constraint data expressed by attributes $z_1, \dots , z_5$ are taken from OpenStreetMap [78] and are shown in Figure 5. There are no national or dendrological parks in the study area, so attributes $z_3$ and $z_4$ are equal to 0 for all areas under consideration.

3.3. Site Suitability Criteria

Site suitability criteria represent the requirements that attributes must meet according to stakeholder needs [15].

The criterion $g_1$ reflects the suitability of sites with varying terrain slopes for the placement of an e-commerce warehouse. Typically, for the construction of industrial facilities, including warehouses, the most suitable slope is around 5% [79], as it ensures proper drainage of surface water, eliminates marshy and flooded areas, and ensures stable access for freight transport. Based on this, sites with a slope ranging from 0% to 5% are considered fully suitable, while sites with a slope greater than 8% are considered completely unsuitable for warehouse placement. The relationship between site suitability and slope is illustrated in Figure 8.

As noted in [15], this relationship can be interpreted in four equivalent ways:

• As a suitability assessment—an undefined quantitative indicator representing how well stakeholder requirements are satisfied;
• As a logical evaluation of the degree of truth of the statement that the slope fully meets all requirements;
• As the degree of membership of the slope value in a fuzzy set representing ideal slope conditions;
• As the percentage of satisfied requirements.

All four interpretations are equivalent for the purposes of constructing a suitability map in our study. This is because all criteria are defined on a normalized unit interval [0, 1], which enables the use of aggregation operators to combine suitability values corresponding to individual attributes.

The criterion $g_2$ represents the site’s suitability based on the attribute $a_2$—distance to highways. According to the DM, sites located within 1 km of a road are considered fully suitable. Conversely, sites located more than 20 km from the nearest road are considered completely unsuitable. The relationship between site suitability and distance to roads is shown graphically in Figure 9.

The criterion $g_3$ reflects the site’s suitability with respect to the attribute $a_3$—average travel time. According to the DM, an average travel time of no more than 1 h is considered fully acceptable. In contrast, an average travel time of more than 2 h is deemed completely unacceptable. The corresponding suitability function is depicted graphically in Figure 10.

The criterion $g_4$ reflects the site’s suitability with respect to the attribute $a_4$—distance to protected areas. According to the decision maker, a distance of less than 5 km from a protected site is considered completely unacceptable. Conversely, if the distance exceeds 10 km, the site is regarded as fully suitable for warehouse placement based on this attribute. The corresponding suitability function is shown in Figure 11.

The criterion $g_5$ reflects the site’s suitability with respect to the attribute $a_5$—average distance to pick-up points. According to the DM, if this distance does not exceed 100 km, the site is considered fully suitable based on this attribute. However, if the distance exceeds 500 km, the site is regarded as completely unsuitable. The corresponding suitability function is shown in Figure 12.

The criteria $g_6, \dots , g_{11}$ reflect the suitability of the site with respect to the binary attributes $z_1,\dots , z_6$, respectively. Each of these criteria takes a value of zero when the corresponding attribute is equal to one: $g_6 = 1 - z_1,$ $g_7 = 1 - z_2,$ $g_{8 }= 1 - z_3,$ $g_9 = 1 - z_4,$ $g_{10} = 1 - z_5, g_{11} = 1 - z_6$. This reflects the fact that if any restriction corresponding to attributes $z_1, \dots , z_6$ is imposed on a site, that site is considered completely unsuitable with respect to the given attribute.

The criteria, their data sources, threshold values, and transformation functions are presented in

Table 1. Criteria and Their Data Sources.

Criterion	Data Source	Threshold Values	Transformation Function
$g_1$ Terrain slope	OpenTopography	0%; 5%; 8%	$\left\{\begin{array}{c}1, if a_1\in \left[0;5\right]\\ {\displaystyle \frac{8-a_1}{3}}, if a_1\in \left(5;8\right]\\ 0, if a_1\in \left(8;100\right]\end{array}\right.$
$g_2$ Distance to highways	OpenStreetMap	0 km; 1 km; 20 km.	$\left\{\begin{array}{c}1, if a_2\in \left[0;1\right]\\ {\displaystyle \frac{20-a_2}{19}}, if a_2\in \left(1;20\right]\\ 0, if a_2>20\end{array}\right.$
$g_3$ Average travel time	OpenStreetMap	0 h; 1 h; 2 h.	$\left\{\begin{array}{c}1, if a_3\in \left[0;1\right]\\ 2-a_3, if a_3\in \left(1;2\right]\\ 0, if a_3>2\end{array}\right.$
$g_4$ Distance to protected areas	Public Cadastral Map	0 km; 5 km; 10 km.	$\left\{\begin{array}{c}0, if a_4\in \left[0;5\right]\\ {\displaystyle \frac{a_4-5}{5}}, if a_4\in \left(5;10\right]\\ 1, if a_4>10\end{array}\right.$
$g_5$ Average distance to pick-up points	OpenStreetMap	0 km; 100 km; 500 km.	$\left\{\begin{array}{c}1, if a_5\in \left[0;100\right]\\ {\displaystyle \frac{500-a_5}{400}}, if a_5\in \left(1;500\right]\\ 0, if a_5>500\end{array}\right.$
$g_6$ Nature reserve	OpenStreetMap	0; 1	$1-z_1$
$g_7$ Wildlife sanctuary territory	OpenStreetMap	0; 1	$1-z_2$
$g_8$ National park territory	OpenStreetMap	0; 1	$1-z_3$
$g_9$ Arboretum territory	OpenStreetMap	0; 1	$1-z_4$
$g_{10}$ Historical heritage site	OpenStreetMap	0; 1	$1-z_5$
$g_{11}$ Water object zone	OpenStreetMap	0; 1	$1-z_6$

.

As shown in Table 1, most of the data sources used are publicly available through platforms such as OpenTopography and OpenStreetMap. The remaining data were obtained from Rosstat via the Public Cadastral Map.

In an international context, alternative publicly available data sources can be used, such as:

• the World Database on Protected Areas, which contains data on national parks, nature reserves, and other types of protected natural areas;
• the National Platform for Common Geospatial Information Services of China, also known as Tianditu, which serves a similar function to the Russian Public Cadastral Map;
• the European Union Digital Elevation Model, which provides digital terrain elevation data for the EU territory.

3.4. Construction of the Criteria Aggregation Operator

The aggregation operator for the criteria $g_1, \dots , g_{11}$ is constructed based on the DM’s knowledge and the information provided by the DM regarding the relative importance and interdependence of these criteria.

Let us first consider the criteria $g_1, \dots , g_5$, which correspond to quantitative attributes. The DM’s reasoning regarding these criteria is as follows. The most important among them are $g_4$ (“Distance to protected areas”) and $g_1$ (“Terrain slope”). However, the decision maker does not rank $g_4$ and $g_1$ relative to each other in terms of importance. Compared to these, the criterion $g_5$ (“Average distance to pick-up points”) is less important. Even less important are the criteria $g_2$ (“Distance to highways”) and $g_3$ (“Average travel time”). Since transport accessibility is essential not only during the construction phase but also for the future operation of the facility, the decision maker does not distinguish between the importance of $g_2$ and $g_3$.

Based on the above reasoning, we can construct the following partial non-strict order of importance:

$$g_5 \prec g_4; g_5\prec g_1; g_2\prec g_5; g_3\prec g_5$$

(1)

Next, we present the DM’s reasoning regarding interdependencies among the quantitative criteria. The criterion $g_3$ (“Average travel time”) directly depends on $g_2$ (“Distance to highways”), since greater distance to major roads typically results in longer travel time. Thus, criteria $g_2$ and $g_3$ are positively correlated. Similarly, since most pick-up points are located in cities, $g_5$ (“Average distance to pick-up points”) is also positively correlated with $g_3$ (“Average travel time”).

As previously mentioned, using the 2-order Choquet integral as the aggregation operator for the quantitative criteria allows these interdependencies to be considered. This operator provides a flexible framework for modeling the DM’s preferences, capturing both the individual importance of criteria and the nature of their interactions. The Choquet integral relies on a fuzzy measure, which assigns values to all subsets of criteria to reflect their combined significance. This measure encodes not only the individual weights of criteria, but also their interactions through interaction indices, which can be positive (indicating mutual reinforcement) or negative (indicating competition).

The positive interaction between criteria can be formalized using the interaction index as defined in [61]. In this context, the following relationships hold:

$$I\left(2, 3\right)<0$$

(2)

$$I\left(3, 5\right)<0$$

(3)

Next, we consider the binary criteria $g_6, \dots , g_{11}$. According to the DM, if at least one of these criteria takes a suitability value of zero for its corresponding attribute, then the overall suitability of the site must also be zero. This condition reflects a logical “AND” operation in the aggregation: any violation of environmental or legal constraints renders the site completely unsuitable, regardless of other favorable conditions.

The overall aggregation of criteria $g_1, \dots , g_{11}$ is illustrated in Figure 13.

The aggregation operator S combines the Choquet integral and the minimum operator. Given the values of criteria $g_1, \dots , g_{11}$ for a specific site, this operator produces an overall site suitability score. The minimum operator returns zero if the site is subject to any restrictions corresponding to the binary attributes $z_1, \dots , z_6$. For sites where none of these restrictions apply, the resulting suitability is equal to the value of the Choquet integral $C_{\mu }(g_1, \dots , g_5)$, computed over the quantitative criteria.

Thus, the final expression for site suitability $S$ can be written as:

$$S = \min (C_{\mu }(g_1, \dots , g_5),g_6, \dots , g_{11})$$

(4)

To identify the fuzzy measure $\mu$, as previously noted, we use the variance minimization method as well as the Kappalab package [80]. The input information for such identification consists of the DM’s preferences, represented by the partial non-strict order (1) and inequalities (2) and (3). To apply the fuzzy measure variance minimization method, these preferences must first be translated into inequalities with specified indifference thresholds. Specifically, the partial non-strict order (1) is converted into the following inequalities:

$$\Phi \left(4\right) - \Phi \left(5\right) \ge {\delta }_{\Phi }$$

(5)

$$\Phi \left(1\right)-\Phi \left(5\right) \ge {\delta }_{\Phi }$$

(6)

$$\Phi \left(5\right)-\Phi \left(2\right) \ge {\delta }_{\Phi }$$

(7)

$$\Phi \left(5\right)-\Phi \left(3\right) \ge {\delta }_{\Phi }$$

(8)

These inequalities $\Phi \left(h\right)$ denote the Shapley indices for the criterion $g_h$, which express the overall relative importance of the corresponding criteria. The indifference threshold ${\delta }_{\Phi } = 0.07$ represents the tolerance level that the DM sets for the Shapley indices.

Inequalities (2) and (3) are translated into the following inequalities with a specified indifference threshold:

$$-1 \le I\left(2, 3\right) \le -{\delta }_I$$

(9)

$$-1 \le I\left(3, 5\right) \le -{\delta }_I$$

(10)

Here, ${\delta }_I = 0.03$ is the indifference threshold set by the DM for the interaction indices.

As a result of the identification of the fuzzy measure, the values of the coefficients of the fuzzy measure were obtained as follows: $\mu \left(1\right) = 0.266; \mu \left(2\right) = 0.139; \mu \left(3\right) = 0.151;$ $\mu \left(4\right) = 0.266; \mu \left(5\right) = 0.209$ and the interaction indices are: $I\left(2, 3\right) = I\left(3, 5\right) = -0.03$. The remaining interaction indices are approximately equal to zero.

Thus, the operator (4), which incorporates the Choquet integral with respect to the identified fuzzy measure $\mu$, effectively captures the preferences of the decision maker, as expressed through the reasoning outlined above.

4. Implementation

Our approach was implemented in two stages. During the first stage, QGIS 3.34.13 tools were used to transform the spatial data of attribute values described in Section 3.2 into spatial data for the corresponding suitability criteria, utilizing the dependencies outlined in Section 3.3.

Specifically:

• The values for the criterion $g_1$ “Terrain slope” were derived from the elevation map (SRTM 30 data, loaded via the OpenTopographyDEM plugin) using the Raster Calculator (Raster → Analysis → Slope).
• The values for the criterion $g_2$ “Distance from highways” were calculated by constructing a distance matrix (Vector → Analysis → Distance matrix) between the layers “Samara region map” (QuickOSM plugin, tag boundary/administrative) and “Samara region highway map” (QuickOSM plugin, tag highway/motorway).
• The values for the criterion $g_3$ “Average travel time” were obtained by averaging (weighted average, where the weight is the city’s population) the results of network analysis (Network analysis → Shortest path (layer to point)) from the layers “Samara region map” and “Samara region road map”. The list of cities (points) was specified manually, including cities with populations exceeding 100,000 people.
• The values for the criterion $g_4$ “Distance to protected areas” were determined by constructing a distance matrix between the layers “Samara region map”, “map of water bodies” (QuickOSM plugin, tag waterway), and “map of protected objects” (plugin rosreestr-search-qgis Natural territories/Specially protected natural territories and Territories of cultural heritage sites of the people of the Russian Federation). The map of protected objects was converted from raster to vector (Raster → Conversion → Create polygons (raster to vector)).
• The values for the criterion $g_5$ “Average distance to the pick-up point” were calculated by averaging (arithmetic mean) the results of network analysis from the layers “map of Samara region” and “map of roads of the Samara region”. The list of pick-up points was created from the “map of pick-up points”, and the pick-up points were clustered to reduce the number of calculations using the ClusterPoints plugin (clustering into 10 groups).

Binary criterion values were mapped to sites using the tool Vector → Data Tools → Merge Attributes by Location.

During the second stage, the spatial data of the suitability criteria values were aggregated using operator (4), employing both QGIS 3.34.13 and Python 3.11.8. For visualizing the results, a graduated color scale was chosen for the “suitability” field, with a Red-Yellow-Green color scale consisting of 30 suitability levels. The least suitable areas were colored red, and the most suitable areas were colored deep green.

The area size during the implementation of the method was chosen to be 600 by 600 m, based on computational limitations for network analysis and the spatial requirements necessary for an e-commerce warehouse facility.

5. Results and Their Use for Spatial Decision-Making

The implementation of our approach produced a suitability map for identifying optimal sites for e-commerce warehouses in the Samara region. Considering the DM’s preferences and computational limitations, a specific area near the cities of Syzran and Tolyatti was selected as the area of interest (Figure 14).

As depicted in the map, the most suitable sites for warehouse placement are located near major transport routes and are distant from protected areas. Additionally, the number of such sites is significantly smaller than the total number of sites in the region under consideration, thus simplifying the decision-making process. Further refinement of the selection can be made based on other implicit criteria considered by the stakeholder, although these criteria are not formalized as legal restrictions and are not reflected in publicly available digital maps.

These implicit criteria include the degree of suitability of the plots for alternative land uses. Specifically, the suitability of plots for agricultural purposes is influenced by the extent of land degradation. According to a previous study [81], the Syzran and Shigonsky districts in the Samara region are most prone to erosion. As a result, the decision maker excludes plots from other districts that are more suitable for agriculture due to higher yields. Figure 15 illustrates a suitability map for the Syzran and Shigonsky districts.

Another implicit suitability criterion concerns the potential presence of unexplored archeological sites on the land. Such information can be derived from Earth remote sensing data. According to a study conducted [82], no signs of such archeological sites were identified in the Syzran and Shigonsky districts.

Based on the preferences of the DM, the area of interest was defined as the region between the cities of Shigony and Syzran, situated along the 36K-616 highway. This area is highlighted in Figure 15 by a rectangle with a dotted line. Within this region, a considerable number of sites with the highest suitability for the construction of e-commerce warehouses are found (Figure 16).

Thus, the set of the most suitable sites for the placement of an e-commerce warehouse has been significantly narrowed, facilitating a more informed decision-making process. The DM can now select a specific site from the map in Figure 16. However, this decision will also be influenced by another important implicit criterion: the possibility of acquiring or leasing the site. This criterion is subject to change over time, and the DM can obtain relevant information from cadastral maps of the Samara region [83,84], as well as from publicly available listings for the sale or lease of land.

The suitability of a given site depends on the values of the criteria assigned to it. Therefore, even minor differences in the suitability values between two candidate sites for warehouse construction can significantly affect both the costs incurred during the construction phase and the long-term operational expenses of the warehouse.

This impact arises from the following factors: terrain slope (criterion $g_1$) affects the amount of earthworks required during site preparation and construction; distance to highways ($g_2$), average travel time ($g_3$), and average distance to pick-up points ($g_5$) all directly influence logistical costs, including time and fuel costs associated with the transportation of goods and order completion; distance to protected areas ($g_4$) affects potential political or regulatory risks that may complicate construction or operations.

As shown in Figure 16, the sites located along major roads tend to exhibit the highest overall suitability. However, their suitability values differ slightly from one another. These subtle differences may lead the DM to prefer one site over another based on the aforementioned impact on costs.

As previously noted, the Choquet integral allows for a more nuanced representation of expert preferences. To illustrate its superior capability in this area, an alternative method—the weighted average operator—was employed for comparison. This operator was constructed based on the DM’s knowledge, represented in the form of the partial non-strict order (1). Suitability maps for several sites within the area of interest outlined by the dashed line in Figure 16, along with their corresponding numerical suitability values, are presented in Figure 17.

These maps show that the use of the Choquet integral can alter the ranking of site suitability compared to the application of the weighted average aggregation operator. This is important when selecting a site for warehouse construction. In particular, depending on the aggregation operator used, the decision maker may prefer a site located on either the right or left side of the road in the area outlined by the dashed line in Figure 17.

6. Discussion of Results and Conclusions

This study proposes an approach to selecting the location for an e-commerce warehouse. The results of implementing this approach based on the SDSS demonstrate that it effectively reduces the decision-making burden by significantly narrowing down the number of alternatives and providing spatial visualization in the form of a color-graded map reflecting land plot suitability.

Furthermore, by employing the Choquet integral, our approach accounts for interdependencies between criteria. The use of the variance minimization method to identify a fuzzy measure ensures that the approach incorporates all available information regarding the relative importance of criteria and their interactions, without introducing additional subjectivity into the results.

Over time, DM’s preferences may evolve due to changes in the relevant socio-cyberphysical system [85], as well as political factors. These changes may require adjustments to the set of attributes and criteria. Such changes can be implemented gradually, with minimal time and material costs. DMs can formalize their preferences regarding new attributes and corresponding criteria by incorporating them into the Choquet integral and/or the minimum operator.

Initially, we intended to include land prices as one of the quantitative criteria. However, this was not implemented for two reasons: (1) the lack of publicly available, free data on land costs and (2) the high cost of acquiring such data. Moreover, the analysis of land prices is more suitable at a later stage—specifically, during the final selection phase, when discerning from a small number of alternative sites.

Our approach assumes the delivery of goods from warehouses to pick-up points, which reflects the prevailing practice of e-commerce operations in Russia. The proposed approach can be adapted to a variety of geographic, legal, and economic contexts outside of Russia, particularly for e-commerce companies that rely on pick-up point delivery models. We believe that the quantitative attributes included in the model may be considered universally applicable, as they can be derived from publicly accessible digital maps and directly influence the suitability of a site for e-commerce warehouse development. Binary attributes, however, require alignment with the legal and regulatory frameworks of the specific region. These attributes can also often be retrieved from open-source cartographic data. At the same time, regional conditions may necessitate the inclusion of additional attributes, such as the degree of land suitability for alternative uses like agriculture or mineral extraction.

In any case, our approach suggests the involvement of a qualified expert whose preferences ultimately inform the suitability map. Therefore, the dependencies between criteria and attribute values for a specific region may differ from those we have proposed.

To address the potential uncertainty or inconsistency in expert judgements, a panel of experts may be engaged. There are several methods for reconciling preferences within such a group. One promising approach involves the visualization of aggregation operators in virtual reality [64], allowing experts to collaboratively explore and adjust their individual judgments in an intuitive, interactive environment, thereby facilitating consensus and compromise.

An intriguing direction for future research is the development of similar aggregation operators for the SDSS using a three-dimensional balance model in a virtual reality environment [64]. Within this direction, it is proposed that the DM constructs an aggregation operator using a formal procedure with objects in virtual reality, instead of the Choquet integral [86], which has been widely used to date. In this scenario, the DM can intuitively and clearly perceive the specified objects by relying on their physical intuition.

Another promising direction for future research involves expanding the area of interest over which the site suitability map is constructed. Such expansion would lead to a substantial increase in the computational load, particularly due to the need to calculate large distance matrices between sites, protected areas, and highways. As the size of these matrices grows, so does the computational load, potentially necessitating the use of multiprocessor systems or cloud-based infrastructure. To achieve the required performance, at scale, it is advisable to use a programming language that supports low-level memory management and efficient operations on large arrays.

Applied to the Samara region, the proposed approach significantly reduced the number of analyzed areas, thereby decreasing the analysis time. As a result, the decision maker was able to examine the available information in greater detail and make a more informed decision. In the future, a formal description of the decision-making process, documenting the changes in preferences using blockchain technology [87], could serve as a legally significant document, validating the decision. The proposed approach can be implemented in both existing and prospective systems for supporting decision-making in the selection of industrial facility construction sites.