EduDonateBlock: a blockchain-enabled crowdfunding for transparent educational smart supply chain

1 Introduction

Proper allocation of educational resources to underserved communities remains a significant challenge. Inadequate infrastructure, limited funding, and systemic inefficiencies are the main reasons for this problem. This may affect the quality of education for impoverished students [1]. Beyond funding, traditional educational supply chain management (SCM) systems face various issues [2, 3]. The SCM process for educational resources not only lacks transparency but also lacks proper coordination among the stakeholders involved. These issues are further exacerbated by centralized governance structures that undermine trust, traceability, and accountability across the ecosystem [4, 5].

In recent years, crowdfunding has been considered a promising support mechanism for educational organizations. It enables collective support through financial contributions or other consumable products from individuals, communities, or other organizations. Crowdfunding facilitates access to funds by enabling direct interaction between donors and beneficiaries [6, 7]. This is done through digital platforms. Traditional systems not only suffer from fraud vulnerability and a lack of transparency but also from a lack of a tracking mechanism for proper fund utilization. These issues erode trust between donors and recipients. Moreover, existing models overlook the integration of supply chain dynamics, which restricts end-to-end visibility from fund generation to resource delivery. Thus, ensuring end-to-end visibility in this application domain is essential across both financial and physical flows [1, 8].

Blockchain technology may be considered a potential solution to the aforementioned challenges. As a decentralized, immutable, and transparent ledger system, blockchain facilitates secure, tamper-resistant recording of transactions across distributed networks [9, 10]. Smart contract-based integrated platforms enable the automated execution of predefined conditions. This ensures that the allotted resources are released and utilized in alignment with verified milestones. Recent studies have demonstrated the potential of blockchain to enhance transparency, traceability, and trust in both crowdfunding systems and SCM. Chen and Luo [11] and Kumar et al. [8] developed a blockchain service that makes it accessible for recyclers to obtain guarantee credit finance.

These technologies significantly help to design strategies that maximize transparency, traceability, and trustworthiness across educational crowdfunding supply chains. Few research studies have explored the application of blockchain in crowdfunding and SCM independently [1, 4]. Most existing work either focuses on enhancing financial transparency in crowdfunding platforms or on improving traceability in supply chains, but it does not explore their integration. Hence, there is a significant research gap in developing an integrated framework that leverages blockchain technology to simultaneously manage crowdfunding processes and ensure transparency in the supply of educational resources.

To address this gap, the present study proposes EduDonateBlock, a blockchain-based crowdfunding framework for transparent educational resource SCM. This methodology enhances the transparency, accountability, and efficiency of educational resources within a crowdfunding framework. EduDonateBlock integrates key stakeholders, including donors, organizations, suppliers, beneficiaries, and auditors, into a decentralized network. It enables real-time tracking of both financial transactions and resource flows. Smart contracts are used not only to reduce the risk of misallocation but also to improve trust among participants. This framework verifies the release of funds after the predefined conditions have been properly verified. These properties are particularly critical in educational donation ecosystems, where transparency, accountability, and effective resource utilization are fundamental to maintaining donor trust and ensuring institutional reliability.

The rest of the study is organized as follows: Section 2 reviews relevant literature on blockchain applications in crowdfunding, supply chain management, and the scope of EduDonateBlock. Section 3 presents the proposed mathematical framework. The blockchain-based system architecture is presented in Section 4. Section 5 discusses the potential benefits and performance evaluation. Finally, Section 6 concludes the work with future research directions.

2 Literature review and scope of EduDonateBlock

There is an increasing demand for transparency, accountability, and efficient resource allocation. This has accelerated the adoption of blockchain technology across multiple application domains, which include crowdfunding, SCM, and decentralized governance systems [4, 8].

2.1 Blockchain-based crowdfunding

Crowdfunding platforms connect distributed contributors and campaign creators through digital infrastructures for fundraising, coordination, and information exchange. The traditional crowdfunding systems provide useful informational and coordination support. However, these are dependent on intermediary-controlled governance, limited post-funding transparency, and weak contributor participation in fund-allocation decisions [12]. Blockchain-based crowdfunding frameworks are considered an alternative to centralized crowdfunding. The dependencies on intermediaries using smart contracts for transparent and programmable fund handling are reduced here. Initially, these frameworks automate contribution recording, escrow logic, and fund release [13]. This system provides limited governance support. Tiganoaia and Alexandru [14] proposed a decentralized application using blockchain technology to improve transparency and effectiveness in educational donations for sustainable development on crowdfunding platforms. Most blockchain-based crowdfunding solutions do not provide user authentication. However, user authentication is limited to trusted entities, posing a risk of a single point of failure [15]. He and Inoue [7] proposed CrowdChain, a blockchain-based crowdfunding framework. The primary objective of this framework is to address security and privacy requirements in blockchain-based crowdfunding applications. To ensure user authentication and transaction confidentiality, this scheme employs decentralized identities, physically unclonable functions, and zero-knowledge proofs, as well as privacy-preserving auditing mechanisms. Their work highlights the growing importance of balancing transparency with privacy preservation in decentralized fundraising environments. Recently, Kumar et al. [8] proposed a blockchain-enabled crowdfunding framework as a decision-support artifact for adaptive fund allocation and participatory governance. It automates campaign creation, contribution management, spending requests, and fund disbursement through decentralized governance mechanisms. This framework balances influence across heterogeneous financial stakeholders and mitigates dominance by large contributors. Although this framework improves trust and accountability in fundraising activities, real-world user interaction issues were not addressed in the present study.

2.2 Blockchain in SCM

In recent scenarios, global supply chain systems have increasingly faced difficulty due to various factors. Therefore, traditional SCM systems struggle to maintain efficiency, transparency, and innovation throughout the chain. Blockchain technology offers a decentralized, secure framework that addresses these challenges in supply chain management. Kouhizadeh et al. [16] demonstrated that blockchain-based traceability systems improve operational visibility and transparency in complex global supply chains within sectors such as food, medicine, and logistics. Chang et al. [17] presented an extensive review of blockchain technology and its rapid adoption across business organizations, highlighting the key feature of traceability in supply chain management. Magar et al. [1] developed a blockchain-based system framework that exploits the intrinsic security and immutability of distributed ledger technology for the management of the vaccine supply chain, which enables stakeholders to verify and ensure the authenticity of vaccine products. Several researchers have investigated the impact of blockchain on supply chain management, with a primary focus on enhancing transparency, traceability, and efficiency across various organizations worldwide [18–20]. A blockchain-enabled BPSCM framework implemented via Ethereum smart contracts to guarantee data provenance, transparency, and integrity was proposed by Padma and Ramaiah [21]. Bhattacharjee et al. [4] established an integrated framework designed with an Ethereum-based blockchain and smart contracts to improve integrity, data provenance, security for stakeholder trust, and decentralized management within supply chain management to significantly reduce fraud and improve real-time visibility. Recently, Cvetkoska et al. [5] introduced the basics of integrating blockchain with supply chain developments to measure the performance of supply chain activities, using four case studies from sectors such as food retail, pharmaceuticals, logistics, and luxury goods. Hence, a blockchain system integrates supply chain management, educational resource management, and crowdfunding by providing transparent, traceable, and reliable resource allocation, enabling efficient tracking of educational assets and secure, decentralized funding.

2.3 Educational resource management and crowdfunding

Educational resource management has gradually integrated digital technologies to address challenges associated with funding accessibility, transparency, and effective resource allocation. Recently, crowdfunding has emerged as a sustainable mechanism to support educational initiatives, enabling students, institutions, and organizations to secure financing from communities and other stakeholders. Wu and Yuan [22] proposed an organized crowdfunding literature survey to develop a crowdfunding core curriculum based on outcome-based education systems. Figueroa-Armijos and Berns [23] contributed a theory-based ethical crowdfunding that linked individual social responsibility and classified crowdfunding campaigns into four types, such as donation-based, lending-based, equity-based, and reward-based. [24] conducted an empirical analysis of the effectiveness of project narratives in stimulating donor contributions and further addressed this gap by investigating how signals of resource allocation interact with narrative appeals to influence donors' decision-making behavior. Liu et al. [6] developed a framework to elucidate how digital crowdfunding platforms can enhance the sustainable performance of SMMEs in emerging markets.

Table 1 presents a comparative assessment of existing blockchain-based systems with special focus on their proposed methodologies, key findings, and research gaps with limitations in the fields of transparency of crowdfunding and SCM. The proposed EduDonateBlock framework responds to all these by presenting an integrated, optimized blockchain-based architecture that highlights transparency, automation, and operational efficiency in a single approach.

Table 1. Comparative analysis of blockchain-based approaches highlighting methodologies, key findings, and research gaps addressed in the proposed EduDonateBlock framework.

2.4 Scope and contributions of EduDonateBlock

Secure fundraising, privacy, and governance are primarily focused upon by blockchain-based crowdfunding frameworks. Blockchain-enabled supply chain research addresses logistics and traceability across domains. Educational crowdfunding studies do address fundraising effectiveness but not infrequently overlook end-to-end resource traceability and operational transparency. Besides this, current approaches lack an integrated framework that combines educational crowdfunding, blockchain-enabled supply chain management, smart contract automation, and mathematical optimization of transparency and operational costs. The proposed EduDonateBlock addresses these limitations by integrating blockchain-enabled crowdfunding, educational SCM, and optimization into a unified framework. Hence, the scope and contributions of EduDonateBlock are summarized below.

• Smart, reliable, and secure contract-based framework: With the help of blockchain-based crowdfunding features, EduDonateBlock enables secure and visible smart donation logistics while incorporating campaign-based strategic decision-making capabilities. This framework focuses on the reduction of resource misallocation, administrative dependency, etc.
• Cost-efficient blockchain-based architecture: An optimized blockchain-based deployment strategy is proposed here. The cost-efficient level of transparency is mathematically and computationally computed to evaluate the feasibility. Moreover, gas consumption analysis, latency evaluation, and modular smart contract architecture collectively ensure the scalability, operational efficiency, and practical applicability of EduDonateBlock.
• Smart SCM for underserved communities: EduDonateBlock with intelligent SCM offers a blockchain solution for crowdfunding educational projects in underprivileged communities. It promotes transparency by directly translating donations into verified educational supplies and automating the supply chain. Hence, it reduces financial leakage, strengthens accountability, and optimizes resource allocation through real-time, community-validated tracking.

3 Mathematical model for EduDonateBlock

This study presents a mathematical framework for modeling how blockchain-based crowdfunding works in practice. It breaks down the recurring funding cycle, sheds light on the key mechanics that drive campaigns, and tracks how donor behavior shifts over time.

Consider an indexed set of educational crowdfunding campaigns, where each campaign is labeled by i (i = 1, 2, …, N). Each campaign i is characterized by the tuple Ci={Ti,Di,τi}, where, T_*i* denotes the funding or resource target, D_*i* denotes the campaign deadline, τ_*i* denotes the minimum success threshold, with 0 < τ_*i* ≤ T_*i* and fic(t) denotes the cumulative contributions accrued by campaign i at time t.

Since the proposed model satisfies the condition, campaign i is classified as successful if fic(Di)≥τi., otherwise the campaign is deemed unsuccessful, and all contributions are automatically reimbursed to contributors through smart-contract–based refund mechanisms.

3.1 Donor contribution behavior

The contribution made by the donor j to the campaign i is represented by c_*ij*≥0 (Where j indexes the set of donors). The total funding raised by the campaign i is written in Equation 1.

fic=∑jcij.(1)

Each donor evaluates campaigns based on publicly verifiable information recorded on the blockchain. For analytical tractability, the perceived quality score of a donor for campaign i is denoted as Q_*i*. This is specified in Equation 2.

Qi=αiNi+βiSi+γiRi(2)

where N_*i* denotes the verified need index of the campaign, S_*i* denotes the historical success rate or delivery reliability of the implementing institution, R_*i* denotes transparency and real-time reporting indicators, and α_*i*, β_*i*, γ_*i* ≥ 0 are weighting parameters that satisfy α_*i* + β_*i* + γ_*i* = 1. For calibration, we assume asymmetric weights α = 0.3, β = 0.4, and γ = 0.3, reflecting the relative importance of campaign need and institutional reliability as primary drivers of donor decision-making. Transparency is assigned a lower baseline weight due to its limited verifiability in the absence of blockchain-like trust-multipliers. Thus, its influence is endogenously amplified in the presence of blockchain through verifiable institutional effort, as subsequently captured by the term θbe_*i*, preserving its structural role.

3.1.1 Contribution decision rule

Donor j decides to give to campaign i if their expected perceived utility U_*ij* is at least zero, that is, U_*ij* = Q_*i*−λc_*ij*≥0, where λ is a donor-specific parameter that reflects how sensitive the donor is to the cost of contributing. Supported by earlier researchers' educational crowdfunding data, this model distinguishes donors as intentional but boundedly logical, stepping away from older suppositions of strict rationality and market equilibrium.

3.1.2 Extended donor utility and contribution function

To measure how blockchain affects risk and trust in a consistent way, the standard donor utility framework is extended by introducing a transparency variable b ∈ [0, 1], where b = 0 denotes a centralized database and b = 1 denotes a fully auditable distributed ledger. Moreover, e_*i* captures the effort put in by educational institution i to manage campaigns, verify financial need, and validate campaign documentation. Based on these, the recognized campaign quality score Q_*i* is defined as

Qi(ei,b)=vi+θbei(3)

where v_*i* captures the intrinsic altruistic value or baseline appeal of the campaign i, and θ reflects the donor's marginal responsiveness to verifiable, blockchain-based information. This operational form of Q_*i* simplifies the mathematical representation of the conceptual foundation of the donor's perceived quality: the need index and institutional reliability are combined into the intrinsic appeal parameter, v_*i* = α_*i*N_*i*+β_*i*S_*i*; and the transparency indicator is expressed as a function of blockchain transparency and institutional effort, γ_*i*R_*i* = θ·b·e_*i*.

To account for the risk of fund misappropriation characteristic of traditional, non-blockchain platforms, the proposed model includes a risk-penalty term δ(1−b), which is strictly decreasing in b, meaning the penalty decreases as blockchain-enabled transparency increases. The extended expected utility of donor j from donating to campaign i is thus represented in the following equation.

Uij=vi+θ·b·ei-cij-δ(1-b)cij(4)

where c_*ij* denotes the (monetary and/or non-monetary) cost borne by donor j when contributing to the campaign i. By aggregating all donors with U_*ij*>0, the model reaches a reduced-form total funding function. This can be interpreted as the effective demand for the campaign i.

Fi(ei,b)=fi+μ·b·ei-ρ(1-b)(5)

where f_*i* denotes the baseline pool of potential donations in the absence of blockchain-facilitated transparency, μ measures the aggregate sensitivity of donations to verified institutional effort, and ρ captures the overall aversion to fraud and misallocation risk.

3.2 Educational institution benchmark

The educational institution aims to maximize net received funds, recognizing that exerting effort e_*i* entails administrative costs. The cost of effort is represented by a quadratic function C(ei)=12kei2, where k is a positive cost coefficient and g·b denotes the operational cost (e.g., gas fees) that the educational organization must bear to utilize the blockchain network.

Before introducing the all-or-nothing crowdfunding mechanism, the educational institution seeks to maximize its expected payoff (Π_*S*).

maxeiΠS=Fi(ei,b)-12kei2-g·b

The following equation represents a simplified specification of F_*i*(e_*i*, b).

maxeiΠS=fi+μ·b·ei-ρ(1-b)-12kei2-g·b

The first-order conditions with respect to e_*i* yield the benchmark effort level e_*i*(*bench*).

∂ΠS∂ei=μ·b-kei=0⇒ei(bench)=μ·bk(6)

Equation 6 represents the analytical result of the model. It represents that with the enhancement of blockchain transparency b or marginal valuation of verification μ, the institution is incentivized to exert more effort.

3.3 Total Expected Cost (TEC) optimization calculation

To enhance both allocative and operational efficiency, the platform is required to minimize its cost function, TEC, in the presence of uncertainty. Individual cost components are specified as parametric functions of the blockchain integration level b ∈ [0, 1]. These components are defined below.

Administrative and Delay Costs (ADC): The ADC cost decreases exponentially due to smart contract automation, which is defined as: Cadmin(b)+Cdelay(b)=C0e-ab.Transaction Costs (TC): The TC cost increases linearly as a consequence of gas fees. This is defined as C_transaction(b) = p·b.

Residual Risk and Fraud Costs (RRFC): RRFC costs exhibit an accelerated, quadratic decline as transparency increases, reflecting the disproportionately higher difficulty of system tampering as auditability or transparency nears completion. It is denoted as Crisk(b)=R0(1-b)2.

Hence, the platform's optimization problem is to solve the following minimization problem.

minbTEC(b)=C0e-ab+p·b+R0(1-b)2(7)

The first-order condition of Equation 7 with respect to b is written below.

∂TEC∂b=-aC0e-ab+p-2R0(1-b)=0(8)

Equation 8, represents a transcendental equation in which the optimal degree of blockchain transparency b^* is determined by the point where the marginal cost of transaction fees (p) is perfectly offset by the sum of marginal gains from automation and fraud reduction. This works better than linear models because it ensures a stable interior minimum even when p<R₀, as the marginal utility of risk reduction realistically decreases with b → 1. In practical terms, this equilibrium condition reduces the cost-minimizing effect (as∂2TEC∂b2>0,b∈[0,1]). The detailed explanation is included in Appendix A.

3.4 Crowdfunding: conditional donor utility in a smart contract campaign

The primary objective of the crowdfunding layer is to provide the assurance that funds are released only upon conditional campaign success. Let τ_*i*, define the minimum funding target for campaign i. In a smart contract setup, donor j's pledge c_*ij* is locked in guarantee. If total contributions F_*i* do not reach τ_*i* by the deadline D_*i*, the contract automatically refunds all covenant amounts. The probability that the campaign hits this funding threshold is denoted as P(F_*i*≥τ_*i*). Therefore, Donor j's expected utility, given the smart contract's execution rules, is then

E[Uij]=P(Fi≥τi)×(vi+θ·b·ei-cij-δ(1-b)cij).

Since v_*i* denotes donor j's intrinsic valuation of campaign (i). Blockchain-driven transparency enhances utility via verifiable effort e_*i* (weighted by θ and b), whereas lack of transparency generates a disutility term δ(1−b)c_*ij* that depends on the donor's aversion parameter δ. Blockchain-enforced refund guarantees do more than shield donors from potential losses—they actively alter donors' willingness to contribute even before any loss could occur. By transforming the worst-case outcome from unbounded and ambiguous into a clearly limited and verifiable state, smart contracts reduce the psychological hurdle to donating. As a result, donors increase their contributions, c_*ij* rises, and the overall robustness of the crowdfunding ecosystem improves.

By limiting uncompensated exposure to campaign failure, smart contracts can increase donors' ex ante readiness to contribute, thereby raising c_*ij* and enhancing overall crowdfunding performance.

3.5 Campaign success probability and target dynamics

The probabilistic funding framework builds on the earlier discussion of ex-ante donor risk aversion by incorporating these concerns—together with other sources of uncertainty—into a more comprehensive probabilistic model. The approach begins with a more realistic representation of total expected funding. It explicitly reflects platform-specific characteristics and the intrinsic volatility of real-world fundraising environments. Therefore, the realized funding is defined as

Fi=fi+μ·b·ei+ϵ(9)

Here, ϵ~N(0,σ2) is a Gaussian random variable introduced to capture idiosyncratic shocks-things like sudden shifts in donor participation or broader market disturbances that are simply impossible to anticipate in advance. By construction, E[ϵ] = 0, meaning that these shocks are mean-zero and do not carry systematic directional bias. The term μ·b·e_*i*, by contrast, represents the deterministic portion of funding: the component that is, at least in principle, within the influence of the project driven jointly by institutional effort (e_*i*) and the degree of transparency that the blockchain infrastructure provides (b). The choice of a Gaussian specification here is deliberate rather than convenient. The most compelling justification comes from the Central Limit Theorem. In practice, total donations to any given campaign aggregate across a large number of individual donor decisions, each shaped by personal circumstances, preferences, and timing. Since these decisions are, to a reasonable approximation, independent of each other, their combined effect on aggregate funding noise will tend to a normal distribution as the donor pool grows. In other words, no single donor's idiosyncratic behavior dominates the aggregate outcome; instead, the noise “averages out” in a manner that the Gaussian distribution captures well.

If f_*i* captures baseline contributions independent of active effort (e_*i* = 0), e.g., organic traffic and seed pledges. Equation 10, represents the total anticipated funding E[F_*i*] is given by :

E[Fi]=fi+μ·b·ei(10)

From Equation 11, the probability of campaign success, P_*i*, is defined as the likelihood that total funding F_*i* meets or exceeds the threshold τ_*i* expressed as

Pi(ei,b)=ℙ(fi+μ·b·ei+ϵ≥τi).(11)

P_*i* is then characterized as a function of the institution's effort, blockchain transparency, and the funding threshold. It is represented in Equation 12.

Pi(ei,b)=p0+α[1-exp(-2μbeiτi)](12)

Here, p₀ and (p₀+α) represent the baseline success probability and the maximum attainable market reach, respectively.

3.6 Educational institution expected payoff

Within a campaign-based setting, the educational institution faces an “all-or-nothing” (i.e., threshold-contingent) payoff structure. The institution incurs both an effort cost, defined by C(ei)=12kei2, and blockchain operational expenses (gas fees) g·b, as sunk costs regardless of the campaign's outcome. Access to the contributed funds is strictly unforeseen until the campaign reaches or exceeds its preset funding threshold. The institution chooses its effort to maximize expected net returns, E[Π_*S*]. It combines probability-weighted funding with the quadratic effort cost and transparency implementation cost. This is represented in the following Equation 13.

maxeiE[ΠS]=Pi(ei,b)·E[Fi]-12kei2-g·b(13)

The optimal effort choice ei* follows from the first-order condition.

∂E[ΠS]∂ei=α(fi+μbei)[2μbτiexp(-2μbeiτi)] +(μb)Pi(ei,b)-kei=0(14)

The core trade-off in blockchain-enabled crowdfunding dictates that institutions must calibrate their effort levels to optimize two outcomes: generating marginal contributions (μb)P_*i* and increasing the probability of surpassing the funding threshold E[Fi]∂Pi∂ei. Finding the right balance minimizes the risk of campaign failure and avoids wasting administrative resources and gas expenditures.

To ensure the practical relevance and analytical validity of the proposed model, the key parameters are calibrated using a combination of empirical observations, realistic crowdfunding scenarios, blockchain operational characteristics, and assumptions commonly adopted in the literature [17, 25]. The selected values are intended to represent a typical small-to-medium educational crowdfunding campaign and are used to illustrate the impact of blockchain-enabled transparency, automation, and donor engagement on campaign performance. Table 2 summarizes the meaning, assigned values, and theoretical justification of each model parameter.

Table 2. Parameter calibration and justification.

4 Blockchain based framework for EduDonateBlock

The present section presents the Blockchain architecture of EduDonateBlock. First, the interdependence between key parameters are established. These are total funding F_*i*, individual donations c_*ij*, campaign threshold τ_*i*, institutional effort e_*i*, and the transparency parameter b. Embedded within immutable, self-executing smart contracts, these quantities facilitate a coherent analytical framework while removing reliance on centralized intermediaries. The block schematic of EduDonateBlock is shown in Figure 1.

4.1 Smart contract design and optimization-theoretic functional mapping

To establish the connection among efficiency, scalability, and functional completeness, EduDonateBlock employs four basic contracts. These are the IAC, campaign and donation contract (CDC), verification and allocation contract (VAC), and supply chain and tracking contract (SCTC). The contracts provide the blockchain implementation layer of the proposed system. However, operationalizing the optimization framework is the primary objective. These contracts transform the mathematical decision-making process into executable actions on the blockchain.

From an optimization perspective, these contracts collectively transform the mathematical decision-making process into executable actions on the blockchain. IAC defines the feasible decision space by restricting participation to verified entities. CDC enforces campaign feasibility through funding-threshold constraints. VAC improves campaign quality and donor utility through verification-based allocation mechanisms, and finally, SCTC executes the optimal effort and payoff policies derived from the expected payoff maximization problem. The flow diagram of the entire methodology of EduDonateBlock is shown in Figure 2, and each contract is briefly discussed below.

4.1.1 IAC

This is the first layer of the EduDonateBlock framework. The main objective of this contract is to manage the identity of participant and to enforce role-based access control. Here, a feasible participation domain of the optimization problem is established to ensure that only authenticated stakeholders can interact with the platform. Let, ψ(U_*i*) represents the verification status of participant u_*i*, then [ Ω = U_*i*:ψ(U_*i*) = 1 ] The procedure of IAC is outlined in Algorithm 1.

Algorithm 1 Identity and access contract (IAC). Text-based pseudocode describes an access control procedure. It includes input and output specifications, mapping and functions for registering, assigning, and verifying address-role pairs, and the access decision condition. Access is granted if a verified address has the required role, otherwise denied.

4.1.2 CDC

From an optimization perspective, the CDC operationalizes the campaign funding dynamics and feasibility constraints as discussed in Section 3.5. Specifically, the contract implements the funding model (Equation 9), the expected funding formulation (Equation 10), and the campaign success condition (Equation 12). The funding variable, F_*i* and the threshold parameter, τ_*i* represent as the sum of donor contribution and minimum funding requirement for campaign viability, respectively. CDC serves as a decentralized constraint-enforcement mechanism that controls campaign success, governs escrow-based fund management, and ensures that resource allocation decisions comply with the optimization framework. Algorithm 2 shows the implementation details of CDC.

Algorithm 2 Campaign and donation contract (CDC). Mathematical and pseudocode diagram outlining a campaign funding process, detailing variables for inputs, outputs, contributions, mapping functions, state transitions, a step-by-step donation procedure, fund checking, release or refund conditions, and binary outcome calculation.

4.1.3 VAC

The main objective of VAC is the beneficiary requests validation, campaign credibility evaluation and conditional allocation of funds. From an optimization perspective, this contract operationalizes the campaign quality, donor utility, and funding formulations. It implements the verification process that influences the transparency parameter, b. This has an impact in campaign quality score, Q_*i* (Equation 3), donor utility, U_*ij* (Equation 4), and the aggregate funding function, F_*i*(e_*i*, b) (Equation 5). This contract reduces issues in information asymmetry and perceived risk of fraud. VAC acts as a trust-enforcement and utility enhancement layer. This contract is outlined in Algorithm 3.

Algorithm 3 Verification and Allocation Contract (VAC) Schematic flow diagram showing pseudocode for a verification and fund release process, including input parameters, mapping equations, conditional fund release logic, and procedural steps for submitting, verifying, allocating, and releasing requests based on milestone and verification.

4.1.4 SCTC

The primary objective of the SCTC is to monitor procurement, shipment, and final delivery of educational resources. Before order confirmation or campaign execution, the institutions have to compute expected payoff and effort optimization for the smart-contract decision using Equations 13, 14, respectively. These values are used to decide whether the campaign should proceed or not. Hence, it establishes the critical link between financial transactions and physical resource flow, enabling end-to-end transparency and accountability. This contract is outlined in Algorithm 4.

Algorithm 4 Supply chain and tracking contract (SCTC) with payoff optimization. Algorithmic flowchart in text form for a blockchain-based order and payment process, including inputs, outputs, mathematical payoff equations, order approval logic, status updates, and fund transfer to the supplier based on delivery confirmation.

5 Results and discussions

To demonstrate the real-world relevance of the mathematical framework, a numerical simulation of a crowdfunding campaign is presented here. The simulation is conducted in two stages. Firstly, the overall platform cost is minimized by choosing the optimal level of blockchain transparency (b^*). This is then followed by the educational institution's payoff maximization by choosing the optimal level of campaign effort (e_*i*).

5.1 Platform TEC optimization

Table 2 lists the parameter values for the simulation. With these values, the equilibrium condition of Equation 8 is used to calculate the target level of blockchain integration, (b), for the smart contracts. A trade-off residual off-chain effect occurs as transaction gas fees (p) negatively affect the economic benefit from reductions in operational and counterparty risks (due to automation). This cost-benefit balance between transparency-benefits and transaction-expenses prevents full on-chain integration, (b = 1). Figure 3 illustrates the convex nature of the TEC function, where the unique interior minimum occurs at approximately 87.16% blockchain transparency. This 87% transparency level represents optimal hybrid blockchain architecture - balancing automation efficiencies and transaction costs for the overall best outcome: i.e., where the competing pressures of gas-related overhead and the economic returns from administrative automation and risk reduction are most effectively reconciled.

5.2 Educational institution expected payoff

To evaluate institutional expected payoff, EduDonateBlock considers platform transparency level of ( b^*) of 0.872, an educational institution initiates a fundraising campaign with a pre-specified success threshold (τ_*i*) of Rs.20,000. The institution's operational characteristics are already listed in Table 2. These parameters define the institution's cost–benefit structure and the incentive environment under the given level of platform transparency. Equation 14 provides the optimal target effort exerted by the educational organization (e.g., the collection of supporting documents and photographs) as ei=15.3059 units. The Equation 10 is used to calculate the expected funding (E[Fi(ei,b)]) based on the educational organization's effort at the given level of platform transparency; E[Fi]=Rs.28,679.82. Assuming market noise (ϵ) is normally distributed, this funding level suggests a P_*i* = 89.45% probability of crossing the τ_*i* threshold based on Equation 12. Equation 13 generates the expected payoff (E[Π_*S*]) for the educational organization by factoring-in the “all-or-nothing” smart contract rules as:

E[ΠS]=Pi(ei,b)·E[Fi(ei,b)]-12k(ei)2-g·b*=Rs.11,335.99

Therefore, by exerting 15.3 units of effort on an 87.2% transparent blockchain platform, the educational institution maximizes its probability of campaign success while absorbing combined effort and gas costs. The net expected payoff is Rs.11, 336, proving that the smart contract-enabled crowdfunding mechanism yields a mathematically positive and economically viable outcome for the institution. Figure 4 shows the expected payoff of the educational institution as a function of institutional effort at the optimal level of blockchain transparency (b^*). The payoff function is concave with a unique interior optimum, confirming the analytical solution obtained from the first-order condition. As administrative costs increase, the marginal returns from additional effort beyond the optimal level diminish.

5.3 Sensitivity analysis

This section shows that the socially optimal level of blockchain transparency is highly sensitive to transaction costs and fraud risk. The marginal welfare gains from full decentralization decline as gas costs rise, whereas the welfare benefits of clarity increase with greater fraud risk. Ultimately, integrating institutional engagement enhances these systems by enhancing donor responsiveness and reducing operating expenses, highlighting the importance of incentive structures in blockchain crowdfunding. Figure 5 demonstrates a three-dimensional surface illustrating the combined effect of institutional effort and blockchain transparency on expected payoff, and the sensitivity analysis of the TEC function is shown in Figure 6. Figure 5 represents the concave payoff optimization landscape for the educational institution. Conversely, Figure 6 shows the sensitivity of TEC across the transparency range b ∈ [0, 1] for different gas fees [p ∈ [1, 000, 2, 000]]. With the increase in gas prices, the minimum achievable cost, TEC-opt, rises from Rs.1, 084 to Rs.1, 957, and the optimal blockchain transparency threshold decreases from 93% to 82%.

5.4 Simulation results

The simulation results evaluate the performance of the EduDonateBlock framework under varying levels of blockchain transparency and institutional effort. The objective is to analyze the impact on total operational cost, processing efficiency, and resource allocation effectiveness within the educational supply chain.

5.4.1 Experimental setup

The smart contracts were implemented in Solidity and evaluated using the Remix EthereumIDE (v0.12.0, [27]). Contract deployment, execution, gas consumption analysis, and latency measurements were performed in the Remix virtual testing environment on a single local machine. Consequently, all reported execution times represent controlled local virtual machine measurements rather than performance observed on a live public Ethereum network. EduDonateBlock framework assumes a fixed Ether (ETH) and Indian Rupee (Rs.) exchange rate for the experimental evaluations. The objective of this study is to evaluate the performance of the mathematical model and the smart contract under controlled conditions. Hence, the simulation does not incorporate any live blockchain pricing oracle.

5.4.2 Gas consumption efficiency

For Ethereum-based systems, gas consumption may be considered a major parameter for efficiency computation. It has a direct influence on the economic feasibility of smart contract execution. To analyze the gas consumption efficiency, EduDonateBlock considers a baseline Ethereum gas price of 20 Gwei. 1 Gwei is equal to 10⁻⁹ ETH. It is adopted solely for controlled experimental evaluation and does not represent a fixed operational gas price. The objective is to provide a reliable standard for comparing the execution costs of the smart contracts. However, in operational blockchain networks, gas prices fluctuate due to varying levels of network congestion. Equation 15 calculates the gas cost of a function ‘f'.

G(f)=αNop+βNstore+γNcond(15)

where N_op, N_store, and N_cond denote the number of operations, storage updates, and conditional checks, respectively. It is seen from Equation 1 that contributions incur a constant gas cost. Thus, CDC exhibits linear complexity, i.e., GCDC(i)=O(ni) The threshold condition F_*i*≥τ_*i* introduces only constant overhead. Similarly, VAC computes as Q_*i* = v_*i*+θbe_*i*. The verification status V(R_*k*) is represented in constant time as GVAC=O(1). STTC also operates with constant complexity due to fixed state transitions. Hence, the overall gas consumption is written as

Gtotal(i)=O(ni+mi)

where the number of contributors and verified requests are represented by n_*i* and m_*i*, respectively.

In brief, the number of donations and the cost-related operations are the primary factors that influence the efficiency of gas consumption. It is worth mentioning that the modular architecture of EduDonateBlock reduces redundant computation and ensures linear scalability. Hence, the cost efficiency and practical feasibility are confirmed. Table 3 lists the empirical evaluations of the contracts using the general convention to calculate the transaction cost:

Transaction Cost(ETH)=Gas Used×Gas Price

Table 3. Gas consumption of EduDonateBlock smart contracts.

For underprivileged educational organizations, the financial burden is a significant concern. This happens due to the unpredictable gas-price spikes during live Ethereum network operation. Hence, to reduce the burden, various deployment strategies can be adopted. A few of them are listed below.

• Non-urgent transactions such as campaign registration, verification, and supply-chain updates may be scheduled during periods of lower network congestion.
• To reduce the average gas cost, multiple operations may be grouped through transaction batching.
• The donors or platform administrators may bear the transaction fees rather than beneficiary institutions.

5.4.3 Latency analysis

In blockchain-based systems, transaction latency is another major performance metric. The responsiveness and timeliness of smart contracts are determined by this method. In the EduDonateBlock framework, latency is defined as the time required for a transaction to be validated and confirmed on the blockchain network. These values reported here are obtained under a controlled single-node local virtual machine environment using the Remix testing platform. The measurements are intended to evaluate the computational efficiency of the proposed smart contracts under reproducible laboratory conditions. These values should not be interpreted as end-to-end transaction confirmation times on a production Ethereum blockchain, where network congestion, validator participation, block propagation delays, and consensus mechanisms introduce additional latency. Equation 16 defines the latency of a function f. It is denoted as L(f).

L(f)=Tprop+Tvalidate+Tconfirm(16)

where, T_prop represents the network propagation delay, T_validate denotes transaction validation time, and T_confirm corresponds to block confirmation time. From the mathematical model, the total funding process involves sequential contribution updates:

Fi=∑j=1nicij

Since each contribution c_*ij* is processed as an independent transaction, the cumulative latency for campaign funding is expressed as:

LCDC(i)=∑j=1niL(cij)

Assuming bounded network conditions, this leads to LCDC(i)=O(ni). The threshold evaluation F_*i*≥τ_*i* introduces negligible latency, as it involves a simple conditional check, and the quality function in VAC becomes:

Qi=vi+θbei

SCTC processes a fixed sequence of state transitions, leading to constant latency, LSCTC=O(1). Therefore, the overall latency for a campaign can be expressed as Ltotal(i)=O(ni+mi) where n_*i* and m_*i* denote the number of contributors and verified requests, respectively. In summary, latency in the proposed framework is primarily influenced by the number of transactions, particularly during donation aggregation. Other operations incur bounded latency, and the modular design ensures that delays remain within acceptable limits for crowdfunding applications. Empirical evaluation of latency is summarized in Table 4. It should be noted that EduDonateBlock achieves an average smart contract execution latency of approximately 6.25 s in a controlled Remix virtual testing environment. This value represents local experimental performance. It should not be considered as an end-to-end confirmation latency on a live Ethereum network.

Table 4. Latency analysis of EduDonateBlock smart contracts (measured in a controlled single-node Remix virtual testing environment).

5.5 Comparative performance analysis

Comparative performance evaluation of EduDonateBlock with a traditional sustainable model [26], a blockchain-enabled supply chain model [4], and Blockchain-based crowdfunding models [7, 8] is shown in Table 5. Notably, EduDonateBlock achieves the highest transparency level among the existing models. Under the controlled Remix virtual testing environment, EduDonateBlock achieves an average smart contract execution latency of approximately 6.25 s. This indicates improved operational efficiency compared with the reference blockchain model. In terms of economic performance, EduDonateBlock attains an expected payoff of Rs. 11,335.99, which is substantially higher than the profit reported by the conventional sustainable model. EduDonateBlock also exhibits lower transaction overhead, approximately 0.0044 ETH in gas costs compared with 0.0068 ETH for the existing blockchain solution. The results highlight the effectiveness of EduDonateBlock in terms of transparency, reduced operational costs, improved economic outcomes, and strengthening accountability within educational crowdfunding ecosystems.

Table 5. Comparison of EduDonateBlock with existing sustainable and blockchain-based crowdfunding frameworks.

6 Conclusions and scope of future works

EduDonateBlock, a blockchain-based crowdfunding framework for intelligent educational SCM, is proposed here. This framework not only ensures transparency but also supports decentralization, immutability, and verifiable transactions. Total Expected Cost provides a quantitative decision rule that balances the process automation against fraud risks and transaction costs. Numerical analysis shows the optimal transparency level of 87.16% on-chain integration. It achieves an institutional pay-off of Rs. 11,335.99 and a campaign success probability of 89.45%. Four smart contracts are written to implement the blockchain framework. These are the IAC, CDC, VAC, and SCTC. Quantitative evaluations show that gas consumption remains within 3.3 × 10⁴ to 7.1 × 10⁴ units, approximately 0.0007 to 0.0018 ETH. The proposed framework achieved an average execution latency of approximately 6.25 s under a controlled local virtual testing environment. The results confirm that for decentralized educational crowdfunding, EduDonateBlock can be a potential solution in terms of scalability, cost-efficiency, and transparency. This framework is based on analytical modeling and simulation results. Hence, implementation and validation for large-scale real-world applications have not been explored. Therefore, to empirically assess system performance under operational conditions, future research should focus on pilot-scale real-world implementation for underprivileged educational organizations. To improve the affordability and economic sustainability of deployments, future work will also focus on implementing practical mechanisms for mitigating the impact of dynamic Ethereum gas-price fluctuations. These may include transaction scheduling and batching, gas sponsorship, etc.

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Appendix-A

Mathematical Analysis: Existence and Uniqueness of the Optimal Strategy

To establish the theoretical validity of the proposed framework, we provide a formal proof demonstrating that the platform's optimization problem possesses a unique, globally optimal blockchain transparency level b^* ∈ [0, 1].

Theorem

Let the Total Expected Cost function be defined on the compact domain b ∈ [0, 1] as:

TEC(b)=C0e-ab+p·b+R0(1-b)2

where the structural parameters satisfy C₀ > 0, a > 0, p > 0, and R₀ > 0. Then, there exists a unique global minimizer b^* ∈ [0, 1].

Proof

1. Existence: The function TEC(b) is a linear combination of an exponential function (C0e-ab), a linear function (p·b), and a quadratic polynomial (R0(1-b)2). Because each constituent function is infinitely differentiable (C∞), TEC(b) is continuous on the closed and bounded (compact) interval I = [0, 1]. By the Extreme Value Theorem, a continuous function operating on a compact set must attain both its supremum and infimum within that set. Hence, a global minimum b^* exists.

2. Uniqueness via Strict Convexity: To prove uniqueness, we evaluate the curvature of the cost surface by calculating the first and second-order derivatives of TEC(b) with respect to the decision variable b:

ddbTEC(b)=-aC0e-ab+p-2R0(1-b)

d2db2TEC(b)=a2C0e-ab+2R0

Given that the parameters are strictly positive (C₀, a, R₀ ∈ ℝ₊₊), and the term e^−*ab*>0 for all b ∈ ℝ, it follows that:

a2C0e-ab>0 and 2R0>0

Therefore, the second derivative is strictly positive across the entire domain:

d2db2TEC(b)>0 ∀b∈[0,1]

A strictly positive second derivative implies that the objective function TEC(b) is Industrial-grade strictly convex over the convex set [0, 1]. A fundamental property of strictly convex functions states that any local minimum on a convex set is also a unique global minimum.

3. Characterization of the Solution: The unique minimizer b^* is determined by evaluating the boundary gradients. If the parameters satisfy the interior condition:

-aC0+p-2R0<0<-aC0e-a+p

then b^* lies strictly within the interior (0, 1) and is the unique transcendental root satisfying the first-order necessary and sufficient condition:

aC0e-ab+2R0b=p+2R0

Otherwise, if the gradient remains unidirectional, b^* cleanly converges to the boundary points (b^* = 0 or b^* = 1).

Footnotes

Edited by: Amrit Das, SRM Institute of Science and Technology (Deemed to be University) Research Kattankulathur, India

Reviewed by: Bakkiyaraj Kanthimathi Malamuthu, Morgan Stanley Financial Services, United States

Ali Çalhan, Duzce University, Türkiye

Md. Tabil Ahammed, Bangladesh University of Engineering and Technology, Bangladesh