A Model for a Circular Food Supply Chain Using Metro Infrastructure for Quito’s Food Bank Network ^†

Abstract

The increasing disparity in global food distribution has amplified the urgency of addressing food waste and food insecurity, both of which exacerbate economic, environmental, and social inequalities. Traditional food bank models often struggle with logistical inefficiencies, limited accessibility, and a lack of transparency in food distribution, hindering their effectiveness in mitigating these challenges. This study proposes a novel Food Bank Network Redesign (FBNR) that leverages the Quito Metro system to create a decentralized food bank network, enhancing efficiency and equity in food redistribution by introducing strategically positioned donation lockers at metro stations for convenient drop-offs, with donations transported using spare metro capacity to designated stations for collection by charities, reducing reliance on dedicated transportation. To ensure transparency and operational efficiency, we integrate a blockchain-based traceability system with smart contracts, enabling secure, real-time tracking of donations to enhance stakeholder trust, prevent food loss, and ensure regulatory compliance. We develop a multi-objective optimization framework that balances food waste reduction, transportation cost minimization, and social impact maximization, supported by a mixed-integer linear programming (MIP) model to optimize donation allocation based on urban demand patterns. By combining decentralized logistics, blockchain-enhanced traceability, and advanced optimization techniques, this study offers a scalable and adaptable framework for urban food redistribution, improving food security in Quito while providing a replicable blueprint for cities worldwide seeking to implement circular and climate-resilient food supply chains.

1. Introduction

Addressing the growing imbalance in global food distribution, food waste and food insecurity have become increasingly critical challenges that demand innovative, scalable, and sustainable solutions. Each year, approximately one-third of food produced for human consumption is lost or wasted, exacerbating hunger, malnutrition, and environmental degradation [1]. Food banks play a pivotal role in mitigating these issues by redistributing surplus food to vulnerable populations. However, traditional centralized models face logistical inefficiencies, limited reach, and opaque supply chains, particularly in large urban areas with fragmented infrastructure [2,3]. This study addresses these gaps by proposing a decentralized food bank network redesign (FBNR) for Quito, Ecuador, leveraging the city’s metro system, blockchain technology, and multi-objective optimization. Our methodology integrates three interconnected components to ensure practicality, traceability, and stakeholder-aligned planning, offering a replicable framework for other cities in Latin America and beyond.

Practical Implementation of the Decentralized Model. Traditionally, food banks operate within centralized networks where recovered food is stored and distributed from central locations. The supply chain operates with products being transferred by both donors and the food bank itself. The distribution of these products is then handled internally using the food bank’s dedicated fleet of vehicles; however, this model often leads to logistical inefficiencies, limited reach, and accessibility issues, particularly in large urban areas [4]. Studies highlight the need for improved logistics, transportation, and real-time tracking to mitigate food waste and enhance crisis preparedness [5,6,7]. To increase efficiency and expand the reach of food banks, it is essential to explore decentralized approaches that leverage existing and accessible infrastructure, such as public transportation networks.

Recent research has increasingly focused on integrated passenger–freight transportation models, which leverage the unused capacity of public transportation to reduce urban congestion and improve efficiency [8]. These models, primarily studied in Europe and Asia, often focus on buses, metros, and trains as transportation modes, and shared vehicles as the most prevalent integration type. Given these advancements in transportation models, there is potential in applying similar strategies to improve food bank operations in urban environments.

Quito, the capital of Ecuador, faces significant socioeconomic challenges, with nearly 30% of its 2.7 million residents living in poverty, experiencing high rates of underemployment and chronic malnutrition [9]. This study focuses on the Quito Food Bank (QFB), a non-profit organization, which aims to combat hunger and reduce food waste by collecting surplus food from various sources and redistributing it to vulnerable populations [10]. Currently, the food bank operates a centralized distribution model. Given these inequitable conditions, optimizing food distribution is vital to ensure that marginalized groups receive adequate support.

The Food Bank Network Redesign (FBNR) problem can be optimized by leveraging the Quito Metro system, which commenced operations in December 2022, to create a decentralized food bank network. The proposed model involves installing food donation lockers at metro stations for convenient drop-offs, using the metro’s spare capacity to transport food to designated stations for collection by charities. To enhance logistics and transparency, a blockchain-based traceability system is implemented, improving data flow and coordination among stakeholders.

The linear sequence of stations, including key sites that serve as collection points, facilitates efficient distribution and improves accessibility to impoverished areas. Furthermore, businesses in the Hotels, Restaurants, and Cafes (HORECA) sector near metro stations are identified as potential donors, strengthening the food bank’s capacity to serve those in need. The diverse objectives of stakeholders must be considered to minimize food waste, reduce transportation costs, and enhance the social impact of food distribution, ultimately contributing to a more sustainable and equitable food system. This FBNR proposal provides not only a potential solution for Quito but also a scalable framework that can be replicated in other metropolitan areas facing similar challenges.

The proposed model reimagines food donation logistics through Quito Metro’s infrastructure. Surplus food from donors—primarily HORECA—is standardized into Traceable Resource Units (TRUs), which are labeled, durable boxes with fixed volume capacities. Volunteers then load the TRUs onto specialized caddies (wheeled containers) during off-peak hours, utilizing spare metro wagon capacity. The metro transports donations to strategically located collection points at the northern (El Labrador) and southern (Quitumbe) termini, proximate to impoverished communities. The final distribution is managed by local charities, ensuring equitable access while reducing reliance on the food bank’s limited vehicle fleet.

Blockchain-Enhanced Traceability. A blockchain-based system underpins the entire supply chain, ensuring transparency and accountability. Each TRU is assigned a unique digital identifier linked to a smart contract, which records critical data such as donor details, food type, expiration dates, handling conditions, and ownership transfers. Donors upload visual documentation (e.g., photos of donations) to the InterPlanetary File System (IPFS), with hashes stored on-chain. Real-time updates—triggered by events like locker drop-off, metro loading, and final distribution—are immutably logged, enabling stakeholders to monitor food quality, minimize spoilage, and audit operations. This system mitigates risks of fraud, loss, and mismanagement while fostering trust among participants [11,12]

Multi-Objective Optimization for Stakeholder-Centric Planning. The operational complexity of coordinating donations, metro schedules, and beneficiary necessitates a balanced approach. We develop a multi-objective optimization model that harmonizes competing priorities:

• City administrators seek to minimize transportation costs and urban congestion.
• Metro users require minimal disruption to passenger services.
• Donors prioritize convenient drop-off locations.
• Beneficiaries depend on timely, nutritious food access.

A mixed-integer programming (MIP) model with weighted objectives generates Pareto-optimal solutions that balance donation waiting time at stations ($Z_1$), total handling and transport time ($Z_2$), and total transportation and storage cost ($Z_3$). By adjusting weights (${\alpha }_1,{\alpha }_2,{\alpha }_3$), decision makers estimate trade-offs to match shifting urban demands [13]. For instance, prioritizing low storage costs (${\alpha }_3=1$) may slow deliveries, while emphasizing speed (${\alpha }_1=1$) can increase operational complexity.

Contextual Relevance and Scalability. Quito’s socioeconomic profile—marked by over 30% poverty, Andean topography, and a linear metro—makes it ideal for decentralized food distribution [9]. With poverty concentrated in northern and southern districts and centralized food banks underperforming, there is a clear need for multimodal logistics. This study introduces a tripartite framework leveraging metro infrastructure, blockchain traceability, and multi-objective optimization to advance Sustainable Development Goals (SDGs) 2 (Zero Hunger) and 12 (Responsible Consumption and Production) [14].

The framework’s modularity enables replication in Latin American cities with similar transit topologies, such as Bogotá’s TransMilenio and the Santiago Metro. Components like blockchain protocols and MIP optimization can be adapted to local factors—urban density, transit schedules, and socioeconomic disparities. This flexibility improves resource use and enhances resilience to supply chain disruptions in rapidly urbanizing areas.

By aligning with the spatial logic of chain-structured transit networks, the framework fosters scalable, equitable food redistribution while minimizing reliance on dedicated freight vehicles—a paradigm shift toward circular urban economies. Such scalability is further bolstered by the integration of open-source blockchain platforms and interoperable optimization algorithms, which reduce implementation costs and technical barriers for adopters. This approach offers a transferable blueprint for cities navigating the dual challenges of food insecurity and sustainable transit integration, advancing global discourse on smart urban logistics and SDGs-driven policymaking.

2. Related Work

Addressing food waste and food insecurity through innovative strategies has garnered significant attention in recent years. Several studies have explored various aspects of food bank operations, optimization of food distribution, and the use of public transportation networks in logistics. Food waste is a critical issue with far-reaching implications for both the environment and society. Globally, an alarming one-third of food intended for human consumption is lost or wasted [15]. This not only represents a substantial economic loss but also contributes to environmental degradation and greenhouse gas emissions. As noted by [16], reducing food waste is essential to improving food security and sustainability, with effective food rescue and redistribution systems playing a key role in achieving these objectives.

2.1. Food Waste and Food Insecurity

Food waste and food insecurity are pressing global issues with significant economic, environmental, and social implications. According to the Food and Agriculture Organization, approximately one-third of all food produced for human consumption is lost or wasted annually, amounting to nearly 1.3 billion tons worldwide [15]. This wastage contributes to greenhouse gas emissions, inefficient resource use, and lost economic value, exacerbating global hunger and food insecurity. In Ecuador, food waste is a major concern, reaching approximately 400 tons per day [17]. Furthermore, around 30% of children under the age of five in the city suffer from chronic malnutrition, underscoring the urgent need for more efficient food redistribution strategies [18].

Food banks play a crucial role in addressing both food waste and food insecurity by redistributing surplus food to vulnerable populations. Research has shown that optimizing food bank operations can significantly improve their effectiveness. Davis et al. [19] emphasize the importance of enhancing logistical and supply chain management practices to maximize the impact of food banks. Their findings suggest that inefficiencies in food collection, storage and distribution can limit the reach of food aid programs, highlighting the need for more systematic and data-driven approaches. Similarly, Bazerghi et al. [20] identify key challenges faced by food banks, including inadequate infrastructure, limited financial resources, and difficulties in managing fluctuating donation volumes.

In Ecuador, food waste is prevalent at multiple levels of the supply chain, including post-harvest losses, inefficient distribution, and lack of consumer awareness [17]. However, its centralized distribution model faces logistical challenges due to the city’s geography and infrastructure limitations. The current reliance on a small fleet of vehicles restricts the bank’s capacity to serve the growing number of people in need.

2.2. Food Bank Logistics and Optimization

Optimization models are widely used to address challenges in food distribution and supply chain management. Laporte et al. [21] provide a comprehensive overview of optimization techniques relevant to allocating food donations in this study. The effectiveness of MIP models in minimizing costs and improving service levels is explored by [22]. Several studies on food bank network redesign propose innovative approaches to improve food distribution efficiency and effectiveness.

Reusken et al. [23] presented an optimization model designed to allocate investment budgets to increase the number of beneficiaries served by food banks. They prioritize investments with the largest social impact and account for real-world challenges like decentralized organizations, data limitations, and varying transport and storage capacities. The Dutch Food Banks Association has applied these findings in practice, recommending targeted investments that could increase capacity and serve approximately 32% more beneficiaries.

2.3. Multi-Objective Optimization for Distribution Networks

The redesign of a multi-echelon food bank network for collecting and distributing donations has already been discussed [24]. Strategic decisions included opening new food banks, determining storage and transport capacities, and potentially closing or expanding existing ones. They proposed an MIP model that integrates economic, environmental, and social sustainability objectives, validated through a computational study on the Portuguese Federation of Food Banks network. Martins and Pato [25] introduced three decompose-and-fix heuristics for the multi-period, multi-product FBNR, focusing on several objectives. Each heuristic simplifies the problem by breaking it into two Multi-Objective MIP (MO-MIP) problems, significantly reducing computation time. These heuristics reduce Central Processing Unit (CPU) time by 80% to 97% compared to exact methods and can be adapted for other large MO problems.

Beheshtian et al. [26] present an MO optimization model for designing food bank networks, focusing on transportation costs, food quality, and service coverage. The findings underscore the importance of balancing multiple objectives to achieve optimal solutions in complex logistical networks. Suarez et al. [27] propose a novel multi-objective, multi-product, and multi-period model to address the challenge of allocating perishable food items in food bank warehouses. The model aims to ensure food safety, meet nutritional needs, and minimize shortages while adhering to a first expired-first out policy. The effectiveness of the model is demonstrated using real-world data from the Diakonia Food Bank in Guayaquil, Ecuador. Optimization models are critically dependent on the accuracy and reliability of their underlying data management systems. As food bank networks increase in complexity and scale, conventional data management approaches may prove insufficient in providing the necessary monitoring across decentralized networks.

2.4. Public Transport Integration in Urban Logistics

One innovative approach to improving food bank logistics is the integration of public transportation networks. Studies suggest that leveraging the unused capacity of metro and bus systems can enhance urban food distribution by reducing transportation costs and minimizing delays [28]. This concept aligns with broader efforts to develop circular food supply chains, ensuring that edible surplus food reaches those in need rather than being discarded. In Quito, the newly operational metro system presents an opportunity to incorporate public transport into food redistribution strategies, potentially reducing food waste and increasing food accessibility in underserved areas.

Marinov et al. [29] highlight the benefits of using public transportation for urban freight, particularly in reducing traffic congestion and emissions. Likewise, Behiri et al. [28] demonstrate the potential for public transportation to improve the efficiency and sustainability of urban logistics. Research shows that decentralizing food manufacturing and distribution can enhance resilience and flexibility during disruptions [30]. Integrating public transportation into this decentralized model further supports resilience by providing a reliable logistics framework.

2.5. Blockchain for Food Traceability and Logistics

In developing economies, low trust and high intermediation costs have persistently hindered sustainability progress [31], while rapid urbanization exacerbates food insecurity through inefficient distribution systems. Blockchain technology could address these dual challenges by creating transparent and cost-effective food redistribution networks that bypass traditional intermediaries. Addressing logistical inefficiencies through technological innovations, such as blockchain-based traceability systems and using existing public transportation infrastructure, can contribute to more sustainable and effective food bank operations [12].

Building on the principles of decentralization, this approach mirrors a peer-to-peer model by distributing responsibility across multiple stakeholders, reducing reliance on centralized control, and fostering a more resilient community-driven food redistribution system. The proposed integration of the Quito Metro into food bank logistics represents a scalable framework that can be replicated in other Latin American cities facing similar challenges, ensuring equitable access while minimizing monopolistic inefficiencies in food supply chains.

Blockchain systems, such as those outlined by Musamih et al. [12] and IBM Food Trust [32], offer a decentralized and secure ledger that significantly enhances data transparency and traceability within supply chains through cryptographic validation. These systems can leverage smart contracts to automate regulatory compliance with legal, environmental and social standards [33]. They also enable us to maintain data integrity of the allocation process based on predefined criteria and streamline operations while ensuring optimal resource distribution [34]. Such frameworks can be adapted to address the specific needs of food bank networks. When integrated with public transportation systems, blockchain technology can complement robust optimization models to foster more efficient and resilient food bank operations [11].

The food supply chain, including food banks, involves multiple stakeholders—donors, transporters, storage facilities, recyclers and beneficiaries. Conventional centralized systems often create information asymmetry, where some entities possess more data than others, leading to inefficiencies or an inequitable distribution. These issues persist despite the growing demand for greater transparency from consumers and stakeholders [35]. Blockchain technology can mitigate delays or unnecessary waste by ensuring all stakeholders have equal access to a shared ledger, improving coordination and decision making [36]. This transparency enhances logistical efficiency, reduces food waste, and enables a fairer redistribution.

3. Information Management in Food Bank Logistics

Blockchain technology can significantly enhance the logistics and transportation aspects of food redistribution by providing immutable traceability, optimized inventory management, and streamlined transaction processing. Its decentralized nature makes it particularly well suited for a food bank network, as it eliminates single points of failure. By leveraging blockchain, the proposed Food Bank Network Redesign (FBNR) can improve decision making and operational efficiency through real-time tracking, automated verification, and fraud prevention.

A critical component of this system is the Traceable Resource Unit (TRU) [37], which functions as a digital twin for each physical food donation, recording its entire lifecycle—from donor to recipient. In the FBNR model, food items are packed into uniquely identifiable boxes that serve as TRUs, enabling granular tracking without overburdening the system. Each TRU logs essential data (e.g., contents, expiration dates, handling conditions) on the blockchain, ensuring end-to-end visibility while dynamically matching supply with demand. This approach not only reduces food waste by preventing spoilage and misallocation but also enhances trust among donors, transporters, and charities through tamper-proof records.

3.1. Blockchain-Enhanced Traceability in FBNR

The proposed system utilizes blockchain technology to improve traceability within the food bank supply chain. By employing a smart contract (SC), stakeholders interact securely and transparently, enabling real-time tracking, maintaining data integrity, and ensuring transactions through decentralized storage. An SC is a self-executing agreement where the terms are encoded and directly written into lines of code. This provides an immutable and decentralized environment, enhancing trust and regulatory compliance, which in turn improves the overall reliability of the supply chain.

A high-level system architecture of the proposed food bank traceability system includes stakeholders and their interactions with the SC (see Figure 1).

Stakeholders will use software devices to interact with the SC and other resources through a user interface layer provided by a Decentralized Application (DApp), a software program that runs on a distributed network. This DApp connects to the SC and storage systems via application programming interfaces (APIs). Stakeholders will be able to execute and access authorized functions, data files from decentralized storage, IPFS hashes, and transaction details from on-chain resources [38].

An event in this context is a distinct action or occurrence within the supply chain that triggers the execution of predefined functions within the SC. Each stakeholder in the supply chain is assigned specific roles and permissions within the SC, ensuring transparency and accountability throughout the process. The SC records every transaction and status update related to the donations, providing real-time traceability to all participants. Each transaction is authenticated, verifiable, and safely logged, further ensuring the integrity and reliability of the system. Details of the donation or other identification techniques, such as the images, can be uploaded to the IPFS, which will then provide a hash to the SC during each event. The supply chain events are as follows:

• Donation Initiation: The HORECA donor will request the initiation of the donation process to the QFB. Once the request is approved, an event is triggered. The donor will pack the food and drop it off at the metro station locker.
• Distribution: The donation is transported via the metro system and the QFB vehicle fleet. Volunteers facilitate the loading of donations from lockers to metro wagons and unloading at destination station from metro wagons to QFB vehicles. The details of the package will be updated at loading and unloading points.
• Classification and Final Distribution: Upon arrival at the collection centers, donations are classified. Depending on the classification, donations are either distributed to beneficiaries or sent to composting facilities. Every action is logged, forming a sequence of events, ensuring traceability from donation initiation to final distribution.

3.2. Implementation of Proposed Traceability System

The donor will deploy a SC defining the details of the food donation lot, triggering an event to notify all supply chain participants. New participants can access these events and track the donation’s history since the information is stored permanently on the ledger. The donor may also upload an image of the lot to the IPFS for visual inspection by participants. The donor will package the lot, drop it off at a secure locker, and announce its availability for transfer via an event. Transporters interested in transferring the lot in the loading and unloading points will use a specialized function. At each step of the transfer, an event will notify participants of the new owner. The approval for the SC deployment is not considered for simplicity.

An entity relationship diagram (see Figure 2) illustrates the key entities and how they interact with the SC. It considers attributes like ownerID, which stores the blockchain address of the current contract owner. The Donation Lot SC can have only one owner at a time. When ownership changes, an event is triggered and recorded on the blockchain, enabling the tracing of the donation lot’s origin.

Since the SC represents a specific donation lot, it includes additional attributes like donationID, lockerID, numBoxes, image, and metroWagonID. There are also five mappings for the authorized entities—donors, transporters, food pantries, beneficiaries, and composting facilities—which have access to certain functions within the contract. Several functions are included to manage the donation process. Donation details, including donationID and numBoxes, are added through the donationDetails function. The SC and IPFS relationship is 1:1, as each donation lot will have one image uploaded to the IPFS.

Each HORECA donor declares to participants that the donation lot is available for pick-up in the locker via the initiateDonation function with lockerID as a parameter. An authorized entity intending to load the lot onto the metro wagon invokes the loadDonation function, inputting the metroWagonID, which subsequently updates the ownership to the designated transporter. Similarly, an entity interested in unloading the lot from the metro wagon executes the unloadDonation function, updating the ownership to the food pantry. The pantry then classifies the boxes suitable for consumption and executes the classifyDonation, which updates the ownership to the composting facilities for unsuitable boxes. The final distribution to the beneficiary is executed with the finalizeDonation function, setting the beneficiary as the ultimate owner.

From a technical standpoint, the implementation can utilize a modular smart contract architecture written in Solidity [39] and deployed on a Hyperledger Fabric-based permissioned ledger [40]. Role-based access control (RBAC) is enforced to ensure only authenticated stakeholders (e.g., volunteers, pantries, composting facilities) can invoke relevant functions [41].

Several technical barriers must be addressed. First, the integration with metro scheduling systems requires near-real-time interoperability, which poses challenges in synchronizing on-chain logic with dynamic transit data. This is mitigated by using off-chain oracles [42] that periodically fetch metro timetables from the Quito Metro API and update smart contract states accordingly. Finally, latency and scalability are managed by batching transactions during off-peak periods and employing layer-2 solutions such as Plasma or rollups to ensure faster confirmation times [43,44].

To minimize disruption to metro operations, donation handling is scheduled during off-peak hours—defined by the Quito Metro authority’s published timetables—and can be adjusted in real time to reflect holiday or emergency schedule changes. This dynamic allocation is supported through a scheduling algorithm embedded in a backend service that interfaces with both metro APIs and the blockchain network, allowing for seamless logistical coordination.

The blockchain-based traceability layer establishes a secure and transparent foundation for managing donation flows and stakeholder interactions. However, to operationalize these flows effectively within the constraints of an urban transit system, strategic and tactical decisions must be guided by rigorous optimization models. These models help determine how donations are best allocated across metro stations and transported through the network while balancing logistical efficiency, resource limitations, and stakeholder priorities.

4. Optimization Models for Efficient Donation Distribution

This section delves into the optimization of the donation distribution chain, employing two distinct mathematical models. The first model focuses on the strategic assignment of donors to specific metro stations, aiming to minimize transportation distances and ensure efficient utilization of station capacities. The second model tackles the operational challenge of optimizing the transportation of donations on metro trains, considering factors such as train schedules, loading/unloading times, and storage costs. Both models are designed to address the diverse and sometimes conflicting interests of various stakeholders, including donors, passengers, transportation authorities, and the food bank itself.

4.1. Assignment Model

This model aims to assign donors to the nearest metro station with sufficient capacity to receive their donations, thus minimizing overall travel distance. Station capacity is defined as a station’s ability to handle cargo without impacting passenger service. In scenarios where station i is closest to donor j and possesses the capacity to accommodate the donor’s load, this station is designated as the optimal drop-off point (see Figure 3 and Figure 4). However, if station i lacks the necessary capacity, the model dynamically selects the nearest station that can fulfill the capacity requirement (see Figure 5).

Considering the aforementioned factors, a straightforward allocation model incorporating capacity constraints is employed. This leads to the formulation of an MIP model, where the specific elements are detailed in

Table 1. Assignment model.

Type	Description
Sets
$j:1,...,J$	Donors
$s:1,...,S$	Stations
Parameters
$Ca{p}_s$	Donation load capacity at station s
$O_j$	Donor j’s offer
$d_{j,s}$	Unit cost of shipping each unit of donations from donor j to station s
Decision Variables
$x_{j,s}$	1 If donor j’s offer is assigned to station s, 0 otherwise

.

The model can be formulated as

$$MinZ=\sum _{j=1}^J\sum _{s=1}^S{d}_{js}{O}_j{x}_{js}$$

(1)

subject to

$$\sum _{j=1}^J{x}_{j,s}{O}_j\le Ca{p}_s,s=1,2,\dots ,S$$

(2)

$$x_{j,s}\ge 0s=1,2,\dots ,S,j=1,2,\dots ,J$$

(3)

The allocation model assumes that when a station’s available capacity is insufficient to receive all goods from a donor, the system dynamically selects the nearest station with adequate capacity. To enhance the model’s realism and operational flexibility, it can be extended to allow for partial allocation, where a portion of the goods is assigned to the initially selected station and the remainder is redirected to one or more nearby stations with remaining capacity. This modification accounts for practical limitations in station storage and ensures that all donations are eventually allocated efficiently, even when capacity constraints prevent a full allocation to a single location.

Given these considerations, we formulate the MO optimization model (4)–(22) whose sets, parameters, and decision variables are detailed in

Table 2. Storage and distribution model.

Type	Description
Sets
$i:1,...,I$	Set of donations
$j:1,...,J$	Set of trains
$s:1,...,S$	Set of stations
$f:1,...,F$	Set of transportation fares
Parameters
$g_i$	Time at which donation i is available for transport
$l{s}_i$	Departure station for donation i
$u{s}_i$	Unload station for donation i
$P_1$	Unit cost of storing a box per time unit at a station
$P_{2,j}$	Unit cost involved in sending a box on train j ($/box)
$F_f$	Trains subject to fare f
$l_j$	Train j’s departure time from station 1
$S{T}_s$	Storage capacity at station s (boxes)
$t{s}_s$	Travel time between station s to the adjacent station
$I_s$	Set of donations needing to pass by station s on their way
$I{I}_s$	Set of donations arriving at station s; $s=1$ or $s=S$
$D_i$	Set of donations departing from the same station as donation i and ready for departure earlier than i: $D_i=$ { k/$g_k\le g_i$ & $l{s}_k=l{s}_i$ }
$V_i$	Volume of donation i
$W_i$	Weight of donation i
$BVC$	Maximum volume capacity of boxes
$BWC$	Maximum weight capacity of boxes
$B_i$	Number of boxes required for donation i
$Q_j$	Train j’s box transport capacity
$W{T}_{max}$	Maximum train dwell time at any station s
$W{T}_{min}$	Minimum train dwell time at any station s
$h_j$	Time required to handle (load/unload) one box on train j
M	Sufficiently large number
Decision Variables
$x_{i,j,s}$	1 if donation i is in train j at station s, 0 otherwise
$u_{k,i}$	1 if k is in $D_i$ and k is not yet loaded when i becomes ready for departure
$C_{j,s}$	Waiting time of train j at station s
$G_i$	Time at which donation i is loaded (at station $l{s}_i$)
$E_i$	Time at which donation i arrives at its destination station 1 or S

.

$$min(Z_1,Z_2,Z_3)\in {\mathbb{R}}^3$$

(4)

where

$$Z_1=\sum _{i=1}^I\sum _{j=1}^J\left(G_i-g_i{x}_{i,j,l{s}_i}\right)$$

(5)

$$Z_2=\sum _{s=1}^S\sum _{i\in {II}_s}\sum _{j=1}^J{h}_j{B}_i{x}_{i,j,s}$$

(6)

$$Z_3=\sum _{i=1}^I{P}_1{B}_i\left(G_i-g_i\right)+\sum _{i=1}^I\sum _{f=1}^F\sum _{j\in F_f}^J{P}_{2,j}{B}_i\left(E_i-\sum _{s\in I_s}{ts}_s\right)$$

(7)

The objective functions, represented by Equations (5)–(7), aim to

• Minimize $Z_1$, the total time that donations remain at stations awaiting loading (5).
• Minimize $Z_2$, the total time spent on loading, unloading, and transporting the boxes (6). Note that the in-transit time for boxes is constant regardless of train assignment; thus, only loading and unloading times vary based on the chosen schedule.
• Minimize $Z_3$, the combined transportation and storage costs from donation arrival at departure stations to delivery at destination stations (7).

Subject to constraints (8)–(22), i.e., subject to

$$\sum _{j=1}^J{x}_{i,j,l{s}_i}=1,i=1,2,\dots ,I$$

(8)

Equation (8) ensures that each donation is assigned to a single train for transportation, and this assignment occurs precisely once.

$$x_{i,j,s}-x_{i,j,s+1}=0,\forall s\in \left[l{s}_i,u{s}_j-1\right],i=1,2,\dots ,I$$

(9)

Equation (9) ensures that once a donation is assigned to a train, it passes through all intermediate stations between its departure and arrival points.

$$\sum _{i\in I_s}^J{x}_{i,j,s}{B}_i\le Q_j,j=1,\dots ,J,s=1,\dots ,S$$

(10)

Equation (10) guarantees that a donation can only be allocated to a metro vehicle that reaches its origin station after the donation’s ready time.

$$x_{i,j,l{s}_i}{g}_i\le l_j+\sum _{s=1}^{l{s}_{i-1}}\left(C_{j,s}+{ts}_s\right),i=1,\dots ,I,j=1,\dots ,J$$

(11)

Equation (11) guarantees that a donation can only be assigned to a metro vehicle that reaches its destination station after departing its origin station.

$$C_{j,s}\ge W{T}_{min},j=1,\dots ,J,s=1,\dots ,S$$

(12)

$$C_{j,s}\le W{T}_{max},j=1,\dots ,J,s=1,\dots ,S$$

(13)

Equations (12) and (13) guarantee that the waiting time at each station adheres to the specified minimum and maximum limits.

$$C_{j,s}\ge \sum _{i\in I{I}_s}{h}_j{x}_{i,j,s}{B}_i,j=1,\dots ,J,s=1,\dots ,S$$

(14)

Equation (14) ensures that the waiting time of each train at each station falls within the feasible range.

$$B_i=Max\left\{⌈{\displaystyle \frac{V_i}{BVC}}⌉,⌈{\displaystyle \frac{W_i}{BWC}}⌉\right\}i=1,\dots ,I$$

(15)

Equation (15) is designed to quantify the number of boxes required to pack each donation.

$$G_i\ge l_j+\sum _{s=1}^{l{s}_{i-1}}\left(C_{j,s}+{ts}_s\right)-M(1-x_{i,j,l{s}_i}),i=1,\dots ,I,j=1,\dots ,J$$

(16)

Equation (16) establishes the earliest feasible time at which each donation can be loaded onto a train.

$$G_k\le g_i+M{u}_{k,i},k\in D_i,i=1,\dots ,I$$

(17)

Equation (17) ensures the logical consistency of variables $u_{k,i}$.

$$\sum _{k\in D_i}^J{u}_{k,i}{B}_k\le {ST}_{l{s}_i}-B_i,i=1,\dots ,I$$

(18)

Equation (18) enforces the storage capacity limit at each station.

$$x_{i,j,s}\in \left\{0,1\right\},i=1,\dots ,I,j=1,\dots ,J,s=1,\dots ,S$$

(19)

$$C_{j,s}\ge 0,j=1,\dots ,J,s=1,\dots ,S$$

(20)

$$G_i\ge 0,i=1,\dots ,I$$

(21)

$$u_{k,i}\in \left\{0,1\right\},k\in D_i,i=1,\dots ,I$$

(22)

Equations (19) to (22) serve to define the nature of the decision variables within the model. They establish that $x_{i,j,s}$ and $u_{k,i}$ are binary variables. Furthermore, they designate $G_i$ and $C_{j,s}$ as non-negative real variables.

One approach to solving the proposed multi-objective (MO) model is to standardize the objective functions, $z_1$, $z_2$ and $z_3$, ensuring that all objectives are rescaled to a common range and are thus directly comparable. This standardization allows for the subsequent transformation of the MO model into a single aggregated objective function using a weighted sum, as established in Ransikarbum and Mason [13]. In this work, the upper and lower bounds required for normalization are effectively determined by applying the linear normalization technique introduced in [13], which enables consistent weighting and fair trade-off analysis among the objectives. Standardization is achieved by transforming the values of each objective function $Z_i$ into values within the interval $[0,1]$, for which the largest and lowest values, $Z_i^U$ and $Z_i^L$, respectively, that $Z_i$ (where i =1,2,3) can achieve are calculated by transforming the MO model represented in Equation (4) into a weighted single objective represented in Equation (23).

$$min{\alpha }_1{\displaystyle \frac{(Z_1-Z_1^L)}{(Z_1^U-Z_1^L)}}+{\alpha }_2{\displaystyle \frac{(Z_2-Z_2^L)}{(Z_2^U-Z_2^L)}}+{\alpha }_3{\displaystyle \frac{(Z_3-Z_3^L)}{(Z_3^U-Z_3^L)}}$$

(23)

where the parameters ${\alpha }_i$ satisfy the conditions ${\alpha }_i\ge 0$ and ${\sum }_i{\alpha }_i=1$. By systematically varying the values within the triplet $({\alpha }_1,{\alpha }_2,{\alpha }_3)$, we can effectively approximate the Pareto front of the MO problem.

The proposed model, solvable using an MIP solver, generates a set of non-dominated solutions and an estimated Pareto front. These results empower food bank managers to assess the trade-offs between competing objectives and select the optimal donation distribution strategy that leverages the metro public transport network. This approach facilitates the minimization of distribution and storage costs while maintaining acceptable service levels for passengers.

From a modeling perspective, the proposed framework is structurally robust and inherently multi-objective. This enables the seamless integration of additional stakeholder-oriented objectives—such as minimizing passenger disruption, promoting social equity, or ensuring regulatory compliance—through the inclusion or reweighting of terms in the objective function. Such modularity allows the model to adapt dynamically to evolving operational demands, policy priorities, or user experience considerations without requiring changes to its underlying structure. Moreover, this flexibility aligns with Ecuador’s national mobility policy, which advocates for sustainable, inclusive urban logistics and the integration of multimodal freight systems [45].

4.2. Storage and Distribution Model

The second model optimizes the food donation transportation from donors to the metro system’s stations, ultimately destined for the food bank’s two food pantries at the network’s northern and southern ends, as shown in Figure 6.

The model considers the loading station $l{s}_i$ for each donation i, the designated unloading station $u{s}_i$, and the transportation time $t{s}_s$ between station s and the next station. The food donations are packaged into standardized boxes as TRUs by the respective donors. The boxes are temporarily stored, incurring a storage cost at their assigned stations. Subsequently, these boxes are loaded onto caddies, wheeled devices for conveying multiple boxes, and they transported via the metro system to their designated destination stations. Upon arrival, each donation is retrieved from the caddies and then transferred to the final food pantry, as shown in Figure 7.

It is important to highlight that the proposed model is based on the assumption of carrying capacity’s partial availability in the Quito Metro during off-peak hours—a condition commonly observed in many metro systems, including Quito’s. We acknowledge that during peak hours, available capacity may be significantly reduced or even null. However, the proposed structure, which involves temporarily storing donations in lockers located at metro stations, allows for flexibility in scheduling deliveries. This ensures that there will be suitable time windows for transporting all donations using the existing system capacity. While this study primarily focuses on the conceptual framework and mathematical modeling, we also recognize the need for a detailed empirical assessment of operational capacity and system constraints to support real-world implementations.

5. Quito Metro Case Study: Findings and Insights

Quito, the capital of Ecuador, is nestled within the Andean mountain range. Its urban area is constrained by mountains and gorges to a long, narrow plateau. With a population of 2.7 million, representing 16% of the national total, Quito faces significant socioeconomic challenges. Notably, nearly 30% of its residents experience poverty, with 7% living in extreme poverty and almost 30% of children under five suffering from chronic malnutrition. Unemployment and underemployment rates stand at 5% and 40%, respectively, with poverty concentrated in the city’s northern and southern parts [9] (see Figure 8).

QFB is a non-profit organization dedicated to fight hunger and reduce food waste in Quito, Ecuador. Founded in 2003, the bank collects surplus food from various donors, including hotels, restaurants, markets and food producers, and redistributes it to beneficiaries.

Currently, the food bank operates a centralized distribution model, with a central warehouse located in the south of the city. Food donations are collected by the bank’s fleet of three vehicles and transported to the warehouse for sorting and storage. From there, food is distributed to beneficiary organizations.

The proposed decentralized model leverages the Quito Metro system to create a network of food donation lockers and collection points. Key elements include the installation of secure lockers at strategically chosen metro stations for convenient food donation drop-offs, the use of the spare capacity of metro trains to transport food donations to designated collection points, the development of a data traceability architecture to track and manage the flow of donations, and the implementation of MO-MIP programming models to optimize the allocation and distribution of donations.

This innovative approach is expected to increase the reach of the food bank by leveraging the extensive metro network, reducing transportation costs by decreasing dependency on the food bank’s vehicle fleet, improving the efficiency of the logistics process by resulting in more efficient distribution, and enhancing social impact by increasing the volume of food rescued and redistributed, thus benefiting more individuals in need [30]. In addition, the implementation of a blockchain can enhance the monitoring of stakeholders by automating compliance reporting, ensuring that they meet their obligations to recover and recycle salvageable goods [46]. This supports the Food Loss and Waste (FLW) law’s focus on prioritizing the responsible treatment of food fit for human consumption while also establishing a “culture of donation” [18].

The Quito Metro, an underground public transport network, commenced operations in December 2022. The fully operational line spans 23 km, and serves as the backbone of the Quito Integrated Mass Transportation System (SITM-Q) [47] (see Figure 9).

The linear structure of the Quito Metro’s first line, featuring a series of stations arranged sequentially, aligns well with the integrated passenger–freight transportation model proposed in [48]. This model serves as a foundation for our proposed food bank supply network design, facilitating the efficient transportation of food to two strategically located food pantries at the northern and southern ends of the city. These nodes are in close proximity to the areas with the highest concentration of poverty, ensuring accessibility for those who would benefit most from the food bank’s services.

Within this framework, Quitumbe station (station 1) and El Labrador station (station 15) function as unloading points for food collected at each of the “interior” stations (stations 2 to 14). These interior stations act as loading and unloading points, enabling donors to conveniently deposit food donations, which are then transported along the metro line to the food pantries. This integrated approach optimizes the utilization of existing infrastructure, reduces transportation costs, and streamlines the distribution of food (see Figure 7).

In this study, establishments in the HORECA sector located near the Quito Metro network are identified as potential food donors. Due to the perishable nature of their products, these businesses are well positioned to contribute to the food bank, with their proximity to metro stations enabling efficient logistics. Figure 10 illustrates the spatial distribution of 1200 establishments—categorized as hotels, restaurants, and cafes—within the metro station stops’ area of influence. Specifically, Figure 10a shows the distribution of hotels, which are primarily concentrated in the central-northern part of the city, reflecting the area’s role as a hub for tourism and business. Figure 10b presents restaurants, which display a more uniform distribution throughout the city. Finally, Figure 10c depicts cafes, which have a noticeably lower density compared to the other two categories, indicating more limited coverage and potential in this segment.

The visualization presented in Figure 11 illustrates the outcome of the donor–station assignment process, wherein each potential donor within the HORECA sector is allocated to the most suitable metro station for their food donations.

To showcase the model’s real-world applicability, we utilized data from the QFB and potential food donations from HORECA establishments. We acknowledge the limitations of both dataset size and quality, and we aim to incorporate more comprehensive and higher-resolution datasets in future work to enhance model robustness. The MIP model in Equation (23) was implemented and solved using GAMS [49] for algebraic modeling and the Gurobi solver version 12.0.1 [50] for optimization, and it executed on a laptop equipped with an Intel Core i7 processor and 16 GB of RAM. For the case study presented, the model reached optimality in 21 s, demonstrating computational efficiency for medium-scale instances. Gurobi’s exact methods efficiently determined optimal solutions for various ${\alpha }_i$ weight combinations.

Table 3. Values of the objective functions for different combinations of ${\alpha }_i$.

(${\mathit{\alpha }}_1$, ${\mathit{\alpha }}_2$, ${\mathit{\alpha }}_3$)	${\mathit{Z}}_1$	${\mathit{Z}}_2$	${\mathit{Z}}_3$	Execution Time (s)
(0, 0, 1)	1.175816	1.45778	0.250568	1.2562
(0, 0.5, 0.5)	1.385439	0.1023	1.709063	1.3231
(0.33, 0.33, 0.33)	0.93239	1.04235	1.693897	1.6598
(0, 1, 0)	1.211361	0.05842	0.918517	1.6924
(0.5, 0.5, 0)	1.94141	0.677836	0.10142	1.9335
(1, 0, 0)	0.31225	1.522893	1.23824	1.7226

presents the values of objective functions $z_1$, $z_2$, and $z_3$ for different ${\alpha }_i$ combinations, along with their respective computation times. The results underscore the model’s computational efficiency in handling real-world scenarios within reasonable time frames. The numerical results reveal inherent conflicts among the considered objectives, underscoring the usefulness of the Pareto front in offering a spectrum of optimal trade-offs. By adjusting the α values in the weighted sum approach, different preferences among cost minimizations, distribution efficiencies, and social impacts are explored, with each combination generating a point on the Pareto front. This provides decision makers with valuable insights to evaluate alternatives according to strategic or policy priorities. Ultimately, the selection of the final solution lies with the decision maker, based on the specific context and goals of the food distribution system.

6. Conclusions

This study proposes a novel redesign of the Quito Food Bank Network by leveraging the city’s metro infrastructure and integrating a decentralized logistics approach. We develop a multi-objective optimization framework that balances food waste reduction, transportation cost minimization, and social impact maximization. This is operationalized through an MIP model that optimizes donation allocation based on spatially distributed urban demand patterns, enhancing the efficiency, reach, and equity of food distribution in large urban environments. The utilization of the unused capacity of mass public transportation, exemplified by the Quito Metro system, represents a promising approach for optimizing food distribution. However, a practical implementation of such systems remains limited in Latin America, including Ecuador.

The proposed information management system incorporates blockchain technology to enhance traceability within the food bank supply chain. By defining clear relationships among stakeholders, on-chain resources, and decentralized storage systems, the system facilitates real-time monitoring of donations through unique smart contracts. These contracts trigger events upon ownership changes, with event data being accessible to DApp users. This approach aims to improve transparency, reduce human intervention, and minimize delays by integrating seamless collection, organization, presentation, and utilization of logistics data.

Several limitations are acknowledged, including the following:

• Full-scale empirical validation: This study primarily focuses on the conceptual development and mathematical modeling framework for integrating metro infrastructure into decentralized food supply chains. While the proposed model has been verified against basic input data, particularly considering the characteristics of the HORECA sector (hotels, restaurants, and cafes) and the documented demand for donations within the city of Quito, it does not yet include full-scale empirical validation or pilot testing. We recognize that rigorous verification experiments are indispensable to confirm the model’s practical applicability, assess its robustness under real-world operational conditions, and establish its generalizability to other urban contexts. Accordingly, future research will be directed toward the design and implementation of such empirical studies, ensuring that the transition from a theoretical contribution to applied practice is robustly supported.
• Constraints related to modeling and network topology: The focus on a linear metro structure, rather than more complex configurations with multiple lines and interchanges, restricts the generalizability of the findings. Furthermore, the smart contract was neither implemented nor tested, which limits the ability to assess its practical effectiveness. Future research should address these limitations by exploring more intricate network topologies while conducting security and cost analyses of the proposed blockchain-based solution.

A further investigation is required into the technical infrastructure necessary to support the model, including the design of TRUs, secure lockers and modified subway cars. The operation management associated with the creation and utilization of standardized boxes warrants additional attention. Standardized boxes could enhance automation, sorting, data management, transportation, and regulatory compliance in the food bank network through consistent labeling, uniform dimensions, and simplified inventory management. Refining these components is essential to optimize the transportation within the food bank network.

Beyond logistics, food banks play a crucial role in urban resilience, particularly in vulnerable communities. As food systems face increasing risks from climate change and supply chain disruptions, future research should explore climate resilience and sustainability considerations in decentralized food bank networks. Applying quantitative assessment frameworks could help evaluate how well these models adapt to environmental and operational uncertainties, ensuring long-term stability and equitable food access. Incorporating these perspectives will be essential for strengthening food security and enhancing the model’s real-world applicability.

Additionally, a comprehensive analysis of the economic, legal, social, and psychological implications of the model is still needed. Finally, the model must also account for the stochastic nature of the system, including variability in donation volumes and potential delays in transportation. Addressing these unpredictable factors is essential for enhancing the efficiency and effectiveness of the food distribution network.