Optimizing Urban Bus Networks Through Mathematical Modeling: Environmental and Operational Gains in Medium-Sized Cities

Abstract

This study aimed to optimize the urban public transportation system in Queretaro, Mexico, while meeting passenger demand by using Linear Programming (LP) and Goal Programming (GP) models to reduce redundant routes, minimize fuel consumption and ${\mathrm{CO}}_2$ emissions, and balance costs with service coverage. Operational data from 316 drivers were collected on diesel consumption, working hours, and vehicle availability while incorporating twelve technical, labor, and regulatory constraints. The LP model reduced the number of routes from 148 to 124, achieving daily savings of 13,789 L of diesel, a reduction of 36,816 kg in ${\mathrm{CO}}_2$ emissions, and an economic benefit of USD 17,071.90, equivalent to 13,253 tons of ${\mathrm{CO}}_2$ avoided annually; these results demonstrate LP’s ability to deliver quantifiable improvements in efficiency and sustainability. The GP model integrated multiple and often conflicting objectives, such as maintaining a maximum fuel cost of USD 9312/day for 1944 buses distributed across five zones while ensuring a minimum coverage of 145 routes and 450,000 daily passengers, showing that it is possible to meet service targets with marginal cost overruns (USD 4118.66) when balancing both coverage and budget. The novelty of this paper lies in combining mathematical optimization models with real operational data and simultaneously reporting both economic and environmental impacts. This allows us to offer a replicable and highly interpretable tool with low computational cost for use in medium-sized cities seeking to align mobility planning with sustainability policies and operational efficiency.

1. Introduction

Public transportation in rapidly growing cities such as Queretaro, Mexico faces significant challenges related to route optimization, operational efficiency, and environmental sustainability. Urban expansion and the increased demand for mobility in industrial and residential areas have tested the transportation system’s ability to adapt to new urban dynamics [1]. Queretaro, with 29.6% population growth in the last decade and significant industrial development [2], has undergone a transformation in its transportation infrastructure. However, issues such as vehicular congestion, route duplication, and resource inefficiencies continue to affect the public transport system, leading to high fuel consumption, pollutant emissions, and negative impacts on both service quality [3] and the working conditions of operators [4].

In general, extensive research has been conducted from 2001 to 2023 on mitigating congestion in medium-sized cities. For instance, [5] highlighted the role of strategic route planning in reducing travel times and congestion. Meanwhile, [6] emphasized the importance of infrastructure design and its direct impact on network efficiency. Finally, [7] addressed inefficiencies in traffic control systems, underscoring the need for integrated approaches to improve urban mobility.

In this context, route optimization and efficient resource allocation have been highlighted as crucial strategies not only to reduce operational costs [1] but also to improve the environmental and economic sustainability of urban transportation [8]. These strategies are equally relevant for cities such as Queretaro which face similar challenges regarding congestion and transportation system efficiency. Several studies have addressed the environmental challenges of urban transportation from complementary perspectives. On the one hand, intelligent systems have been developed to monitor vehicle emissions under different driving modes, allowing the identification of significant variations in pollutants such as CO, ${\mathrm{CO}}_2$, and NOx [9]; these tools contribute to the design of more efficient environmental control strategies. On the other, systematic reviews have proposed hierarchical evaluation frameworks that integrate environmental, social, and economic criteria, facilitating the application of multi-criteria methodologies in the planning and management of sustainable urban transport [10].

In economic terms, excessive fuel consumption represents one of the largest expenses for transportation companies, creating significant financial pressure. Reducing this consumption not only improves economic efficiency but also contributes to more sustainable financial management. In [8], the authors showed that optimizing fuel use directly lowers operational costs for public transport operators. In addition, [11] emphasized the broader benefits of efficient resource allocation in ensuring long-term economic stability within urban mobility systems. Furthermore, [12] highlighted that sustainable financial practices in transportation can generate positive externalities, including enhanced service quality and greater resilience of the transport network. In Queretaro, which has experienced notable industrial growth, optimizing routes is key to improving service quality and reducing congestion, with direct impacts on system efficiency and emission reduction [2].

Queretaro’s public transportation system has undergone transformations designed to streamline fare collection and reduce cash usage, such as the introduction of the Qrobus smart card; however, challenges such as operator dissatisfaction with working conditions persist, reflecting the need for comprehensive modernization that addresses both infrastructure and operational efficiency. Additionally, demand analysis in specific city areas has revealed that route duplication and lack of integration can increase fuel consumption and emissions [13], necessitating route redesign [14].

In this context, several strategies have been identified to improve the efficiency of public transportation in Queretaro, such as the incorporation of hybrid or electric buses to reduce fuel consumption [13]. Despite efforts on the part of the Queretaro Transport Institute (IQT), problems related to route duplication and misalignment with user needs persist. The challenge lies in finding a balance between economic, environmental, and social sustainability while adapting the transportation system to the city’s current needs and improving quality of life for its residents [15].

The allocation of vehicles to specific routes, while respecting established constraints, has been the subject of analysis for many years. This has become a serious issue in the city of Querétaro in particular, as the city has experienced rapid growth and the availability of sufficient buses to meet residents’ demand has yet to be resolved.

In this work, we propose a goal-based scheduling technique which provides results that could be adopted by the city government.

The following goals were defined:

Goal 1:

Maintain at least 145 routes.

Goal 2:

Keep the daily fuel cost at no more than USD 91,574 across the four areas of the city (A–D).

Goal 3:

Serve at least 450,000 passengers per day in the city of Querétaro.

To achieve these objectives, the following scenario was considered: operate at least 145 routes (the current number in the city), with a maximum daily cost of USD 91,574 for all routes, and serve a minimum of 450,000 passengers per day citywide. These operating data were obtained through surveys of more than 300 drivers.

Subsequently, a multi-objective scheduling approach was applied, taking into account twelve constraints. The aim was to improve and maintain fuel costs at or below USD 9312 per day for the 1944 buses serving Zones 1 through 5 and areas A–D of the city of Querétaro while also considering restrictions on daily bus availability per zone. The GP model integrates multiple and often conflicting objectives, such as maintaining a maximum fuel cost of USD 9312/day for 1944 buses distributed across five zones while ensuring a minimum coverage of 145 routes and 450,000 daily passengers, showing that it is possible to meet service targets with marginal cost overruns (USD 4118.66) when balancing coverage and restrictions. The novelty lies in combining mathematical optimization models with real operational data and simultaneously reporting both economic and environmental impacts, offering a replicable and highly interpretable tool with low computational cost for use by medium-sized cities seeking to align mobility planning with sustainability policies and operational efficiency.

This study presents three significant contributions to the field of urban transportation route optimization:

• The implementation of a mathematical model based on linear programming to eliminate redundant routes and enhance operational efficiency.
• The integration of real-world operational data collected through structured surveys administered to public transport operators, ensuring context-specific modeling.
• A comprehensive assessment that incorporates both economic and environmental dimensions, providing a multidimensional understanding of the benefits of route optimization in rapidly growing urban settings.

The primary objective of this study is to develop and implement a linear programming-based optimization model to improve the efficiency of urban public transportation routes in the city of Queretaro, Mexico. The research aims to reduce route redundancies, minimize fuel consumption, and lower environmental impact by leveraging real operational data collected from public transport operators. This model seeks to support decision-making processes in public transportation planning and promote more sustainable, cost-effective, and environmentally responsible mobility systems in medium-sized urban contexts.

In the context of optimizing Querétaro’s public transportation system, Goal Programming (GP) was applied to address multiple and often conflicting objectives, seeking “good enough” solutions by minimizing deviations from aspiration levels. The primary goal was to maintain a maximum daily fuel cost of USD 9312 for 1944 buses distributed across five zones, with availability constraints per zone (84, 444, 528, 492, and 240 units). The model achieved this goal by adjusting fleet allocation, notably reducing Zone 2 from 444 to 271 buses. In a complementary simulation, three goals were set: to preserve at least 145 routes, limit total daily fuel cost to USD 91,574, and serve a minimum of 450,000 passengers per day. Results showed that the route and passenger coverage targets were met while incurring a cost overrun of USD 4118.66/day, demonstrating GP’s capability to balance service coverage and budget constraints in complex urban planning scenarios.

The rest of this paper is organized as follows. Section 1, Introduction, outlines the urban and industrial growth of Queretaro and the resulting transportation challenges, highlighting the urgency of route optimization to reduce fuel consumption and emissions. Section 2, State of the Art, reviews international and local research on transportation route optimization, supported by bibliometric analysis to identify prevailing trends. Section 3, Materials and Methods, describes the linear programming model used to minimize diesel costs, detailing the variables, constraints, and data collection protocol through validated surveys. Section 4,Results and Discussion, presents and analyzes the optimized configuration of urban transport routes using real operational data from the city of Queretaro. The results are discussed in light of Queretaro’s socio-territorial transformation, illustrating the practical implications of implementing the model within a medium-sized city undergoing rapid urban and industrial expansion. Finally, Section 5, Conclusions, synthesizes the main findings and emphasizes the model’s potential for broader application in cities facing similar mobility and environmental issues.

2. State of the Art

The increasing complexity of urban mobility systems and the environmental challenges posed by modern transportation have driven a growing interest in optimizing transportation routes. In this context, transportation route optimization emerges as a critical field of research that combines engineering, sustainability, and computational modeling. This section aims to systematically review the scientific literature related to transportation route optimization, with particular emphasis on sustainable urban mobility and public transport networks. A comprehensive search strategy was developed to identify relevant publications and assess the evolution of key research trends through bibliometric mapping. In addition, a case analysis was conducted focusing on the metropolitan area of Queretaro, Mexico, where recent socio-territorial transformations and urban growth have intensified the need for efficient transportation planning. This combined approach allows for a robust understanding of both global research directions and local implementation challenges.

2.1. Systematic Review Protocol and Search Strategy

To ensure transparency, rigor, and replicability, this systematic review was guided by a predefined protocol. Systematic reviews demand both methodological accuracy and strict inclusion criteria to assess the relevance and quality of eligible studies. Despite their increasing prevalence in the scientific literature, many reviews still suffer from methodological weaknesses, leading to reduced validity and academic impact. To mitigate this, we applied a structured search strategy and exclusion framework.

2.2. Research Objective

The present review aims to identify and analyze optimization strategies for transportation routes, with a specific emphasis on urban settings, sustainable mobility, and public transport efficiency. The review explores how different computational techniques and planning models have been applied to improve route design and network performance.

2.3. Search Strategy and Inclusion Criteria

A broad search query was constructed to retrieve relevant literature from Scopus, targeting keywords that represent various formulations of transportation route optimization. The following query was used:

• TITLE-ABS-KEY (“transportation route optimization” OR

“optimization of transportation routes” OR

“urban transportation route optimization” OR

“route planning for transportation” OR

“transportation network optimization” OR

“transportation route design” OR

“improving transportation routes” OR

“efficient transportation routes” OR

“route optimization in public transport” OR

“optimization of urban transport networks” OR

“sustainable transportation route optimization”)

This query consists of three main components:

• TITLE-ABS-KEY: This operator searches for the specified phrases within the article title, abstract, or author keywords.
• Logical Operators (OR): The use of OR ensures that the query captures a wide range of terminologies related to transportation route optimization. This includes general terms as well as specific applications to urban and public transportation contexts.
• Thematic Scope: The terms included reflect a diverse but focused set of topics such as route efficiency, planning, design, and sustainability, thereby ensuring a relevant and coherent dataset of studies.

2.4. Bibliometric Analysis

This search formulation is suitable for systematic or scoping reviews aiming to explore optimization techniques used in the design and improvement of transportation networks. The selected expressions cover both technical approaches (e.g., optimization models) and societal needs (e.g., sustainable urban mobility), allowing for a comprehensive evaluation of interdisciplinary contributions in the field.

2.5. Bibliometric Synthesis and Implications for the Model

In our review, the VOSviewer 1.6.20 mapping is not merely descriptive; it structures the state of the art and directly informs our modeling choices. Four salient clusters emerge: (i) network design/linear programming, (ii) metaheuristics (genetic and heuristic search), (iii) sustainability and emissions, and (iv) public transport operations. Consistent with these clusters, we adopt a transparent and low-data/compute LP core to minimize daily fuel cost using survey-based coefficients. We then extend this core with Goal Programming (GP) to encode multi-objective priorities (cost ceiling and coverage by area with deviation variables). Finally, we explicitly connect operational efficiency to environmental outcomes by reporting fuel-to-${\mathrm{CO}}_2$ conversions alongside cost results. Table 1 summarizes this crosswalk from clusters and keywords to concrete model elements (objective coefficients, minimum-service constraints, and coverage targets).

Figure 1 from the VOSviewer [16] analysis illustrates a co-occurrence network of terms related to transportation route optimization. Key terms include transportation system, network design, linear programming, sustainability, genetic algorithms, carbon emissions, and heuristic algorithms. These terms are grouped into clusters that represent specific research areas such as network planning, environmental impact, optimization methods, and public transport. The density and interconnections of the terms reflect the interdisciplinary nature of transportation optimization, linking technical methods (e.g., linear programming, stochastic models) with sustainability concerns and logistics applications. In our study, the prominence of the LP/operations cluster supports using an LP core, while the sustainability cluster motivates explicit fuel-to-${\mathrm{CO}}_2$ reporting and the public transport operations cluster informs coverage constraints by zone/area; the metaheuristics cluster is acknowledged but deprioritized here due to interpretability and deployment needs in the context of a medium-sized city with resource constraints.

The international scientific landscape revealed by the bibliometric network reflects a growing interest in the optimization of transportation routes, especially concerning sustainability, public transport systems, and computational modeling techniques such as linear programming and metaheuristics. This global research agenda resonates strongly with the challenges currently faced in Queretaro, Mexico, a region undergoing rapid socio-territorial transformation driven by industrial expansion and increased urban mobility demands. The overlap between global keyword clusters and the specific needs of Queretaro, including issues such as route duplication, fuel consumption, and ${\mathrm{CO}}_2$ emissions, highlights the relevance of adopting internationally recognized optimization strategies at the local level. Operationally, this alignment is enacted in our model by (i) using survey-based cost coefficients to reflect local operating conditions; (ii) imposing minimum-service constraints by zone and coverage targets by area that mirror spatial equity concerns; and (iii) reporting fuel/${\mathrm{CO}}_2$ impacts alongside cost results to link efficiency gains with environmental goals. Therefore, integrating insights from the global literature with the regional context enhances the scientific robustness of this study, supporting locally-grounded and evidence-based solutions for medium-sized industrial cities such as Queretaro.

The socio-territorial transformation in Queretaro has been notable, particularly in the Navajas–Galeras microregion located between El Marques and Colon, where agricultural activity has declined due to industrial growth driven by the establishment of industrial parks and the opening of the Queretaro International Airport (AIQ) in 2005. This change has generated greater daily mobility towards industrial zones and the city of Queretaro, favoring a reconfiguration of the territorial landscape [17]. Despite industrial growth, studies such as those by González and Nieto [14] have highlighted the lack of industrial specialization in the region, leading to weak inter-industrial relationships. In turn, regional public policy has promoted the development of an aerospace cluster, attracting first- and second-tier suppliers, as well as the establishment of technical training centers [14].

Queretaro’s public transportation system faces additional challenges on its path toward greater sustainability. While the implementation of advanced technologies such as Euro 5 and Euro 6 standards for reducing ${\mathrm{CO}}_2$ emissions has made progress, the adoption of hybrid or electric buses is limited by a lack of infrastructure and economic constraints [13]. Although system modernization such as the implementation of the Qrobus smart card has improved fare collection and reduced cash use [18], problems such as route duplication persist, leading to increased fuel consumption and emissions. This highlights the need to optimize route planning and reduce operational inefficiencies [18]. Such adjustments are essential to improving the economic and environmental sustainability of the transportation system, which remains a priority on Queretaro’s public agenda [18,19]. Aligned with the bibliometric clusters, our modeling approach operationalizes these priorities by minimizing daily fuel cost (LP), setting explicit coverage/demand goals (GP), and quantifying fuel-to-${\mathrm{CO}}_2$ effects in order to make environmental co-benefits transparent to policy makers.

Regarding the estimation of pollutant emissions, studies such as that of Torres et al. [20] have proposed methods to calculate fuel consumption and emissions in freight transport. Still, these approaches are not directly applicable to urban passenger transport due to the need to optimize routes more efficiently. Instead of using methods based on Chebyshev intervals, a Linear Programming (LP) model is proposed to optimize urban routes and eliminate redundancies, thereby complementing current efforts to improve system efficiency.

Table 1. Crosswalk from VOSviewer clusters (Figure 1) to the literature review and specific LP/GP model elements (objective coefficients, constraints, priorities).

Cluster (VOSviewer)	Representative Keywords	Exemplar References	Implications for Our MODEL
Network design & Linear Programming (LP)/Operations	network design; linear programming; route optimization; public transport networks; integer programming	See Section 2 (LP studies).	LP core to minimize daily fuel cost with survey-based coefficients; transparent, low data/compute; deployable in mid-sized cities; basis for minimum-service constraints by zone.
Metaheuristics (GA/heuristics/SA)	genetic algorithms; heuristic algorithms; simulated annealing; ant colony optimization; multiobjective	See Section 2 (metaheuristics).	Acknowledged but de-prioritized for this case due to interpretability and deployment needs; considered for future hybridization once LP/GP is institutionalized.
Sustainability & Emissions	carbon emissions; fuel consumption; emission control; sustainability	[20,21]	Explicit fuel→${\mathrm{CO}}_2$ conversion and reporting alongside cost outcomes; links operational efficiency to environmental gains; supports policy targets.
Public Transport Operations & Coverage	transportation system; public transportation networks; coverage; demand; service quality	[22]	Goal Programming (GP) layer for multi-objective priorities: cost ceiling + coverage by area; use of deviation variables/priorities; minimum-service constraints by zone.
Regional socio-territorial context (Querétaro)	industrial growth; AIQ; aerospace cluster; mobility demand; route duplication	[14]	Zoning and demand assumptions grounded in local transformation motivate the de-overlapping of routes and coverage targets tailored to spatial patterns.

Table 1. Crosswalk from VOSviewer clusters (Figure 1) to the literature review and specific LP/GP model elements (objective coefficients, constraints, priorities).

Cluster (VOSviewer)	Representative Keywords	Exemplar References	Implications for Our MODEL
Network design & Linear Programming (LP)/Operations	network design; linear programming; route optimization; public transport networks; integer programming	See Section 2 (LP studies).	LP core to minimize daily fuel cost with survey-based coefficients; transparent, low data/compute; deployable in mid-sized cities; basis for minimum-service constraints by zone.
Metaheuristics (GA/heuristics/SA)	genetic algorithms; heuristic algorithms; simulated annealing; ant colony optimization; multiobjective	See Section 2 (metaheuristics).	Acknowledged but de-prioritized for this case due to interpretability and deployment needs; considered for future hybridization once LP/GP is institutionalized.
Sustainability & Emissions	carbon emissions; fuel consumption; emission control; sustainability	[20,21]	Explicit fuel→${\mathrm{CO}}_2$ conversion and reporting alongside cost outcomes; links operational efficiency to environmental gains; supports policy targets.
Public Transport Operations & Coverage	transportation system; public transportation networks; coverage; demand; service quality	[22]	Goal Programming (GP) layer for multi-objective priorities: cost ceiling + coverage by area; use of deviation variables/priorities; minimum-service constraints by zone.
Regional socio-territorial context (Querétaro)	industrial growth; AIQ; aerospace cluster; mobility demand; route duplication	[14]	Zoning and demand assumptions grounded in local transformation motivate the de-overlapping of routes and coverage targets tailored to spatial patterns.

The bibliometric evidence justifies the methodological pathway adopted here; the LP core provides interpretability and immediate deployability in a mid-sized city, while the GP layer accommodates multiple potentially competing goals (cost containment and spatial coverage). The explicit fuel-to-${\mathrm{CO}}_2$ reporting aligns the operational focus of route optimization with environmental objectives identified in the sustainability cluster. Two limitations should be noted. First, bibliometric co-occurrence reflects publication patterns, and may under-represent emerging niches (e.g., hybrid LP–metaheuristic frameworks) that could be valuable in future extensions. Second, choices such as cluster resolution and thresholding, although reported, can influence the visual prominence of themes. Notwithstanding these caveats, the revised integration ties the mapping to concrete modeling decisions, and the resulting framework remains transparent, data-efficient, and policy-oriented for the Querétaro context. Future work may hybridize LP/GP with selective metaheuristics for dynamic scheduling while preserving interpretability for public deployment.

Similar work in this area has been developed, demonstrating the efficiency of Linear Programming (LP) in route optimization. For example, the study in [23] aimed to minimize the gap between the demand and supply of bus seats. Another example is provided in [24], where LP was used to optimize school bus routes throughout central Ankara, Turkey. Although school transportation represents a real-world problem, it is simpler than optimizing the entire public transportation system of a city. Additionally, the work presented in [25] illustrated the use of LP to optimize a single route. While that study focused on real public transportation, it is distinguished by being limited to only one route.

The most comparable studies that optimize city-wide transportation routes using LP are [26], which focused on Nigeria; [27], which addressed transportation in the city center of Antalya, Turkey; and [28], which focused on Kuwait.

Table 2. Comparison of this research with similar works.

Investigation	City	Variable to Optimize	Restrictions	${\mathrm{CO}}_2$ Estimating	Saving Estimation
Our Work	Queretaro	Fuel consumption	12	X	X
[26]	Lagos	Waiting time	5	-	-
[27]	Antalya	Number of vehicles	10	-	-
[28]	Kuwait	Number of vehicles	7	-	X

highlights the key differences between these studies and the research presented in this paper.

In summary, Queretaro faces significant challenges related to vehicular congestion, excessive fuel consumption, and pollutant emissions in its public transportation system. Despite efforts to implement cleaner technologies and optimize routes, the sustainability of the system remains a challenge that requires innovative solutions and a comprehensive approach to public policy and technological improvements [15].

3. Materials and Methods

The technique proposed in this study to optimize the number of urban transport routes in the city of Queretaro is LP, which is implemented through the development of a mathematical model derived from survey responses collected from public transport operators. In 2024, surveys were conducted with 316 urban transportation drivers in Queretaro to gather key operational data, particularly diesel fuel consumption. This information was then used to estimate ${\mathrm{CO}}_2$ emissions for each vehicle using a standard emissions equation based on diesel emission factors. The resulting emissions estimates, applied to the minimized route configuration obtained from the LP model, will be presented to the Mobility Agency of the State of Queretaro (AMEQ).

To estimate mobility demand, Artificial Neural Networks (ANNs) have been explored as an alternative methodology. ANNs can produce robust demand forecasts using simple and accessible input variables, offering valuable tools for transportation planning. Previous research (e.g., [29,30,31]) has demonstrated the application of ANNs in solving continuous LP problems. However, challenges arise in discrete problem spaces, where convergence issues can occur. Additionally, ref. [32] examined a class of neural networks modeled by dynamic gradient systems with exact non-differentiable penalty functions to address LP problems.

Despite these advances, Deep Neural Networks (DNNs) face persistent challenges such as slow convergence rates and pathological curvature when using first-order gradient methods. To mitigate these issues, higher-order and optimized training techniques have been proposed to improve backpropagation efficiency [33].

Nonetheless, practical limitations such as the selection of appropriate network architecture, high computational cost, and the need for extensive datasets can hinder the applicability of neural networks in urban environments where data and resources may be limited, including Queretaro. In contrast, linear programming offers a more immediate and interpretable approach. This method allows for the formulation of systems of inequalities and an objective function that can be tailored to minimize fuel consumption and ${\mathrm{CO}}_2$ emissions. Specifically, Ref. [34] demonstrated how LP models simplify complex urban mobility problems into solvable structures, Ref. [35] showed the effectiveness of this approach in directly reducing operational costs and environmental impacts, and Ref. [36] emphasized its advantage in providing interpretable results that support decision-making for sustainable transport planning.

In contrast, linear programming offers a more immediate and interpretable approach. LP involves the formulation of a system of inequalities and an objective function, aiming either to minimize or maximize a specific quantity, in this case fuel consumption and ${\mathrm{CO}}_2$ emissions. Prior research has demonstrated the usefulness of LP in simplifying complex transportation problems into tractable optimization models [34]. Other studies have highlighted its capacity to improve the allocation of resources and reduce operational inefficiencies in public transport networks [37]. More recently, evidence has shown that LP can be successfully applied to design sustainable strategies that balance environmental goals with economic feasibility [38]. By translating real-world constraints such as route coverage, driver availability, and demand fulfillment into mathematical expressions, LP provides an efficient framework for identifying optimal routing strategies. Optimizing the number of routes in each city zone requires a detailed analysis of transport demand across various urban sectors. This enables the identification of high-traffic corridors and facilitates the merging or reconfiguration of overlapping routes, thereby eliminating redundancies and inefficiencies. These improvements directly reduce the total kilometers traveled, which in turn leads to lower fuel consumption and a reduction in ${\mathrm{CO}}_2$ emissions.

A summary of the findings is presented in Figure 2.

As can be seen in the flowchart in Figure 1, the constants Ci = Diesel consumption per day and D1 are missing the deviation variable. These constants were collected from surveys conducted among 316 urban transport operators in the city of Queretaro. To develop the LP model, it is necessary to know the Ci constant, i.e., diesel consumption in liters per operator per day for each zone.

3.1. Linear Programming Model

To define the decision variables, we assume that the city of Queretaro is divided into ten zones. Each variable $x_i$ represents the number of transportation routes in zone i.

• Decision variables.

Let

$$x\triangleq {(x_1,x_2,\dots ,x_{10})}^{\mathsf{T}},x_i\in {\mathbb{Z}}_{\ge 0}=\#\mathrm{of} \mathrm{routes} \mathrm{in} \mathrm{zone}i(i=1,\dots ,10).$$

Minimum per zone (proposed, August 2024).

In compact form:

$$x\ge d,\mathrm{with}d\triangleq {(8,5,7,10,12,14,18,15,14,17)}^{\mathsf{T}}.$$

• Equivalently, in concise expanded form:

$$\begin{array}{cc}\hfill x_1& \ge 8,x_2\ge 5,x_3\ge 7,x_4\ge 10,x_5\ge 12,\hfill \\ \hfill x_6& \ge 14,x_7\ge 18,x_8\ge 15,x_9\ge 14,x_{10}\ge 17.\hfill \end{array}$$

(1)

3.2. Step 2: Objective Function Statement (USD Monetary Units)

The objective of this linear programming model is to minimize the total cost of fuel consumption associated with the number of transportation routes in each zone. Each coefficient represents the cost in USD per route in the corresponding zone.

• Equation (2): Objective function to minimize total cost of routes.

$$\mathrm{MinW}=748x_1+648x_2+673x_3+973x_4+1047x_5+1197x_6+748x_7+523x_8+773x_9+773x_{10}$$

(2)

Each parameter is considered per operator and per day. The amounts of 748, 648, 673, 973, …, 773 represent the monetary units (in USD) for daily diesel consumption, averaged per day and per route. The objective function coefficients of each region are provided in the linear programming model section of this paper; however, the source and rationality of these values are not explained in detail. It is recommended to supplement the relevant data collection and calculation basis to enhance the persuasiveness of the model (

Table 3. Survey-based minimum number of routes per zone (August 2024).

Zone	Minimum Routes
1	8
2	5
3	7
4	10
5	12
6	14
7	18
8	15
9	14
10	17

).

The objective function coefficients were obtained by collecting data from the questionnaire administered to the operators of urban transport units in the city of Queretaro.

3.3. Step 3: Minimum-Service (Lower-Bound) Constraints

The right-hand sides below are the survey-based route minima proposed for each zone (August 2024).

• Decision variable:

$$x_i\in {\mathbb{Z}}_{\ge 0}(\mathrm{number}\mathrm{of}\mathrm{routes}\mathrm{in}\mathrm{zone}i),i=1,\dots ,10.$$

(3)

• Compact form:

Let

$$x\triangleq {(x_1,\dots ,x_{10})}^{\mathsf{T}},d\triangleq {(8,5,7,10,12,14,18,15,14,17)}^{\mathsf{T}}.$$

Then, the lower-bound (minimum-service) constraints are

$$x\ge d.$$

(4)

• Expanded form:

  $$\begin{array}{cccccccccc}\hfill x_1& \ge 8,\hfill & \hfill x_2& \ge 5,\hfill & \hfill x_3& \ge 7,\hfill & \hfill x_4& \ge 10,\hfill & \hfill x_5& \ge 12,\hfill \\ \hfill x_6& \ge 14,\hfill & \hfill x_7& \ge 18,\hfill & \hfill x_8& \ge 15,\hfill & \hfill x_9& \ge 14,\hfill & \hfill x_{10}& \ge 17.\hfill \end{array}$$

  (5)

  A tabular summary is provided below.

• Equation (6): Daily hours per operator, per route, and per zone must exceed 1300.

$$\begin{array}{c}10x_1+10x_2+12x_3+9x_4+11x_5+10x_6+10x_7+10x_8+12x_9+11x_{10}\ge 1300\hfill \\ \hfill (\mathrm{Hours}\mathrm{per}\mathrm{operator},\mathrm{per}\mathrm{day},\mathrm{per}\mathrm{route},\mathrm{and}\mathrm{per}\mathrm{zone}).\end{array}$$

(6)

• Equation (7): Total number of operators per day must exceed 1100.

$$\begin{array}{c}12x_1+8x_2+8x_3+9x_4+13x_5+12x_6+8x_7+7x_8+9x_9+10x_{10}\ge 1100\hfill \\ \hfill (\mathrm{Operators},\mathrm{per}\mathrm{day},\mathrm{per}\mathrm{route},\mathrm{and}\mathrm{per}\mathrm{zone}).\end{array}$$

(7)

3.4. Surveys and Statistical Analysis

A structured questionnaire with closed questions on a Likert scale was used to collect data while addressing socioeconomic variables. The number of respondents was determined by calculating a random sample. In this study, Cronbach’s alpha was 0.77 [39].

The application of the questionnaires to the 316 urban transport operators took place over six months in 2024. This long time frame was due to the challenges posed by their work schedules, running from 5:00 a.m. to 11:00 p.m. These long hours made it difficult to conduct interviews in a timely manner. The instrument was tested and validated using Cronbach’s alpha, which measures the internal consistency of a questionnaire and ranges from 0 to 1 [39]. In this study, the alpha value of 0.77 indicated acceptable reliability.

The questionnaire was designed to gather information from operators on aspects such as daily fuel consumption, working hours, number of drivers per route, meal times, and other relevant operational data. Validation of the questionnaire was carried out using IBM SPSS Statistics v.20. A total of 33 items were designed and administered to the 316 urban transport operators in the city of Queretaro. The collected data were statistically analyzed and Cronbach’s alpha was calculated. A value close to 1 indicates strong internal consistency and greater reliability. The goal was to gather data on route characteristics, travel times, operator demand, and other factors that influence diesel consumption in public transportation.

The study used non-probability sampling (specifically snowball sampling, also known as “judgmental sampling”), which is recommended when information is difficult to obtain. Questions such as “How much do you spend on fuel per day?” or “How many hours do you work each day?” are often considered sensitive or confidential. In such cases, snowball sampling allows one participant to refer another, creating a chain of referrals until the target sample size is reached [40].

The structured data collection process facilitated efficient and agile information management. With these data, a linear programming model was proposed by defining the study variables, objective function, and constraints, as illustrated in Figure 2. Cronbach’s alpha was recalculated using statistical software. To achieve a reliability score of 0.77, 16 of the original 33 questions were eliminated. The Cronbach’s alpha coefficient is based on the average correlation between questionnaire items. One of its advantages is that it can indicate how reliability would change if specific questions were removed.

The mathematical technique of Linear Programming (LP) was used to solve the optimization problem. LP operates by minimizing or maximizing a linear function subject to linear constraints. The software used in this study was QM for Windows v.5.2 [41]. Previous studies have shown the effectiveness of LP in addressing transportation and energy optimization problems [42]. In addition, multiobjective approaches have extended its use to scenarios where both operational efficiency and environmental sustainability must be balanced [43]. Finally, applications in urban mobility have demonstrated how LP-based models can be tailored to the specific conditions of medium-sized cities [44]. This user-friendly platform enables the efficient formulation and resolution of LP problems. The resulting model aimed to identify the optimal combination of routes and resource allocation in order to minimize diesel consumption in Queretaro’s public transport system. Variables such as operator demand, route-specific fuel efficiency, and travel times were included.

The correlation between the minimized number of routes, diesel consumption, and emissions was also examined. The purpose of applying linear programming in this project was to identify strategies that can reduce fuel consumption and improve environmental outcomes.

The model incorporated twelve constraints, which are presented in step 3 of the linear programming section. These constraints addressed various operational and logistical aspects. Additionally, ten variables represented adjustable elements in the allocation of routes and resources. These variables enabled identification of the optimal configuration that minimizes diesel usage while respecting operational requirements. Overall, the use of QM for Windows together with the defined constraints and variables enabled an efficient approach to improving the sustainability and performance of Queretaro’s urban transportation system.

4. Results and Discussion

The Linear Programming (LP) model developed and implemented in this study generated clear and measurable improvements in the performance of Queretaro’s public transportation system. Through a formulation consisting of an objective function to minimize total diesel cost and twelve operational constraints (

Table 4. Statement of the system of twelve equations by ten variables. POM, QM software V.20.

	${\mathit{X}}_1$	${\mathit{X}}_2$	${\mathit{X}}_3$	${\mathit{X}}_4$	${\mathit{X}}_5$	${\mathit{X}}_6$	${\mathit{X}}_7$	${\mathit{X}}_8$	${\mathit{X}}_9$	${\mathit{X}}_{10}$		RHS
Minimize	748	648	673	973	1047	1197	748	499	748	749
Constraint 1	1	0	0	0	0	0	0	0	0	0	≥	8
Constraint 2	0	1	0	0	0	0	0	0	0	0	≥	5
Constraint 3	0	0	1	0	0	0	0	0	0	0	≥	7
Constraint 4	0	0	0	1	0	0	0	0	0	0	≥	10
Constraint 5	0	0	0	0	1	0	0	0	0	0	≥	12
Constraint 6	0	0	0	0	0	1	0	0	0	0	≥	14
Constraint 7	0	0	0	0	0	0	1	0	0	0	≥	18
Constraint 8	0	0	0	0	0	0	0	1	0	0	≥	15
Constraint 9	0	0	0	0	0	0	0	0	1	0	≥	14
Constraint 10	0	0	0	0	0	0	0	0	0	1	≥	17
Constraint 11	10	10	12	9	11	10	10	10	12	11	≥	1300
Constraint 12	12	8	8	9	13	12	8	7	9	10	≥	1100

), the model translated real-life technical and labor conditions into a structured decision-making tool. This case study not only provides quantitative evidence of efficiency gains but also demonstrates how mathematical modeling can directly support public transport planning in contexts of constrained budgets and growing mobility demand.

Table 4 presents the structure of the linear programming model, including the objective function and the full set of constraints applied to optimize the number of urban transport routes in Querétaro. Each coefficient and inequality reflects a real operational restriction obtained through field data from public transport operators, including working hours, fuel costs, and service requirements.

By capturing these real-world limitations, the model ensures that the optimization outcome is not only cost-effective but also socially and logistically feasible. The formulation demonstrates how abstract mathematical tools can be rooted in daily realities, allowing cities to transition from heuristic decision-making to structured evidence-based policies.

Table 5. Results obtained with the number of optimal routes per zone.

	${\mathit{X}}_1$	${\mathit{X}}_2$	${\mathit{X}}_3$	${\mathit{X}}_4$	${\mathit{X}}_5$	${\mathit{X}}_6$	${\mathit{X}}_7$	${\mathit{X}}_8$	${\mathit{X}}_9$	${\mathit{X}}_{10}$	RHS
Minimize	748	648	673	973	1047	1197	748	499	748	749
Solution	8	5	7	10	12	14	18	18.9	14	17	99,070.1

displays the optimal distribution of transport routes by zone, demonstrating that the LP model can reduce operating costs while meeting all required service thresholds. Notably, the model produces an actionable result that can directly inform decisions on fleet deployment and resource allocation.

The explanation for the fuel cost coefficients per operator per day was obtained from the responses of transport operators. They commented that they spend an average of between USD 66 and 80 per day. However, the constraints of the LP model were derived directly from the problem of route duplication. The idea is to minimize daily fuel costs per truck based on the existing routes. When proposing the LP model, the constraints were obtained naturally. The cost objective achieved (USD 99,070.10 daily) highlights the model’s capacity to yield significant operational savings. Furthermore, fractional outputs such as 18.9 for zone 8 illustrate flexibility in application, allowing for adaptive policies that balance optimization with political and service delivery considerations.

Table 6. Savings considering the optimal number of routes.

Current Number of Routes	Optimal Number of Routes	Daily Savings
148	124	USD 17,071.90
USD 116,142	USD 99,070.10

Price of US dollar: MXN 20.04, as of 31 October 2024.

quantifies the economic advantage obtained by implementing the optimized route system, with daily savings of over USD 17,000. When projected over an annual period, this level of cost efficiency could yield substantial financial relief for municipal governments.

These funds could be reinvested in infrastructure upgrades, low-emission vehicle procurement, or even operator training programs. In this way, the model in this paper represents not merely a tool for optimization but a catalyst for sustainable reinvestment and continuous improvement of the system.

Table 7. Fuel savings and CO₂ emissions reduction in Querétaro’s public transportation system (October 2024).

Daily Savings (USD)	Fuel Saved (Liters/Day)	CO2 Avoided (kg/Day)
17,071.90	13,789	35,681

Annual CO₂ reduction per zone: 13,253 tons/year. Fuel price: MXN 24.81/liter (8 October 2024).

highlights the environmental implications of route optimization. The reduction of 13,789 L of diesel per day and more than 13,000 tons of CO₂ emissions per year is a major contribution to the sustainability goals.

One liter of diesel produces 2.67 kg of CO₂ when burned, depending on factors such as the exact composition of the fuel and combustion conditions; 2.67 kg is a widely accepted average value. Thus, performing the corresponding calculations results in a reduction in CO₂ emissions of up to 13,000 tons per year. Although there are a few recent estimates of global fuel consumption and related CO₂ emissions of road transport [20], the effects of vehicle weight and road grade have not been studied in detail. Most models include a number of vehicle characteristics as well as travel and driving modes; however, other important elements such as vehicle weight, road grades, and weather effects are not sufficiently addressed because they are difficult to predict or measure. There are also estimates of global fuel consumption and CO₂ emissions related to road transport [20,21]. While most emissions models include various characteristics, mileage, and driving modes of vehicles, other important factors such as vehicle weight, road gradient, and weather effects are often not adequately addressed due to the difficulty of predicting them. The common equation used to measure CO₂ emissions depends on the amount of required power, a factor that is extremely difficult to obtain when it comes to urban transport. The equation is as follows (8):

$${\mathrm{CO}}_2=\left({\displaystyle \frac{\mathrm{Distance}}{\mathrm{fuel}\mathrm{efficiency}}}\right)\left(\mathrm{HV}\times \mathrm{EF}\right)$$

(8)

where D is distance, HV is the diesel health value, and EF is the emission factor.

This formula applies to road transport; for urban transport, fuel efficiency is difficult to determine given constant stops and factors such as traffic congestion. Therefore, the average of 2.67 kg of COCO₂ per day per liter of diesel burned was readily used [21].

These reductions directly support climate action plans and air quality improvement goals. From a public health perspective, fewer emissions translate into reduced exposure to pollutants for urban residents, reinforcing the public value of technical models such as this LP-based approach.

4.1. Integer Programming Results

In response to the methodological requirements of the study, the model was also solved as an Integer Linear Programming (ILP) problem using the Integer Programming module of QM for Windows v5.2. All ten decision variables were defined as integers while maintaining the route-specific minimum operation constraints as well as the global requirements of service hours (≥1300) and operators (≥1100).

The optimal integer solution differs from the continuous case only in variable $x_8$, which increases from 18 to 19 units in order to satisfy the service hours constraint. The final integer solution is

$$x=(8,5,7,10,12,14,18,19,14,17),$$

with a 1301 total service hours, 1179 operators, and a total cost of 99,137 monetary units.

Compared to the continuous model, the increase in total cost is marginal; however, the ILP formulation ensures feasibility and optimality in the integer domain. This result confirms the robustness of the proposed approach, as the overall structure of the solution remains virtually unchanged while guaranteeing practical implementability where fractional allocations are not admissible.

4.2. Results: Goal Programming for Cost, Coverage, and Demand

This subsection reports the Goal Programming (GP) results, keeping the original coefficients, matrices, and targets intact. We first recall the planning logic and the network structure, then present the GP model, solver rows as entered in QM, and route-level simulation that couples cost and demand.

Table 8. Source: authors’ elaboration.

Linear Programming (LP)	Goal Programming (GP)
Uses only one objective	Has more than one objective
Variables and the objective function must be linear	Variation of LP
Linear functions in decision variables are linear constraints, optimizing a linear objective function	Achieves an efficient solution
The optimal solution (maximum or minimum) must occur at each vertex of the feasible set	Uses goal constraints
	Has three types of models: Without priority With priority With priority and weighting Each objective is viewed as a goal

contrasts Linear Programming (LP) and Goal Programming (GP). GP is used here because multiple goals must be satisfied simultaneously (cost ceiling and bus coverage by area), with deviations explicitly accounted for at each priority level.

The urban transportation network is geographically classified into five zones ($Z_1,\dots ,Z_5$) and four areas ($A,B,C,D$). The 5 × 4 configuration is shown in

Table 9. Number of routes in the city of Querétaro by zone and area.

Zone/Area	A (Routes)	B (Routes)	C (Routes)	D (Routes)
$Z_1$	3	3	1	0
$Z_2$	15	12	10	0
$Z_3$	14	17	10	3
$Z_4$	4	21	13	3
$Z_5$	5	12	2	1

. This is the same configuration previously stated in the study.

The supply–demand transportation matrix, used as an approximation of existing routes and buses in the city, is unbalanced (supply differs from demand); see

Table 10. Number of routes and supply–demand matrix for Querétaro.

O/D	A	B	C	D	Supply
$Z_1$	3	3	1	0	84
$Z_2$	15	12	10	0	444
$Z_3$	14	17	10	3	528
$Z_4$	4	21	13	3	492
$Z_5$	5	12	2	1	240
Demand	492	780	432	240

. Supply and demand were obtained by multiplying the number of routes by the average number of buses per route (12).

Currently, there are 149 routes with ≈12 buses per route on average. The matrix W collects the (approximate) number of buses by zone and area:

$$W=\left(\begin{array}{cccc}{X}_{1A}& X_{1B}& X_{1C}& X_{1D}\\ X_{2A}& X_{2B}& X_{2C}& X_{2D}\\ X_{3A}& X_{3B}& X_{3C}& X_{3D}\\ X_{4A}& X_{4B}& X_{4C}& X_{4D}\\ X_{5A}& X_{5B}& X_{5C}& X_{5D}\end{array}\right),X_{ij}=\mathrm{number}\mathrm{of}\mathrm{buses}\mathrm{in}\mathrm{zone}i\mathrm{and}\mathrm{area}j.$$

• Goal Programming formulation.

The fuel cost goal relation (Goal 1) is provided by (9); the constants are the 2023 survey-based daily fuel costs per bus:

$$\begin{array}{cc}\hfill & 56X_{1A}+62X_{1B}+66X_{1C}+60X_{1D}\hfill \\ \hfill & +54X_{2A}+62X_{2B}+67X_{2C}+61X_{2D}\hfill \\ \hfill & +64X_{3A}+62X_{3B}+63X_{3C}+70X_{3D}\hfill \\ \hfill & +74X_{4A}+63X_{4B}+61X_{4C}+59X_{4D}\hfill \\ \hfill & +64X_{5A}+62X_{5B}+59X_{5C}+60X_{5D}+D_1-E_1=9312\mathrm{USD}.\hfill \end{array}$$

(9)

Coverage goals by area (Goals 2–5) are enforced as equality-with-deviations:

$$X_{1A}+X_{2A}+X_{3A}+X_{4A}+X_{5A}+D_2-E_2=492\mathrm{buses},$$

(10)

$$X_{1B}+X_{2B}+X_{3B}+X_{4B}+X_{5B}+D_3-E_3=780\mathrm{buses},$$

(11)

$$X_{1C}+X_{2C}+X_{3C}+X_{4C}+X_{5C}+D_4-E_4=432\mathrm{buses},$$

(12)

$$X_{1D}+X_{2D}+X_{3D}+X_{4D}+X_{5D}+D_5-E_5=240\mathrm{buses}.$$

(13)

Hard (supply) constraints reflect bus availability in each zone:

$$\begin{array}{cc}\hfill X_{1A}+X_{1B}+X_{1C}+X_{1D}& \le 84,\hfill \\ \hfill X_{2A}+X_{2B}+X_{2C}+X_{2D}& \le 444,\hfill \\ \hfill X_{3A}+X_{3B}+X_{3C}+X_{3D}& \le 528,\hfill \\ \hfill X_{4A}+X_{4B}+X_{4C}+X_{4D}& \le 492,\hfill \\ \hfill X_{5A}+X_{5B}+X_{5C}+X_{5D}& \le 240.\hfill \end{array}$$

Constants from INEGI (2025).

• QM model rows.

Table 11. Goal Programming run (QM for Windows): weights, priorities, coefficients, and RHS.

Row	Wt (d+)	Prty (d+)	Wt (d−)	Prty (d−)	${\mathit{X}}_1$	${\mathit{X}}_2$	${\mathit{X}}_3$	${\mathit{X}}_4$	${\mathit{X}}_5$	${\mathit{X}}_6$	${\mathit{X}}_7$	${\mathit{X}}_8$	${\mathit{X}}_9$	${\mathit{X}}_{10}$	${\mathit{X}}_{11}$	${\mathit{X}}_{12}$	${\mathit{X}}_{13}$	${\mathit{X}}_{14}$	${\mathit{X}}_{15}$	${\mathit{X}}_{16}$	${\mathit{X}}_{17}$	${\mathit{X}}_{18}$	${\mathit{X}}_{19}$	${\mathit{X}}_{20}$	RHS	Rel
Goal 1	1	1	0	0	56	62	66	60	54	62	67	61	64	62	63	70	74	63	61	59	64	62	59	60	9312	=
Constraint 1	0	0	0	0	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	84	≤
Constraint 2	0	0	0	0	0	0	0	0	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	444	≤
Constraint 3	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	1	0	0	0	0	0	0	0	0	528	≤
Constraint 4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	1	0	0	0	0	492	≤
Constraint 5	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	1	240	≤

shows the exact GP rows (weights, priorities, coefficients over $(X_1,\dots ,X_{20})\equiv (X_{1A},X_{1B},X_{1C},X_{1D},X_{2A},\dots ,X_{5D})$) and RHS used in QM.

• Constraint analysis.

At optimality, the deviation summary (

Table 12. Constraint analysis (QM for Windows).

Constraint Analysis	RHS	${\mathit{d}}^{+}$ (Row i)	${\mathit{d}}^{-}$ (Row i)
Goal 1	9312	0	0
Restriction 1	84	0	0
Restriction 2	444	0	271.5555
Restriction 3	528	0	528
Restriction 4	492	0	492

) shows that the fuel cost target is met with zero deviation, while some supply rows display nonzero $d^{-}$ (unused capacity), consistent with the adopted priorities.

It can be observed that Goal 1 is achieved, that is, the deviation $E_1$ is minimized, which implies that the fuel cost expressed in the objective function remains at most USD 9312 in the city of Queretaro under the following constraints: maintaining a supply of up to 84 buses, reducing the supply from 444 to 271 buses, and maintaining a supply of 528 and 492 buses for the rest of the city.

• Simulation 1: Routes

We consider at least 145 routes in the city of Querétaro, with a maximum total daily cost of USD 91,574 for all routes and serving at least 450,000 passengers per day across all routes.

A solution $\mathbf{X}=(X_1,X_2,\dots ,X_n)$ is feasible if it satisfies all the constraints of the problem.

In this case, $\mathbf{X}=(X_1,X_2,X_3,X_4)\in {\mathbb{R}}^4$ is defined as follows:

$$X_i=\mathrm{Number}\mathrm{of}\mathrm{routes},i=\overline{1,4}$$

where the demand for buses is considered per region:

• 1: Region A
• 2: Region B
• 3: Region C
• 4: Region D.

• Goal 1: $min{D}_1$

  $$X_1+X_2+X_3+X_4\ge 145\left(\mathrm{Routes}\right)$$

  $$X_1+X_2+X_3+X_4+D_1-E_1\ge 145\left(\mathrm{Routes}\right)$$

  where the total number of routes in the city of Querétaro in May 2025 is 145.

• Goal 2: $min{E}_2$

  $$612X_1+650X_2+599X_3+493X_4+D_1-E_1\le \mathrm{91,574}\left(\mathrm{USD}\right)$$

  where 612, 650, 599, and 493 are the approximate daily fuel costs per route in USD.

• Goal 3: $min{D}_3$

  $$3710X_1+2915X_2+2820X_3+3103X_4+D_1-E_1\ge \mathrm{450,000}(\mathrm{passengers}/\mathrm{day}).$$

  The estimated numbers of passengers per route per day are 3710, 2915, 2820, and 3103.

• Solution: As shown in the following table, at least 145 routes would be covered, while that there would be a difference of USD 4,118.66 in fuel cost. The demand of at least 450,000 passengers per day across all routes would still be met.

• Three Goals:
  • Maintain at least 145 routes.
  • Keep total daily fuel costs below USD 91,574.
  • Serve at least 450,000 passengers per day.

• Simulation outcome.

The solution satisfies the route floor and passenger floor with zero shortfall while incurring a cost overrun of USD 4118.66; see

Table 13. Simulation 1 (routes): Goal deviations.

Constraint	RHS	${\mathit{d}}^{+}$ (Row i)	${\mathit{d}}^{-}$ (Row i)
Goal 1 (Routes)	145	0	0
Goal 2 (Cost, USD)	91,574	0	4118.66
Goal 3 (Passengers)	450,000	0	0

. This quantifies the budget pressure induced by coverage and demand commitments.

• Takeaway.

Equations (9)–(13) and Table 11, Table 12 and Table 13 show that the GP structure protects the highest-priority fiscal target (USD 9312 citywide fuel cost) while making explicit the extra USD 4118.66 needed to simultaneously guarantee 145 routes and 450,000 daily riders under the specified per-route parameters.

4.3. Comparative and Socio-Environmental Implications

Route optimization, with all its inherent constraints and conditions, can be a challenging problem; however, linear programming and multi-objective programming can significantly improve efficiency in such complex scenarios. This study demonstrates not only the mathematical soundness of the model but also its practical and social relevance for urban and peri-urban regions undergoing rapid demographic and infrastructural transformations. In the context of Querétaro, where regional mobility has evolved significantly since the 1990s, LP and MOP provide a data-driven approach to adapting transport systems to emerging commuter patterns.

Optimization offers benefits across multiple domains. From an environmental perspective, studies based on stoichiometric calculations indicate a ${\mathrm{CO}}_2$ emission factor of 2.68 kg per liter of diesel. This factor is widely recognized by entities such as the IPCC, the US EPA, and the New Zealand Ministry of Environment [1].

With current expenditures of approximately USD 17,100 on diesel, and based on prevailing fuel prices in Querétaro, this amount corresponds to between 12,100 and 12,400 L of diesel. This translates into avoided emissions of approximately 32 to 34 tons of ${\mathrm{CO}}_2$ per day, or nearly 13,000 tons annually. These savings have multiple implications. Local air quality improves as lower emissions reduce concentrations of pollutants such as NOx and PM$2.5$, decreasing respiratory and cardiovascular risks for nearby populations. Optimized routes also reduce fuel consumption, enhancing service speed and reliability. In addition, participation in emissions reduction aligns with climate goals, offering potential environmental certifications or incentives that enhance the reputation and competitiveness of businesses and municipalities. Reductions in air pollution also benefit rural–urban transition zones where industrial development and residential settlements coexist, such as Navajas–Galeras, leading to lower disease incidence, reduced absenteeism, and improved overall quality of life.

Fieldwork in these microregions reveals a rural population increasingly dependent on urban employment, often commuting long distances daily. The LP model addresses this spatial mismatch by providing efficient, cost-sensitive, and environmentally responsible transport options. Importantly, it enables policymakers to extend service coverage proactively while maintaining budgetary discipline.

The model’s social impact is reinforced by its empirical foundation, built on operational data from local drivers, as well as its alignment with the region’s ongoing transport modernization agenda. Insights from the AMEQ Technical Director indicate that even if route reductions slightly increase user wait times (e.g., from 15 to 20–25 min), the improvement in overall service efficiency benefits both operators and passengers.

Moreover, this study contributes to the limited body of research that transcends qualitative sustainability discussions by introducing a quantitative and transferable model.

Table 14. Contributions related to this study.

Work	Vehicular Congestion	Estimating of ${\mathbf{CO}}_2$	Optimization of Fuel Consumption	New Transportation Routes	Survey	New Transportation Policies	Mathematical Model
Our work	X	X	X	X	X	X	X
[45,46]	X	–	–	X	X	X	–
[20]	–	X	X	–	–	–	X
[47,48,49,50]	X	–	–	X	–	X	–
[51]	–	X	–	–	–	–	X

compares this work to other national and international studies.

The versatility and low implementation cost of LP make it especially suitable for medium-sized cities where financial and technical resources are limited. Compared to other optimization techniques, LP is more transparent, more interpretable, and requires fewer computational resources while maintaining high accuracy and practical applicability.

Table 15. Comparison of optimization methods in urban transport planning.

Method	Cost	Computational Demand	Interpretability	Suitability for Public Policy
Linear Programming (LP)	Low	Low	High	High
Genetic Algorithms (GA)	Medium	High	Medium	Medium
Simulated Annealing	Medium	High	Low	Low
Machine Learning Models	High	Very High	Low	Medium
Chebyshev Interval Models	Low	Medium	Medium	Low

emphasizes LP’s superiority in balancing performance and ease of integration into policy frameworks. While metaheuristic and data-driven models are gaining popularity, their complexity and high cost often hinder adoption by public entities. In contrast, LP’s maturity and straightforward implementation make it a strategic choice for decision-makers committed to sustainable and inclusive urban growth.

In conclusion, this work illustrates that integrating LP into urban mobility planning not only delivers operational and environmental improvements but also promotes a deeper understanding of social needs and system limitations. It empowers local governments to design transport strategies that are not only efficient but also equitable and responsive to the evolving dynamics of urban–rural territories.

5. Conclusions

This study offers a replicable and effective strategy for addressing the inefficiencies of urban public transport systems through the application of Linear Programming (LP). Limitations of this project’s approach include the lack of consideration of population growth, which would lead to the creation of more routes in the future, resulting in more trucks and consequently more emissions. Therefore, Goal Programming (GP) is introduced in this paper as a complement. This implementation greatly reduces the limitations of the original work, as a number of interesting results were obtained. The proposal based on linear programming reduced 24 duplicate routes, thereby saving fuel and emissions. The proposal based on GP then led to the following results.

Daily fuel costs were kept below USD 91,574 while serving at least 450,000 passengers per day. The solution provided by the simulation outcome satisfies both the route floor and passenger floor with zero shortfall, and incurs a cost overrun of USD 4118.66.

The proposed model was specifically tailored to the dynamics of Queretaro, a city facing rapid urbanization and complex rural–urban mobility patterns. By optimizing the number of routes and eliminating duplications, this study generated a measurable economic impact by achieving daily fuel savings of over USD 17,000 and an environmental benefit equivalent to a reduction of more than 13,000 tons of ${\mathrm{CO}}_2$ emissions per year.

In addition to technical and economic metrics, the social and environmental relevance of this research is significant. By improving connectivity in underserved peripheral zones and reducing the reliance on overlapping and inefficient transport routes, the proposed model fosters greater equity in mobility access. Simultaneously, fewer emissions contribute to improved air quality, public health, and environmental resilience, which are critical goals for cities adapting to the realities of climate change.

One of the principal contributions of this research is the development of a low-cost data-driven optimization model that is easy to implement and does not require large-scale infrastructure or high computational resources. Its foundations in real-world data collected from transport operators ensure its practicality and alignment with labor conditions. This enables informed public policy, reinforcing the social role of transportation systems as engines of development and sustainability.

This study also aligns with national and global environmental policies, including the gradual implementation of the Euro VI and VII emission standards in Queretaro’s bus fleet. The proposed model not only complements these policy efforts but enhances their effectiveness by ensuring that new technologies are deployed along optimal routes.

From a research perspective, this work opens a valuable line of inquiry into the use of LP and other hybrid optimization techniques for public service systems. Future studies could integrate dynamic scheduling, real-time data analytics, or equity-based access indicators into the modeling framework. Moreover, the methodology has potential applications in other domains such as freight logistics, emergency response, or rural transit planning, which can broaden the scope of mathematical tools in building smarter, more inclusive, and sustainable cities.