Optimizing Reserve Decisions in Relief Supply Chains with a Blockchain-Supported Second-Hand E-Commerce Platform

Abstract

This paper develops a novel government reserve strategy, employing a blockchain-supported second-hand E-commerce platform, specifically designed to mitigate the depreciation and expiration of disaster relief supplies. Utilizing the newsvendor model and convex optimization techniques, this study evaluates the efficacy of a rotational strategy for optimal pre-positioning of supplies, considering the dynamic conditions of supply chain performance. Additionally, the paper demonstrates how blockchain technology significantly enhances the traceability of supplies, which is crucial for effective supply management. Empirical data analysis reveals that exceeding a critical price threshold on the platform not only augments the government’s optimal reserve levels but also substantially decreases operational costs. In scenarios where the supply chain is well coordinated, optimal reserve quantities are affected by variables such as the likelihood of disaster events, the success rate of sales, and a supply traceability index. This research extends the application of blockchain and E-commerce technologies within disaster management supply chains and offers new insights and practical approaches for improving E-commerce practices in this context.

1. Introduction

Effective relief supply pre-positioning is a crucial strategy for enhancing a nation’s capability to withstand risks [1]. In recent years, frequent natural disasters, such as earthquakes, typhoons, and heavy rains, coupled with the unprecedented emergence of the COVID-19 pandemic in late 2019, have posed increasingly severe threats to national economies and public safety. These emergencies highlight a critical issue: the need for effective stockpiling of relief supplies to ensure precise, reliable, and timely provision during disasters. Addressing this issue has become an urgent and important research topic in the field of emergency management [2,3,4]. Presently, global relief supply reserves are primarily overseen by government agencies and humanitarian organizations. The government, as the core responsible body for responding to emergencies, has actively adopted a variety of operational modes, such as government physical stockpiles [5] and joint stockpiles managed by government agencies and companies [6,7], to enhance the effectiveness of relief supply reserves. Concurrently, the government coordinates the relief supply chain effectively through various contractual mechanisms, including options contracts [8], repurchase agreements [9,10], and profit-sharing agreements [11], ensuring the smooth provision of supplies in emergency situations [12,13,14]. Although these measures have greatly ensured the stability of supply, the storage and management of materials still face some challenges.

The unpredictability of disasters creates significant supply risks for relief supplies. Firstly, the government needs to stockpile substantial amounts of supplies in advance to be prepared for emergencies. However, items with fixed shelf lives, such as pharmaceuticals and beverages, might expire without the occurrence of a disaster, leading to wastage. Secondly, rapid technological advancements may degrade the performance of supplies, such as cold weather clothing and emergency lights, thus reducing their utility in emergency situations. Therefore, it is essential for the government to update supplies in a timely manner [15,16]. Failure to rotate supplies promptly may result in a decline in the quality of stockpiled supplies, which could adversely affect disaster relief efforts.

To address the challenges of surplus and outdated supplies in government reserves, we propose, for the first time, to utilize a ‘second-hand E-commerce platform’ for the consignment of supplies, coupled with the purchase of new supplies for rotation. The rotation and reserve process of relief supplies on the ‘second-hand E-commerce platform’ is illustrated in Figure 1. This platform utilizes Internet technology to trade goods through E-commerce [17]. Specifically, the government assesses the proportion of supplies that need to be rotated based on their wear and tear, technological obsolescence, and unused surplus. These supplies are then consigned to a professional third-party second-hand platform. The government can earn revenue based on the success rate of the consignment, and at the same time, can repurchase newer supplies for stockpiling. Traditional strategies for updating relief supplies have primarily relied on buy-back methods [18], but these often ignore the fact that many enterprises have not yet established an effective reverse logistics system, thus lacking the ability to efficiently handle repurchased supplies. In contrast, E-commerce platforms offer a convenient market interface and efficient logistics solutions for the sale of used materials. Consigning supplies through the ‘second-hand E-commerce platform’ not only reduces the waste of supplies but also recovers funds for enterprises, promoting sustainable societal development [19]. Although the consignment model of ‘second-hand E-commerce platforms’ is already used in the commercial sector, it has not yet been applied to relief supply chain management.

Second-hand E-commerce platforms have opened new avenues for the rotation of relief supplies. Enhancing the traceability of these supplies is critical to improving their consignment success rate. Difficulty in real-time monitoring of the supplies’ origin, flow, and condition can impede their timely updating, thus compromising the rapid response capabilities in disaster scenarios. In these circumstances, blockchain technology presents a highly promising solution [20]. In the field of relief supply management, blockchain technology has garnered extensive academic attention due to its potential to enhance information sharing, increase transparency, and bolster security [21,22,23]. The blockchain’s timestamp technology can precisely record the flow of supplies, including the specific times of intake, storage, and rotation [24]. This measure can enhance transparency and trust in transactions, while improving the success of supplies during the marketing period. However, there is a lack of specific research that directly integrates blockchain technology into decision optimization models.

Motivated by observations from both practice and academic research, this paper aims to address the following questions:

(1)

How can the optimal reserve quantity of the government’s advance physical pre-positioning in the “second-hand E-commerce platform” consignment strategy be determined considering blockchain?

(2)

How can we utilize the profit function of the “second-hand E-commerce platform” to explore the key conditions for supply chain coordination?

(3)

What is the impact of blockchain technology and second-hand E-commerce platform transaction characteristics on the government’s optimal reserve decision?

To address these issues, we develop a “second-hand E-commerce platform” consignment mechanism considering blockchain technology. We employ convex optimization theory and the newsvendor model to determine the government’s optimal reserve quantities under this scheme. We also integrate the profit function of the “second-hand platform” to explore conditions necessary for achieving relief supply chain coordination. Furthermore, we investigate the decision-making process regarding the government’s optimal reserve quantities and its impact on supply chain collaborative performance in a diverse parameter environment.

The novelty and contributions of this study are summarized as follows: Firstly, we introduce an innovative consignment and rotation strategy on a ‘second-hand platform’ for government physical supply rotation, aiming to optimize the material rotation process and enhance the effectiveness and reliability of relief supplies. This strategy not only improves material management efficiency but also sheds new light on the application of E-commerce platforms in government management. Secondly, our research framework incorporates various complex factors, offering a fresh perspective on the management of relief supply rotation. Lastly, the integration of blockchain timestamping technology into the transaction process on the second-hand platform enhances the traceability of supplies and demonstrates the practical application value of blockchain technology in the field of emergency management.

The remainder of this paper is organized as follows. Section 2 presents the literature review. Section 3 introduces the relevant variables and assumptions. In Section 4, we present and analyze mathematical models for consignment rotation on a “second-hand platform” considering blockchain. Section 5 is dedicated to conducting a numerical analysis. Finally, Section 6 concludes the paper with our findings.

2. Literature Review

This paper synthesizes three key areas of literature: the supply chain of relief supplies, the rotation of supplies on second-hand E-commerce platforms, and the adoption of blockchain technology. It provides a comprehensive analysis of the challenges and innovations in pre-positioning and rotating supplies.

2.1. Relief Supplies Supply Chain

The characteristics of relief supplies significantly impact inventory management [25]. To effectively respond to disaster events, governments often need to reserve emergency supplies. Due to the low probability and uncertainty of disaster occurrences, some supplies face risks of expiration or performance degradation [16]. For instance, medical supplies, such as medicines and disinfectants, have specific expiration dates. Similarly, electronic devices, such as radios and flashlights, may experience performance decline due to battery aging or prolonged non-use.

To address this problem, scholars have begun to explore storage strategies for relief supplies with fixed shelf lives. Some scholars consider the time window based on the fixed shelf-life characteristics of relief supplies, introducing expiration cost functions [26], considering the number of emergency occurrences [5], the intervals between occurrences [5], and the randomness of occurrence times to design inventory models for emergency supplies [27]. Other researchers have divided the storage cycle of relief supplies into two phases based on critical time points, implementing inventory transfer decisions at these key moments [16]. There are also scholars who have innovatively proposed inventory optimization for perishable relief supplies under the emergency reserve center and supplier recovery replacement model, suggesting two replacement mechanisms based on the remaining lifecycle of relief supplies and the number of emergency supply reserve centers [11,28,29].

These studies alleviate the risk of expiration and waste of government physical reserves, but frequent supply transfers and recovery exchanges have also increased the cost of government reserves. With the help of internet platforms and the rise of E-commerce, this paper proposes that the government can use second-hand E-commerce platforms to facilitate the trade-in of supplies.

2.2. Rotation of Perishable Supplies on Second-Hand E-Commerce Platforms

The rotation strategy ensures the availability of supplies in the Government’s physical reserves, and at the same time, a low-carbon recycling economy can be realized through the recovery and reuse of surplus supplies. Previous literature has primarily adopted repurchase strategies for the rotation and updating of emergency supplies. Repurchase, mainly used in the commercial sector, refers to suppliers repurchasing the retailer’s unsold products at a pre-agreed price. This stimulates the retailer to order more products and increases sales, especially relevant for products characterized by uncertain demand and short lifecycles [18]. Essentially, repurchase is a way for suppliers to share the retailers’ sales risk arising from demand uncertainty, enhancing the overall risk resilience of the supply chain and improving its operational efficiency to achieve coordinated performance [10,30]. The repurchase model has also been extensively developed in the emergency field, primarily to explore coordination and strategies in response to sudden incidents. For instance, repurchase can help upstream suppliers alleviate opportunistic problems arising from strategic uncertainty [10]. However, the repurchase strategy does not fully consider the process of handling supplies after repurchasing or the possible economic losses to the enterprise, as it presupposes that the company has the willingness to recycle the supplies.

In the face of the above challenges, this paper proposes the use of a ‘second-hand E-commerce platform’ to consign old supplies. This model can reduce the waste of supplies and promote the effective recycling of resources. The second-hand economy has been characterized as ‘sequential sharing’, by which used products are reused [31,32], sometimes called ‘recommerce’ [33]. As technology evolves and consumer preferences shift, more consumers are buying used goods. Up to 40 percent of U.S. consumers used online resale websites in 2022 [34]. In Europe, by 2027, the online market is expected to have 85.5 million users [35]. Depop, eBay, and Taobao are famous second-hand trading platforms. According to an investigation, almost two-thirds of U.S. consumers surveyed said they had bought used products on eBay [36]. Chinese consumers most frequently used Xianyu, otherwise known as Taobao [34].

Consignment and resale are two common operation modes of E-commerce platforms [37]. Under the consignment model, consignors place their goods on a third-party sales platform but retain ownership of the goods. When the goods are sold, the platform takes a percentage of the sale price as a commission for its services, with the remainder going to the consignor [15,37]. In the resale model, second-hand platforms purchase goods directly from the original owners and then add them to their own inventory. Afterward, the resellers proceed to sell the goods [38].

The second-hand E-commerce platform model has been used in the commercial sector [17], but there is a lack of research related to emergency supplies’ management. Considering the need to ensure transparency, traceability, and control over emergency supplies when selling government reserves, this paper adopts a consignment operational model to study the rotation strategy of emergency supplies.

2.3. The Adoption of Blockchain Technology

The most obvious side effect of online shopping is product uncertainty. Enhancing the traceability of supplies in the consignment process on second-hand E-commerce platforms is a key strategy to ensure the quality of supply management. Blockchain technology, as a distributed ledger technology [39], greatly enhances data security and trust by providing a decentralized, tamper-proof, and highly transparent system of recording information [20,40]. In the financial sector, blockchain technology has been widely applied to cryptocurrencies, smart contracts, and cross-border payments, revolutionizing traditional financial transaction models [41,42,43]. Additionally, blockchain has demonstrated its wide application prospects in supply chain management, copyright protection, identity verification, and medical health records [44]. Moreover, the application of blockchain in ensuring personal privacy and data security has provided new solutions for the protection of personal information [45].

Blockchain technology has also been widely discussed in the field of emergency supplies’ management. Through a comprehensive analysis of the existing literature, scholars have proposed research frameworks that illustrate how organizations can leverage blockchain technology to enhance supply chain resilience and performance [46,47]. Particularly in the context of humanitarian supply chains, existing studies have validated theoretical models of blockchain technology in promoting rapid trust, collaboration, and supply chain resilience through surveys of international non-governmental organizations. These studies confirm the positive role of blockchain in enhancing supply chain transparency and facilitating rapid trust and collaboration among participants in disaster relief efforts [48,49]. From the perspective of transparency, the authors of [50] emphasized that by sharing the whereabouts of supplies in real time, blockchain is expected to solve the social trust problem caused by information asymmetry. Similarly, from the perspective of traceability, blockchain can promote information disclosure and material traceability in the material security in response to emergencies [51,52]. In addition, some scholars have proposed a blockchain application framework in actual disaster prevention and rescue operations [47]. Smart contracts within blockchain technology can automatically execute contract terms, thus ensuring timely payment and product delivery [53,54,55,56].

In addition, some scholars focus on the application of blockchain in E-commerce platforms. For example, Jain et al. [57] examined the factors influencing consumer adoption of Blockchain-Enabled E-commerce Platforms (BEEP) in the second-hand apparel market, integrating consumer buying motives and the Unified Theory of Acceptance and Use of Technology (UTAUT) to understand how blockchain can mitigate risks and enhance sustainability in the industry. Devrani et al. [58] outlined a blockchain-based E-commerce system that issues NFTs as digital warranty cards post-transaction, facilitating easier product management and supporting re-commerce by allowing users to trade products directly.

However, despite these positive discussions, existing research and practice lack specific models for directly integrating blockchain technology into relief supply chain reserves. This paper applies timestamping technology to the trade of relief supplies on second-hand platforms, and then forms a transparent and unalterable archive of material flow. Time-stamped materials are more likely to win the trust of consumers, which in turn improves the consignment success rate.

3. Model Description and Assumption

3.1. Problem Description

Physical stockpiling is often used by governments in emergency disaster response, especially in cases where there is an urgent need for relief supplies that can be easily stored. This approach ensures that these critical supplies can be quickly mobilized and distributed in the event of a disaster.

However, this method of stockpiling faces challenges, such as high costs and the potential for waste. Supplies may suffer from natural wear or become technologically obsolete during long-term storage, thus periodic updates and replacements are necessary. This paper proposes a “second-hand platform” consignment strategy utilizing blockchain technology to address the government’s need for relief supplies’ rotation. The government determines the rotation ratio based on the wear and obsolescence of supplies within the contract period, and selectively sells supplies through third-party second-hand platforms, earning revenue based on the success rate of sales. Additionally, the government purchases an equivalent number of new supplies from partnering companies and improves the traceability of the supplies’ selling process through blockchain technology, such as timestamps.

In summary, this section constructs a blockchain “second-hand platform” consignment–repurchase model, aimed at providing an effective management and rotation scheme for government pre-positioned supplies.

To enhance readability, the definitions of variables are described in

Table 1. Model parameter settings.

Notation	Definition
$x$	Randomized requirements for relief supplies. Following a specific probability distribution, defining $U$ as the maximum, $\mu$ as the mean, and the probability density function as $f(x)$. $F(x)$ denotes the cumulative distribution function, and $F^{-1}(x)$ is its inverse function.
$\alpha$	Emergency level parameters: the initial range is [0, 1], with 0 indicating not urgent and 1 indicating very urgent.
${\delta }^{\prime }$	Base unit loss cost of full relief supplies ($\alpha =1$) for unmet needs. Unit loss cost adjusted for urgency: $\delta =\alpha \times {\delta }^{\prime }$.
$\beta$	Reserve difficulty parameter: the initial range is [0, 1], where 0 means easy to reserve, and 1 means very difficult to reserve.
${\varphi }^{\prime }$	The base unit material loss or expiration cost of a totally difficult reserve stock ($\gamma =1$). $\varphi =\beta \times {\varphi }^{\prime }$: adjusted unit loss costs, weighted for reserve difficulty.
$\rho$	Probability of a disaster occurring during the agreement cycle.
$Q_{RE}$	Physical reserves held in advance by the government.
$p_r$	Regular procurement prices for emergency supplies.
$c_p$	Unit cost of production of relief supplies in an enterprise.
$p_m$	Cost of spot purchases of relief supplies for post-disaster units.
${\omega }_{RE}$	Government’s willingness to use blockchain to introduce a “second-hand platform” for consignments: ${\omega }_{RE}=1-p_{RE}/(p_r-v)$.
$p_{RE}$	Selling price of “second-hand platform” goods.
$c_{RE}$	Unit cost of consigning relief supplies on second-hand platforms introducing blockchain technology.
$S_{avg}$	The platform’s average success rate in previous selling cycles, in [0, 1].
$G$	Item traceability index, between 0 (completely untraceable) and 1 (completely traceable), with 0.5 equal to the neutral point.
$\mu$	Adjustment factor to quantify the impact of blockchain technology’s enhanced supplies’ traceability on the success rate of the sale, $0<\mu <1$.
$S$	Success rate of selling, $S=S_{\mathrm{avg}}\left(1+\mu (G-0.5)\right)$, $0\le S\le 1$.
$v_s$	Unsold salvage value.
$\lambda$	Second-hand E-commerce platform commission.

.

3.2. Decision Sequence

According to the previous problem description, the decision sequence of supply rotation under the “second-hand platform” consignment model of blockchain is as follows:

(1)

The government will first stockpile the supplies in advance and set a rotation cycle. The parameter for the urgency of the materiel is $\alpha$, and the parameter for the ease of stockpiling is $\beta$.

(2)

When the single-cycle stockpile period arrives, the government needs to rotate and renew the supplies:

First, when no disaster occurs during the reserve period, the government can choose the blockchain “second-hand platform” to consign the supplies for rotation, and the supplies that are sold successfully will gain revenue, while those that fail will be disposed of at salvage value, and brand-new supplies will be purchased to make up for the shortfall.

(3)

When a disaster event occurs during the stockpile cycle T, the rotation of relief supplies follows the change in demand for supplies:

• If $0\le x<Q_{RE}$, i.e., the demand for emergency supplies is less than the government’s physical stockpile. This is similar to a no-disaster scenario, but the base number of supplies that need to be replaced is $Q_{RE}-x$.
• If $Q_{RE}\le x\le U$, surplus goods need to be purchased on the spot, in the order of preference to the agreed enterprise, and when the agreed company is unable to meet it, the market is used to purchase it, incurring the cost of losses due to the demand not met by the fixed channels (own reserves and the agreed company). Figure 2 illustrates the logical structure of the model.

3.3. Assumption

In accordance with the modeling analysis above, this paper sets the relevant assumption as follows:

(1)

Referring to the assumptions of existing studies [1,44,59], the demand for relief supplies is $x$, and there exists a maximum value $U$, which reflects the fact that the coverage of the emergency stockpile is limited, not infinite.

(2)

During the procurement phase of the physical pre-positioning, which consists of a single-cycle procurement contract between the government (the purchaser of relief supplies) and the enterprise (the supplier of relief supplies). There are two main bodies, the government and the “second-hand platform”, in the rotation of supplies.

(3)

Utilizing blockchain timestamp technology to improve the traceability of supplies will significantly increase the efficiency and profitability of the government’s consignment of used supplies through second-hand platforms. Blockchain technology can reduce information asymmetry in the circulation of materials and increase the trust of buyers, thus improving the success rate and price of the sale of used goods.

(4)

Based on the logical requirements, consignment prices on second-hand platforms are less than the market purchase price of the supplies, $p_{RE}<p_r$.

4. Reserve Model for Rotation on Blockchain-Enabled Second-Hand Platforms

4.1. Government Decision Model

4.1.1. Government Cost Function in the Absence of Disasters

At the beginning of the agreement period, the government will need to pre-position an emergency stockpile of $Q_{RE}$. If no disaster occurs during the agreement period, the government will dispose of the surplus at the end of the agreement using a timestamped “second-hand platform” consignment strategy and plan to re-purchase it into the market. Therefore, the cost function for the government in the no-disaster scenario can be defined as follows:

$$\begin{array}{cc}\hfill {\mathrm{\Pi }}_{RE}^{d_1}& =p_r{Q}_{RE}-S{\displaystyle \frac{p_{RE}}{p_r-v}}{p}_{RE}{Q}_{RE}\left(1-\lambda \right)\hfill \\ & -\left(1-S\right){\displaystyle \frac{p_{RE}}{p_r-v}}v{Q}_{RE}\left(1-\lambda \right)+\varphi Q_{RE}+p_r{Q}_{RE}-\left(1-{\displaystyle \frac{p_{RE}}{p_r-v}}\right)v{Q}_{RE}\hfill \end{array}$$

(1)

where $p_r{Q}_{RE}$ is the cost of the government’s physical stockpile of relief supplies, and $S{p}_{RE}/(p_r-v)p_{RE}{Q}_{RE}\left(1-\lambda \right)$ is the benefit in the absence of a disaster. Specifically, the willingness to consign on the government’s “second-hand platform” using blockchain technology, $p_{RE}/(p_r-v)$, and the success rate of selling on the second-hand platform, $S$, are adjusted by the success rate of the successful consignment and subtracted from the commission paid to the “second-hand platform”. $\left(1-S\right)p_{RE}/(p_r-v)v{Q}_{RE}\left(1-\lambda \right)$ represents the residual value of unsuccessful sales of emergency supplies. $\varphi Q_{RE}$ represents the cost of expiration or damage to unused government relief supplies adjusted for stockpile difficulty. $\left(1-p_{RE}/(p_r-v)\right)v{Q}_{RE}$ represents the residual value of relief supplies not considered for consignment on the “second-hand platform”, as adjusted by the government’s willingness to consign on the “second-hand platform”. The second $p_r{Q}_{RE}$ is the cost of physically re-stocking the supplies at regular purchase prices after the supplies to be rotated have been disposed of. The government’s cost function is simplified as follows:

$$\begin{array}{cc}\hfill {\mathrm{\Pi }}_{RE}^{d_1}& =Q_{RE}{\displaystyle \frac{p_{RE}}{p_r-v}}\left[S\left(v-p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]\hfill \\ & +Q_{RE}\left[2p_r+\varphi -v\right]\hfill \end{array}$$

(2)

4.1.2. Government Cost Function in the Event of a Disaster

If there is a disaster during the agreement period, the government’s cost function is discussed in two different scenarios as the demand for relief supplies changes.

(1)

If $0\le x<Q_{RE}$, i.e., the demand for relief supplies is less than the government’s physical stockpile, the government’s cost function is:

$$\begin{array}{cc}\hfill {\mathrm{\Pi }}_{RE}^{d_2}& =p_r{Q}_{RE}-S{\displaystyle \frac{p_{RE}}{p_r-v}}{p}_{RE}\left(Q_{RE}-x\right)\left(1-\lambda \right)\hfill \\ & -\left(1-S\right){\displaystyle \frac{p_{RE}}{p_r-v}}v\left(Q_{RE}-x\right)\left(1-\lambda \right)\hfill \\ & +\varphi \left(Q_{RE}-x\right)+p_r\left(Q_{RE}-x\right)-\left(1-{\displaystyle \frac{p_{RE}}{p_r-v}}\right)v\left(Q_{RE}-x\right)\hfill \end{array}$$

(3)

Under the constraint $0\le x<Q_{RE}$ on the demand for emergency supplies, rotational quantities of supplies are those remaining in the physical stockpile and those that have not been utilized, $Q_{RE}-x$. By simplification, the above equation can be written as:

$$\begin{array}{cc}\hfill {\mathrm{\Pi }}_{RE}^{d_2}& =p_r{Q}_{RE}+S{\displaystyle \frac{p_{RE}}{p_r-v}}\left(v-p_{RE}\right)\left(Q_{RE}-x\right)\left(1-\lambda \right)\hfill \\ & +\left(Q_{RE}-x\right)\left[\varphi +p_r-v\right]+\left(Q_{RE}-x\right)v\lambda {\displaystyle \frac{p_{RE}}{p_r-v}}\hfill \end{array}$$

(4)

(2)

If $Q_{RE}\le x\le U$, i.e., the government’s physical stockpile of goods is less than the demand for emergency goods, $x$. At this point, the surplus goods need to be purchased off the shelf and incur a cost of loss due to the demand not met by the physical stockpile (own stockpile). The government cost is expressed as:

$${\mathrm{\Pi }}_{RE}^{d_3}=p_r{Q}_{RE}+p_m(x-Q_{RE})+\delta \left(x-Q_{RE}\right)$$

(5)

Since the stockpile is fully utilized and there is no rotation involved, the government’s cost function in condition $Q_{RE}\le x\le U$ keeps the same structure, which simplifies to:

$${\mathrm{\Pi }}_{RE}^{d_3}=Q_{RE}\left(p_r-p_m-\delta \right)+x\left(p_m+\delta \right)$$

(6)

Based on the above profit analysis, under the probability, $p$, of a disaster occurring during the protocol period, the government cost function for the blockchain’s “second-hand platform” consignment rotation strategy is as follows:

$$\begin{array}{cc}\hfill {\mathrm{\Pi }}_{RE}^d& =\left(1-\rho \right)\left(Q_{RE}{\displaystyle \frac{p_{RE}}{p_r-v}}\left[S\left(v-p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]+Q_{RE}\left[2p_r+\varphi -v\right]\right)\hfill \\ & +\rho \left\{\begin{array}{l}{\displaystyle {\int }_0^{Q_{RE}}\left[\begin{array}{c}{p}_r{Q}_{RE}+S\frac{p_{RE}}{p_r-v}\left(v-p_{RE}\right)\left(Q_{RE}-x\right)\left(1-\lambda \right)\\ +\left(Q_{RE}-x\right)\left[\varphi +p_r-v\right]+\left(Q_{RE}-x\right)v\lambda \frac{p_{RE}}{p_r-v}\end{array}\right]f(x)dx}\\ +{\displaystyle {\int }_{Q_{RE}}^U\left[Q_{RE}\left(p_r-p_m-\delta \right)+x\left(p_m+\delta \right)\right]f(x)dx}\end{array}\right\}\hfill \end{array}$$

(7)

(3)

Analysis of results

Proposition 1. 

When the government introduces blockchain technology to the “second-hand platform” for consignment for emergency supply rotation, the government’s optimal physical reserve, $Q_{RE}^{\ast }$, is:

$$Q_{RE}^{\ast }=\left\{\begin{array}{l}0 Q_{RE}^{\ast }<0;\\ Q_{RE}^{\ast } \mathrm{other};\\ Q_{max}^{RE} Q_{RE}^{\ast }>q_{max};\end{array}\right.$$

(8)

Proof of Proposition 1. 

Solve for the first-order derivative of $Q_{RE}$ in the cost function (Equation (7)) for the government (demand side) under the blockchain’s second-hand platform consignment rotation strategy:

$$\begin{array}{cc}\hfill {\displaystyle \frac{\partial {\mathrm{\Pi }}_{RE}^d}{\partial Q_{RE}}}& =\left(1-\rho \right)\left[{\displaystyle \frac{p_{RE}}{p_r-v}}\left[S\left(v-p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]+\left(2p_r+\varphi -v\right)\right]\hfill \\ & +\rho \left[{\displaystyle \frac{p_{RE}}{p_r-v}}\left[S\left(v-p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]+\left(p_r+\varphi -v+p_m+\delta \right)\right]F(Q_{RE})\hfill \\ & +\rho \left(p_r-p_m-\delta \right)\hfill \end{array}$$

(9)

The second-order derivative of $Q_{RE}$ is further solved and the result is given below:

$${\displaystyle \frac{{\partial }^2{\mathrm{\Pi }}_{RE}^d}{\partial {(Q_{RE})}^2}}=\rho \left[{\displaystyle \frac{p_{RE}}{p_r-v}}\left[S\left(v-p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]+\left(p_r+\varphi -v+p_m+\delta \right)\right]f(Q_{RE})>0$$

(10)

Since the second-order derivative of the government’s cost function with respect to $Q_{RE}$ under this strategy, i.e., Equation (10) > 0, this indicates that the government’s cost function is convex, and that there exists an optimal physical stockpile of emergency supplies, $Q_{RE}^{\ast }$, that minimizes the government’s cost function, which is based on the willingness of the government to consign on the “second-hand platform” at $0\le \omega =p_{RE}/(p_r-v)\le 1$, i.e., $0\le p_{RE}\le p_r-v$.

$$Q_{RE}^{\ast }=F^{-1}\left({\displaystyle \frac{\rho -1}{\rho }}-{\displaystyle \frac{\left(p_r-p_m-\delta \right)}{\rho \left[\frac{p_{RE}}{p_r-v}\left[S\left(v-p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]+\left(p_r+\varphi -v+p_m+\delta \right)\right]}}\right)$$

(11)

Similarly, since the minimum reserve of $Q_{RE}^{\ast }$ is 0 and the maximum is no greater than the government’s maximum reserve capacity, $Q_{max}^{RE}$, the government’s optimal physical reserve, $Q_{RE}^{\ast }$, under the “second-hand platform” consignment rotation strategy is:

$$Q_{RE}^{\ast }=\left\{\begin{array}{l}0 Q_{RE}^{\ast }<0;\\ Q_{RE}^{\ast } \mathrm{other};\\ Q_{max}^{RE} Q_{RE}^{\ast }>q_{max};\end{array}\right.$$

(12)

□

Proposition 2. 

When the government’s optimal physical reserve, $Q_{RE}^{\ast }$, is under the blockchain “second-hand platform” consignment strategy, its optimal physical reserve, $Q_{RE}^{\ast }$, will be adjusted according to the disaster probability, $p$. When the disaster probability, $p$, increases, the government’s optimal physical reserve, $Q_{RE}^{\ast }$, will also increase.

Proof of Proposition 2. 

First, solve for the first-order derivative with respect to $p$ in the government’s optimal physical reserve, $Q_{RE}^{\ast }$, under this strategy:

$${\displaystyle \frac{\partial Q_{RE}^{\ast }}{\partial \rho }}=-{\displaystyle \frac{\left[\frac{p_{RE}}{p_r-v}\left[S\left(v-p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]+\left(p_r+\varphi -v+p_m+\delta \right)\right]\left[F(Q_{RE})-1\right]}{\rho \left[\frac{p_{RE}}{p_r-v}\left[S\left(v-p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]+\left(p_r+\varphi -v+p_m+\delta \right)\right]f(Q_{RE})}}>0$$

(13)

Proposition 2 is proven. This proposition confirms that when the probability of a disaster increases, the risk to the government increases. To cope with this risk, the government may increase its physical stockpile to ensure that it has sufficient resources to provide relief in the event of a disaster. □

Proposition 3. 

When the government’s optimal physical reserve, $Q_{RE}^{\ast }$, is under the blockchain “second-hand platform” consignment strategy, the government’s optimal physical reserve, $Q_{RE}^{\ast }$, is affected by the success rate, $S$, of second-hand platform sales. Specifically, the government will increase its physical reserves, $Q_{RE}^{\ast }$, when the success rate, $S$, of second-hand platform sales increases. In addition, the government cost function, ${\mathrm{\Pi }}_{RE}^d$, is also affected by the success rate, $S$, of second-hand platform sales: the government cost function, ${\mathrm{\Pi }}_{RE}^d$, is a decreasing function of the success rate, $S$, of sales.

Proof of Proposition 3. 

Solve for the first-order derivative with respect to $S$ with respect to $Q_{RE}^{\ast }$:

$${\displaystyle \frac{\partial Q_{RE}^{\ast }}{\partial S}}=-{\displaystyle \frac{\left(1-\rho +\rho F(Q)\right)\frac{p_{RE}}{p_r-v}\left(v-p_{RE}\right)\left(1-\lambda \right)}{\rho \left[\frac{p_{RE}}{p_r-v}\left[S\left(v-p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]+\left(p_r+\varphi -v+p_m+\delta \right)\right]f(Q_{RE})}}$$

(14)

At this point, the positive or negative value of $\partial Q_{RE}^{\ast }/\partial S$ depends on $\left(v-p_{RE}\right)$, since the government chooses the timestamped “second-hand platform” consignment when the salvage value, $v$, is less than the second-hand platform sale price, $p_{RE}$. The optimal decision quantity, $Q_{RE}^{\ast }$, rises as the success rate, $S$, increases, i.e., $\partial Q_{RE}^{\ast }/\partial S>0$.

Similarly, for the government cost function, ${\mathrm{\Pi }}_{RE}^d$, solve for the first-order derivative with respect to $S$:

$${\displaystyle \frac{\partial {\mathrm{\Pi }}_{RE}^d}{\partial S}}={\displaystyle \frac{p_{RE}}{p_r-v}}\left(v-p_{RE}\right)\left(1-\lambda \right)\left[\left(1-\rho \right)Q_{RE}+\rho {\displaystyle {\int }_0^{Q_{RE}}\left(Q_{RE}-x\right)f(x)dx}\right]$$

(15)

At this point, the positivity or negativity of $\partial {\mathrm{\Pi }}_{RE}^d/\partial S$ also depends on $\left(v-p_{RE}\right)$. When $\left(v-p_{RE}\right)<0$, $\partial {\mathrm{\Pi }}_{RE}^d/\partial S<0$. As the success rate, $S$, grows, the government’s cost function decreases.

Therefore, Proposition 3 is proven. The success rate, $S$, of selling on the secondary platform reflects the likelihood that the government will sell supplies on that platform. When $S$ increases, the government’s chances of selling supplies on the platform also increase. When the government has a higher level of confidence that it will be able to successfully sell supplies on the secondary platform, it is likely to increase its physical stockpile. This is because, even if the government stockpiles more supplies now, it can easily sell them through the secondary platform in the future if it no longer needs them. In addition, this strategy reduces the risk to the government of having too many stockpiles compared to the traditional stockpiling strategy. This is because when supplies are no longer needed, they can be moved to the market instead of being wasted. When the sale success rate, $S$, increases, the government is more likely to sell the supplies at a better price on a secondary platform. This provides revenue for the government and also reduces the costs associated with having too many stockpiles. Thus, as $S$ increases, the government’s overall cost decreases, i.e., ${\mathrm{\Pi }}_{RE}^d$ is a decreasing function of $S$. □

Corollary 1. 

Given that $\left(v-p_{RE}\right)<0$, that is, $\partial Q_{RE}^{\ast }/\partial S>0$, $\partial {\mathrm{\Pi }}_{RN}^d/\partial S<0$, $Q_{RE}^{\ast }$ is an increasing function on the average success rate, $S_{\mathrm{avg}}$, and the material traceability index, $G$, over the platform’s selling cycle. When $S_{\mathrm{avg}}$ and $G$ increase, the government also increases the physical stock, $Q_{RE}^{\ast }$. Moreover, the government’s optimal cost function, ${\mathrm{\Pi }}_{RE}^d$, decreases as $S_{\mathrm{avg}}$ and $G$ increase.

Considering the equation $S=S_{\mathrm{avg}}\left(1+\mu (G-0.5)\right)$, the first derivatives of $Q_{RE}^{\ast }$ with respect to $S_{\mathrm{avg}}$ and $G$ are:

$${\displaystyle \frac{\partial Q_{RE}^{\ast }}{\partial G}}={\displaystyle \frac{\partial Q_{RE}^{\ast }}{\partial S}}\times {\displaystyle \frac{\partial S}{\partial G}}={\displaystyle \frac{\partial Q_{RE}^{\ast }}{\partial S}}\times \mu S_{avg}$$

(16)

$${\displaystyle \frac{\partial Q_{RE}^{\ast }}{\partial S_{avg}}}={\displaystyle \frac{\partial Q_{RE}^{\ast }}{\partial S}}\times {\displaystyle \frac{\partial S}{\partial S_{avg}}}={\displaystyle \frac{\partial Q_{RE}^{\ast }}{\partial S}}\times \left(1+\mu (G-0.5)\right)$$

(17)

Similarly, solve for the first-order derivative of ${\mathrm{\Pi }}_{RE}^d$ with respect to $S_{\mathrm{avg}}$ and $G$:

$${\displaystyle \frac{\partial {\mathrm{\Pi }}_{RE}^d}{\partial G}}={\displaystyle \frac{\partial {\mathrm{\Pi }}_{RE}^d}{\partial S}}\times {\displaystyle \frac{\partial S}{\partial G}}={\displaystyle \frac{\partial {\mathrm{\Pi }}_{RE}^d}{\partial S}}\times \mu S_{avg}$$

(18)

$${\displaystyle \frac{\partial {\mathrm{\Pi }}_{RE}^d}{\partial S_{avg}}}={\displaystyle \frac{\partial {\mathrm{\Pi }}_{RE}^d}{\partial S}}\times {\displaystyle \frac{\partial S}{\partial S_{avg}}}={\displaystyle \frac{\partial {\mathrm{\Pi }}_{RE}^d}{\partial S}}\times \left(1+\mu (G-0.5)\right)$$

(19)

Therefore, Corollary 1 is proven. Under the condition that $\left(v-p_{RE}\right)<0$, a healthy and active market with a high average transaction success rate and full traceability of materials might increase the government’s success rate in selling supplies on the platform. That is, as $S_{\mathrm{avg}}$ and $G$ increase, the government may be more confident in successfully selling its supplies on a secondary platform. Consequently, the government may choose to store more supplies, knowing that even if there is currently a surplus, these can potentially be sold successfully on the platform in the future. This strategy enables the government to better prepare for future uncertainties while also being able to quickly access necessary supplies when needed. As the platform’s average sale success rate, $S_{\mathrm{avg}}$, and the traceability index, $G$, increase, the government’s revenue from selling supplies on the platform may increase, while the costs associated with overstocking or understocking may decrease. This leads to a reduction in overall costs for the government.

Proposition 4. 

Under the consignment rotation strategy of a “secondary platform” with blockchain consideration, the government’s optimal physical reserve quantity, $Q_{RE}^{\ast }$, and cost function, ${\mathrm{\Pi }}_{RE}^d$, will be influenced by the selling price, $p_{RE}$, on the secondary platform. When $S\left(v-2p_{RE}\right)\left(1-\lambda \right)+\lambda v>0$, as $p_{RE}$ increases, $Q_{RE}^{\ast }$ will decrease, and the government’s cost function, ${\mathrm{\Pi }}_{RE}^d$, is an increasing function of the secondary platform’s selling price, $p_{RE}$. When $S\left(v-2p_{RE}\right)\left(1-\lambda \right)+\lambda v<0$, the government’s optimal reserve quantity, $Q_{RE}^{\ast }$, is an increasing function of the selling price, $p_{RE}$, on the secondary platform, while the government cost function, ${\mathrm{\Pi }}_{RE}^d$, is a decreasing function of the selling price, $p_{RE}$.

Proof of Proposition 4. 

First, solve for the first derivative of the government’s optimal reserve quantity, $Q_{RE}^{\ast }$, with respect to $p_{RE}$:

$${\displaystyle \frac{\partial Q_{RE}^{\ast }}{\partial p_{RE}}}=-{\displaystyle \frac{\left(1+\rho \left(F(Q_{RE})-1\right)\right)\left[\frac{1}{p_r-v}\left[S\left(v-2p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]\right]}{\rho \left[\frac{p_{RE}}{p_r-v}\left[S\left(v-p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]+\left(p_r+\varphi -v+p_m+\delta \right)\right]f(Q_{RE})}}$$

(20)

Further, solve for the first derivative of the government’s cost function, ${\mathrm{\Pi }}_{RE}^d$, with respect to $p_{RE}$:

$${\displaystyle \frac{\partial {\mathrm{\Pi }}_{RE}^d}{\partial p_{RE}}}={\displaystyle \frac{1}{p_r-v}}\left[S\left(v-2p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]\left[\rho {\displaystyle {\int }_0^{Q_{RE}}\left(Q_{RE}-x\right)f(x)dx}+\left(1-\rho \right)Q_{RE}\right]$$

(21)

At this point, the signs of $\partial Q_{RE}^{\ast }/\partial p_{RE}$ and $\partial {\mathrm{\Pi }}_{RE}^d/\partial p_{RE}$ depend on the magnitude of $S\left(v-2p_{RE}\right)\left(1-\lambda \right)+\lambda v$. Specifically, when $S\left(v-2p_{RE}\right)\left(1-\lambda \right)+\lambda v>0$, $\partial Q_{RE}^{\ast }/\partial p_{RE}<0$ and $\partial {\mathrm{\Pi }}_{RE}^d/\partial p_{RE}>0$, meaning that the government’s optimal reserve quantity, $Q_{RE}^{\ast }$, is a decreasing function of the secondary platform’s selling price, $p_{RE}$, and the government’s cost function, ${\mathrm{\Pi }}_{RE}^d$, is an increasing function of $p_{RE}$. Conversely, when $S\left(v-2p_{RE}\right)\left(1-\lambda \right)+\lambda v<0$ and $\partial Q_{RE}^{\ast }/\partial p_{RE}>0$, $\partial {\mathrm{\Pi }}_{RE}^d/\partial p_{RE}<0$, meaning that the government’s optimal reserve quantity, $Q_{RE}^{\ast }$, is an increasing function of $p_{RE}$, and the government’s cost function, ${\mathrm{\Pi }}_{RE}^d$, is a decreasing function of $p_{RE}$. Thus, Proposition 4 is proven. □

Proposition 5. 

Under the consignment strategy of a blockchain-based “secondary platform”, when the government’s optimal physical reserve quantity is $Q_{RE}^{\ast }$, if condition $-p_{RE}/{\left(p_r-v\right)}^2\left[S\left(v-p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]+1>-1/\left[1-\rho +\rho F(Q_{RE})\right]$ is satisfied, the government’s optimal physical reserve quantity, $Q_{RE}^{\ast }$, is a decreasing function of the conventional purchase price, $p_{RE}$. Specifically, as the conventional purchase price, $p_{RE}$, increases, the government’s optimal physical reserve quantity, $Q_{RE}^{\ast }$, decreases.

Proof of Proposition 5. 

Solve for the first derivatives of $Q_{RE}^{\ast }$ and ${\mathrm{\Pi }}_{RE}^d$ with respect to the conventional purchase price, $p_{RE}$:

$${\displaystyle \frac{\partial Q_{RE}^{\ast }}{\partial p_r}}=-{\displaystyle \frac{\left[\frac{-p_{RE}}{{\left(p_r-v\right)}^2}\left[S\left(v-p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]+1\right]\left[1-\rho +\rho F(Q_{RE})\right]+1}{\rho \left[\frac{p_{RE}}{p_r-v}\left[S\left(v-p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]+\left(p_r+\varphi -v+p_m+\delta \right)\right]f(Q_{RE})}}$$

(22)

When condition $-p_{RE}/{\left(p_r-v\right)}^2\left[S\left(v-p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]+1>-1/\left[1-\rho +\rho F(Q_{RE})\right]$, and $\partial Q_{RE}^{\ast }/\partial p_r<0$, Proposition 5 is proven. Under these conditions, as the conventional purchase price, $p_{RE}$, rises, the direct costs of purchasing new supplies increase. Consequently, for economic efficiency, the government may consider reducing purchases from conventional channels or decreasing reserves and rely more on already reserved supplies or trade via a secondary platform. Additionally, because the market price of supplies increases, the pre-stored purchase costs for the government increase, leading to a rise in overall costs. □

Proposition 6. 

When the government opts to introduce a blockchain-based “second-hand platform” for rotating unused supplies, the government’s optimal physical reserve quantity, $Q_{RE}^{\ast }$, is an increasing function of the spot purchase cost, $p_m$, for emergency supplies after a disaster. Specifically, as the spot purchase cost, $p_m$, for post-disaster emergency supplies increases, the government’s optimal physical reserve quantity, $Q_{RE}^{\ast }$, will correspondingly increase. Additionally, the government’s cost function, ${\mathrm{\Pi }}_{RE}^d$, is also an increasing function of the spot purchase cost, $p_m$, for post-disaster emergency supplies.

Proof of Proposition 6. 

Solve for the first-order derivative of $p_m$ with respect to the government’s physical reserves, $Q_{RE}^{\ast }$, and the cost function, ${\mathrm{\Pi }}_{RE}^d$:

$${\displaystyle \frac{\partial Q_{RE}^{\ast }}{\partial p_m}}=-{\displaystyle \frac{\rho \left[F(Q_{RE})-1\right]}{\rho \left[\frac{p_{RE}}{p_r-v}\left[S\left(v-p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]+\left(p_r+\varphi -v+p_m+\delta \right)\right]f(Q_{RE})}}>0$$

(23)

$${\displaystyle \frac{\partial {\mathrm{\Pi }}_{RE}^d}{\partial p_m}}=\rho {\displaystyle {\int }_{Q_{RE}}^U\left(x-Q_{RE}\right)f(x)dx}>0$$

(24)

Thus, Proposition 6 is confirmed. As the spot purchase cost, $p_m$, for post-disaster emergency supplies increases, the cost of buying on the spot becomes higher. To avoid these high spot purchase costs, the government may choose to increase its reserves to ensure there is a sufficient supply of materials available in the event of a disaster, without needing to pay higher spot prices. While increasing reserves can reduce dependence on the spot market, storing reserves also incurs costs. These include storage, upkeep, and management expenses. As $p_m$ increases, indicating higher prices on the spot market, the government may increase its reserves to avoid future high purchase costs. However, increasing reserves also raises the government’s reserve costs, and thus, the overall cost function, ${\mathrm{\Pi }}_{RE}^d$, for the government will increase with $p_m$. □

Proposition 7. 

The inherent characteristics of supplies, including their urgency and the difficulty of storage, will impact the government’s optimal physical reserve quantity, $Q_{RE}^{\ast }$, and the government’s expected cost function, ${\mathrm{\Pi }}_{RE}^d$, under a “secondary platform” model enabled by timestamping. Specifically, when the cost adjusted for urgency, $\delta$, increases and the cost adjusted for storage difficulty, $\varphi$, decreases, the government’s optimal physical reserve quantity, $Q_{RE}^{\ast }$, will increase. When both costs ($\delta$ and $\varphi$) increase, the government’s overall cost, ${\mathrm{\Pi }}_{RE}^d$, will also increase.

Proof of Proposition 7. 

First, verify the relationship between the cost adjusted for urgency, $\delta$, and the government’s optimal physical reserve quantity, $Q_{RE}^{\ast }$, and expected cost, ${\mathrm{\Pi }}_{RE}^d$:

$${\displaystyle \frac{\partial Q_{RE}^{\ast }}{\partial \delta }}=-{\displaystyle \frac{\rho \left[F(Q_{RE})-1\right]}{\rho \left[\frac{p_{RE}}{p_r-v}\left[S\left(v-p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]+\left(p_r+\varphi -v+p_m+\delta \right)\right]f(Q_{RE})}}>0$$

(25)

$${\displaystyle \frac{\partial {\mathrm{\Pi }}_{RE}^d}{\partial \delta }}=\rho {\displaystyle {\int }_{Q_{RE}}^U\left(x-Q_{RE}\right)f(x)dx}>0$$

(26)

Similarly, verify the relationship between the cost adjusted for storage difficulty, $\delta$, $Q_{RE}^{\ast }$ and ${\mathrm{\Pi }}_{RE}^d$:

$${\displaystyle \frac{\partial Q_{RE}^{\ast }}{\partial \varphi }}=-{\displaystyle \frac{\rho F(Q_{RE})+\left(1-\rho \right)}{\rho \left[\frac{p_{RE}}{p_r-v}\left[S\left(v-p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]+\left(p_r+\varphi -v+p_m+\delta \right)\right]f(Q_{RE})}}<0$$

(27)

$${\displaystyle \frac{\partial {\mathrm{\Pi }}_{RE}^d}{\partial \varphi }}=\left(1-\rho \right)Q_{RE}+\rho {\displaystyle {\int }_0^{Q_{RE}}\left(Q_{RE}-x\right)f(x)dx}>0$$

(28)

Based on the results above, Proposition 7 is proven. When the cost adjusted for urgency, $\delta$, increases, it implies that the absence of these emergency supplies could lead to higher losses. To avoid these additional losses, the government may choose to increase the reserves of these supplies to ensure they can meet the demand promptly in the event of a disaster. Some supplies may be difficult to store, possibly due to their perishability, special storage conditions, or other reasons. When the cost adjusted for storage difficulty, $\varphi$, decreases, it means that storing these supplies becomes relatively easier or less costly. Therefore, the government may choose to increase the reserves of these supplies because it is more economical compared to the past. The urgency and difficulty of storing supplies are both cost-related: when the costs adjusted for urgency and storage difficulty ($\delta$ and $\varphi$) increase, it means the cost of lacking these supplies or storing them is also increasing. Thus, the overall cost for the government will also increase. □

4.2. Profit Function of Second-Hand Platforms

4.2.1. Profit Function of the Second-Hand Platform in the Absence of Disasters

At the beginning of the agreement period, the government needs to pre-stock relief supplies in quantity, $Q_{RE}$. If no disasters occur during the entire agreement period, the government will, at the end of the period, consign some of the supplies to a second-hand platform according to the ‘Second-hand Platform Disposal’ intention parameter: ${\omega }_{RE}=p_{RE}/(p_r-v)$. The consignment price is $p_{RE}$, and the success rate of consignment is $S$, which is related to the average success rate, $S_{avg}$, during the past sales cycles of the platform and the traceability index, $G$, of the relief supplies, represented as $S=S_{\mathrm{avg}}\left(1+\mu (G-0.5)\right)$. The residual value of the unsold relief supplies is $v$, and the cost of relief supplies consigned based on the timestamp by the platform is $c_{RE}$. The second-hand platform charges a commission, $\lambda$, on the government’s sales revenue and the residual value. Based on the above analysis, the profit function for consigning emergency supplies on the second-hand platform during the agreement period without disasters, enabled by the timestamp, is as follows:

$${\mathrm{\Pi }}_{RE}^{s_1}=\lambda S{\displaystyle \frac{p_{RE}}{p_r-v}}{Q}_{RE}{p}_{RE}+\lambda \left(1-S\right){\displaystyle \frac{p_{RE}}{p_r-v}}{Q}_{RE}v-{\displaystyle \frac{p_{RE}}{p_r-v}}{Q}_{RE}{c}_{RE}$$

(29)

$\lambda S{p}_{RE}/(p_r-v)Q_{RE}{p}_{RE}$ is the commission earned from successful consignment sales of emergency supplies needing rotation provided by the government on the second-hand platform. $\lambda \left(1-S\right)p_{RE}/(p_r-v)Q_{RE}v$ is the commission for handling the residual value of unsold emergency supplies needing rotation provided by the government, managed by the second-hand platform. $p_{RE}/(p_r-v)Q_{RE}{c}_{RE}$ represents the fixed costs incurred by the second-hand platform based on blockchain technology to attempt to sell these supplies, including the cost of using blockchain technology. The following formula is derived through simplification:

$${\mathrm{\Pi }}_{RE}^{s_1}=Q{\displaystyle \frac{p_{RE}}{p_r-v}}\left[\lambda S\left(p_{RE}-v\right)+\left(\lambda v-c_{RE}\right)\right]$$

(30)

4.2.2. Profit Function of the Second-Hand Platform in the Event of a Disaster

If a disaster occurs during the agreement period, there will only be leftover emergency supplies from the government reserves if $0\le x<Q_{RE}$. In this case, the government may opt to consign the supplies for rotation through a ‘second-hand platform’ that incorporates blockchain technology. At this point, the profit function for the second-hand platform is as follows:

$$\begin{array}{cc}\hfill {\mathrm{\Pi }}_{RE}^{s_2}& =\lambda S{\displaystyle \frac{p_{RE}}{p_r-v}}\left(Q_{RE}-x\right)p_{RE}+\lambda \left(1-S\right){\displaystyle \frac{p_{RE}}{p_r-v}}\left(Q_{RE}-x\right)v\hfill \\ & -{\displaystyle \frac{p_{RE}}{p_r-v}}\left(Q_{RE}-x\right)c_{RE}\end{array}$$

(31)

Similarly, the profit function structure for the “second-hand platform” in this scenario is similar to that in the scenario where no disaster occurred. However, within this demand constraint ($0\le x<Q_{RE}$), the quantity of supplies the government needs to rotate is $Q_{RE}-x$. Through formula simplification, the following result is obtained:

$${\mathrm{\Pi }}_{RE}^{s_2}={\displaystyle \frac{p_{RE}}{p_r-v}}\left(Q_{RE}-x\right)\left[\lambda S\left(p_{RE}-v\right)+\lambda v-c_{RE}\right]$$

(32)

Based on the above profit analysis, considering the probability, $\rho$, of a disaster occurring within the agreement period, the profit function for the second-hand platform responsible for resale under the consignment strategy with blockchain-integrated ‘second-hand platform’ is as follows. Moreover, the resale success rate is influenced by the platform’s average success rate and the traceability index of supplies developed using blockchain technology, namely: $S=S_{\mathrm{avg}}\left(1+\mu (G-0.5)\right)$.

$$\begin{array}{cc}\hfill {\mathrm{\Pi }}_{RE}^s& =\left(1-\rho \right)\left[Q_{RE}{\displaystyle \frac{p_{RE}}{p_r-v}}\left[\lambda S\left(p_{RE}-v\right)+\left(\lambda v-c_{RE}\right)\right]\right]\hfill \\ & +\rho {\displaystyle {\int }_0^{Q_{RE}}\left[\frac{p_{RE}}{p_r-v}\left(Q_{RE}-x\right)\left[\lambda S\left(p_{RE}-v\right)+\lambda v-c_{RE}\right]\right]f(x)dx}\end{array}$$

(33)

4.3. Model of Supply Chain Coordination

4.3.1. Profit Model for Supply Chain Coordination

Under the consignment model of the “second-hand platform” that incorporates blockchain, the government’s cost function is ${\mathrm{\Pi }}_{RE}^d$, and the profit function for the supply-side enterprise is ${\mathrm{\Pi }}_{RE}^s$. Therefore, when $-{\mathrm{\Pi }}_{RE}^d{|}_{Q_{RE}=Q_{RE}^{\ast }}+{\mathrm{\Pi }}_{RE}^s{|}_{Q_{RE}=Q_{RE}^{\ast }}={\mathrm{\Pi }}_{RE}^{sc}{|}_{Q_{RE}^{sc}=Q_{RE}^{sc*}}$, the supply chain reaches a coordinated state. The profit formula for supply chain coordination is as follows:

$$\begin{array}{cc}\hfill {\mathrm{\Pi }}_{RE}^{sc}& =\left(1-\rho \right)\left[Q_{RE}{\displaystyle \frac{p_{RE}}{p_r-v}}\left(S\left(p_{RE}-v\right)-c_{RE}\right)-Q_{RE}\left[2p_r+\varphi -v\right]\right]\hfill \\ & +\rho {\displaystyle {\int }_0^{Q_{RE}}\left[\begin{array}{c}\frac{p_{RE}}{p_r-v}\left(Q_{RE}-x\right)\left[S\left(p_{RE}-v\right)-c_{RE}\right]\\ -\left(Q_{RE}-x\right)\left[\varphi +p_r-v\right]-p_r{Q}_{RE}\end{array}\right]f(x)dx}\hfill \\ & +\rho {\displaystyle {\int }_{Q_{RE}}^U\left[-Q_{RE}\left(p_r-p_m-\delta \right)-x\left(p_m+\delta \right)\right]f(x)dx}\hfill \end{array}$$

(34)

4.3.2. Analysis of Model Results

Proposition 8. 

Under the consignment strategy of the blockchain second-hand platform, when $S=(c_{RE}-\lambda v)/\lambda (p_{RE}-v)$, the supply chain reaches a coordinated state.

Proof of Proposition 8. 

First, solve for the first derivative of Formula (34) with respect to $Q_{RE}^{sc}$:

$$\begin{array}{cc}\hfill {\displaystyle \frac{\partial {\mathrm{\Pi }}_{RE}^{sc}}{\partial Q_{RE}^{sc}}}& =\left(1-\rho \right)\left[{\displaystyle \frac{p_{RE}}{p_r-v}}\left(S\left(p_{RE}-v\right)-c_{RE}\right)-\left[2p_r+\varphi -v\right]\right]\hfill \\ & +\rho \left[{\displaystyle \frac{p_{RE}}{p_r-v}}\left[S\left(p_{RE}-v\right)-c_{RE}\right]-\left(\varphi +p_r-v+p_m+\delta \right)\right]F(Q_{RE})\hfill \\ & +\rho \left(p_m-p_r+\delta \right)\hfill \end{array}$$

(35)

Further, solve for the second derivative of Formula (35) with respect to $Q_{RE}^{sc}$:

$${\displaystyle \frac{{\partial }^2{\mathrm{\Pi }}_{RE}^{sc}}{\partial {(Q_{RE}^{sc})}^2}}=\rho \left[{\displaystyle \frac{p_{RE}}{p_r-v}}\left[S\left(p_{RE}-v\right)-c_{RE}\right]-\left(\varphi +p_r-v+p_m+\delta \right)\right]f(Q_{RE})<0$$

(36)

From Formula (36), it is known that under a coordinated state, the second derivative of the profit function with respect to $Q_{RE}^{sc}$ is less than 0, indicating that the profit function is convex at this point. Therefore, there exists an optimal physical reserve quantity, $Q_{RE}^{sc*}$, that maximizes the profit of the supply chain. At this point, by setting the first derivative of the profit function with respect to $Q_{RE}^{sc*}$ equal to zero, solve for the optimal reserve quantity, $Q_{RE}^{sc*}$, as shown below:

$$Q_{RE}^{sc*}=F^{-1}\left({\displaystyle \frac{\rho -1}{\rho }}-{\displaystyle \frac{\left(p_m-p_r+\delta \right)}{\rho \left[\frac{p_{RE}}{p_r-v}\left[S\left(p_{RE}-v\right)-c_{RE}\right]-\varphi -p_r+v-p_m-\delta \right]}}\right)$$

(37)

When $Q_{RE}^{sc*}=Q_{RE}^{\ast }$, the supply chain reaches a coordinated state, satisfying the following formula condition:

$$\begin{array}{l}{\displaystyle \frac{\left(p_m-p_r+\delta \right)}{\rho \left[\frac{p_{RE}}{p_r-v}\left[S\left(p_{RE}-v\right)\left(1-\lambda \right)-\lambda v\right]-\varphi -p_r+v-p_m-\delta \right]}}=\\ {\displaystyle \frac{\left(p_m-p_r+\delta \right)}{\rho \left[\frac{p_{RE}}{p_r-v}\left[S\left(p_{RE}-v\right)-c_{RE}\right]-\varphi -p_r+v-p_m-\delta \right]}}\end{array}$$

(38)

Simplified as follows:

$$S={\displaystyle \frac{c_{RE}-\lambda v}{\lambda \left(p_{RE}-v\right)}}$$

(39)

Therefore, Proposition 8 is proven. □

Proposition 9. 

Under the consignment strategy of the blockchain second-hand platform, when the supply chain is in a coordinated state, the government’s optimal physical reserve quantity, $Q_{RE}^{sc\ast }$, and the supply chain’s optimal profit function, ${\mathrm{\Pi }}_{RE}^{sc}$, are not affected by the second-hand platform’s commission rate, $\lambda$. However, they are influenced by the cost, $c_{RE}$, of consigned goods based on the timestamp by the second-hand platform. Specifically, as the consignment unit cost, $c_{RE}$, of the second-hand platform increases, the optimal physical reserve quantity, $Q_{RE}^{sc\ast }$, under supply chain coordination decreases; similarly, the optimal profit function, ${\mathrm{\Pi }}_{RE}^{sc}$, of the supply chain also decreases.

Proof of Proposition 9. 

Considering the consignment model of the “second-hand platform” with blockchain technology, the government’s cost function, ${\mathrm{\Pi }}_{RE}^d$, and the profit function, ${\mathrm{\Pi }}_{RE}^s$, of the supply-side enterprise have terms related to the second-hand platform’s commission rate, $\lambda$, that cancel each other out. Therefore, in the optimal physical reserve quantity, $Q_{RE}^{sc*}$, and the optimal profit function, ${\mathrm{\Pi }}_{RE}^{sc}$, under supply chain coordination, there are no terms related to $\lambda$. Next, to further verify the impact of the consignment unit cost, $c_{RE}$, of emergency supplies on $Q_{RE}^{sc*}$ and ${\mathrm{\Pi }}_{RE}^{sc}$, first solve for the first derivative of $Q_{RE}^{sc*}$ with respect to $c_{RE}$:

$${\displaystyle \frac{\partial Q_{RE}^{sc}}{\partial c_{RE}}}=-{\displaystyle \frac{\frac{p_{RE}}{p_r-v}\left[\rho \left(1-F(Q_{RE})\right)-1\right]}{\rho \left[\frac{p_{RE}}{p_r-v}\left[S\left(p_{RE}-v\right)-c_{RE}\right]-\left(\varphi +p_r-v+p_m+\delta \right)\right]f(Q_{RE})}}<0$$

(40)

Then, solve for the first derivative of the supply chain’s optimal profit function, ${\mathrm{\Pi }}_{RE}^{sc}$, with respect to $c_{RE}$, obtaining:

$${\displaystyle \frac{\partial {\mathrm{\Pi }}_{RE}^{sc}}{\partial c_{RE}}}=-\left(1-\rho \right)Q_{RE}{\displaystyle \frac{p_{RE}}{p_r-v}}-\rho {\displaystyle \frac{p_{RE}}{p_r-v}}{\displaystyle {\int }_0^{Q_{RE}}\left(Q_{RE}-x\right)f(x)dx}<0$$

(41)

Based on the above results, Proposition 9 is verified. In this “second-hand platform” strategy, the higher the unit cost, $c_{RE}$, of consigning emergency supplies, the higher the costs the government incurs when choosing the ‘second-hand platform’ to handle products that need rotation. Considering the limitation of costs, the optimal physical reserve quantity, $Q_{RE}^{sc*}$, under supply chain coordination will also decrease. Similarly, the rise in costs under this model choice will lead to an increase in the costs incurred by the supply chain, thereby reducing the expected profit, F, of the supply chain. □

5. Numerical Examples

To further investigate the impact of the blockchain ‘second-hand platform’ consignment strategy on government inventory and material rotation, we chose the “7.20” major rainstorm event of 2021 in Zhengzhou, Henan Province, China, as a subject for numerical examples.

5.1. Parameter Settings

This rainstorm and flooding disaster in Henan Province had a severe impact on Zhengzhou and its surrounding areas, resulting in considerable loss of life and property. Effectively managing this crisis necessitated prioritizing the allocation of substantial numbers of rescue personnel and supplies to Zhengzhou. In this section, we randomly selected emergency-type, easy-to-store supplies, specifically, pharmaceuticals and life jackets, designated by the subscripts A and B, respectively. The main parameters for this study were determined by examining the prices of these supplies before and after the disaster and by integrating parameter settings from relevant emergency management literature, as detailed in

Table 2. Model parameter assignment.

Parameters	Supply Names		Parameters	Supply Names
	Pharmaceuticals (Packs)	Life Jackets (Pieces)		Pharmaceuticals (Packs)	Life Jackets (Pieces)
Basic Parameters
$x$	$x\sim U\left(0,100000\right)$	$x\sim U\left(0,60000\right)$	$\varphi$	29.394	8.304
$\alpha$	0.9871	0.7231	$\rho$	0.5	0.5
${\delta }^{\prime }$	100	100	$p_r$	258	169
$\delta$	98.71	72.31	$c_p$	178	119
$\beta$	0.5101	0.7924	$p_m$	588	398
${\varphi }^{\prime }$	60	40
Parameters related to the consignment strategy of the ‘second-hand platform’ considering blockchain factors
$p_{RE}$	189	109	$S$	0.826	0.826
$c_{RE}$	5	5	$v$	40	10
$S_{avg}$	0.7	0.7	$\lambda$	0.05	0.05
$G$	0.8	0.8	${\omega }_{RE}$	0.867	0.689
$\mu$	0.6	0.6

.

5.2. Optimal Decision and Sensitivity Analysis for Second-Hand Platform Consignment

Figure 3 shows the impact of the probability of a disaster on the government’s optimal physical reserve quantity, $Q_{RE}^{\ast }$, under the consignment strategy of the ‘second-hand platform’ with blockchain considerations. From the figure, it is evident that the optimal reserve quantities of materials A and B for the government increased with the rising probability of a disaster. The results presented in Figure 3 are consistent with those shown in Proposition 2.

Figure 4 shows the impact of the second-hand platform’s sales success rate, $S$, on the government’s optimal physical reserve quantity, $Q_{RE}^{\ast }$, under the “second-hand platform” consignment strategy. From the figure, it is evident that the optimal reserve quantities of supplies A and B for the government increased with the rising success rate, $S$, of the second-hand platform. The results presented in Figure 4 are consistent with those shown in Proposition 3.

Figure 5 illustrates the impact of the selling price, $p_{RE}$, on the government’s optimal physical reserve quantity, $Q_{RE}^{\ast }$, under the “second-hand platform” consignment strategy. The figure shows that the optimal reserve quantities for supplies increased with the rise in the second-hand platform’s selling price, $p_{RE}$. At this point, $S\left(v-2p_{RE}\right)\left(1-\lambda \right)+\lambda v\le 0$.

Figure 6 depicts the impact of procurement costs on the government’s optimal physical reserve quantity, $Q_{RE}^{\ast }$, under the “second-hand platform” consignment strategy. These procurement costs include post-disaster spot procurement costs, $p_m$, and the regular procurement prices, $p_r$, of emergency supplies. Using the probability of disaster occurrence as the x-axis, the figure reveals that the optimal reserve quantities of materials A and B increased with the rise in post-disaster spot procurement costs. At this time, the parameter setting satisfied $-p_{RE}/{\left(p_r-v\right)}^2\left[S\left(v-p_{RE}\right)\left(1-\lambda \right)+\lambda v\right]+1>-1/\left[1-\rho +\rho F(Q)\right]$; thus, the optimal reserve quantities of materials A and B decreased as the prices of regularly procured emergency supplies increased.

Figure 7 illustrates the impact of storage loss costs on the government’s optimal physical reserve quantity, $Q_{RE}^{\ast }$, under the ‘second-hand platform’ consignment strategy with blockchain consideration. Storage loss costs include the difficulty of storing the supplies themselves, denoted as $\varphi$, and the urgency of the supplies, denoted as $\delta$. From Figure 7, it can be seen that the optimal reserve quantities of materials increased with the difficulty of storing the materials themselves and decreased with the increase in the urgency of the materials. The results presented in the figure are consistent with those shown in Proposition 7.

Let the optimal material reserve quantity before coordination be $Q_d^{RE}$, and the optimal reserve quantity after supply chain coordination be $Q_{sc}^{RE}$. Figure 8 shows the changes in the optimal physical reserve quantity, $Q_{RE}^{\ast }$, before and after supply chain coordination under the “second-hand platform” consignment strategy considering blockchain. The figure summarizes that after supply chain coordination, the government’s optimal physical reserve quantities, $Q_{RE}^{\ast }$, for materials A and B showed different trends, indicating that the coordinated supply chain does not necessarily increase the decision on optimal physical reserve quantities of emergency supplies.

The profit of the supply chain after coordination is denoted as ${\mathrm{\Pi }}_{sc}^{RE}$. Figure 9 displays how the profit, ${\mathrm{\Pi }}_{sc}^{RE}$, of the supply chain, considering the ‘second-hand platform’ consignment strategy with blockchain, changed with the probability of disaster occurrence. After achieving supply chain coordination, the profit, ${\mathrm{\Pi }}_{sc}^{RE}$, of the supply chain decreased with the increase in the probability of disasters, whether for reserve materials A or B. This decrease in profit occurred because achieving supply chain coordination led to an increase in the optimal reserve quantities, which in turn increased the related costs for the government, thus reducing the profit of the supply chain.

6. Conclusions and Future Works

6.1. Conclusions

This paper focused on government reserves and conducted a comprehensive study on the optimization of emergency relief supplies. Recognizing the unique perishability of rescue materials, the study proposed a material rotation model under a ‘second-hand platform’ consignment arrangement, enhanced by the introduction of blockchain technology. We methodically derived the conditions for the government’s optimal reserve decisions and analyzed how these decisions, as well as the impacts on profits and costs, are influenced by various parameters. Simulation and comparative analysis have led to the following conclusions.

The relationship between government reserves and cost functions revealed that the government’s cost function is convex, with an optimal physical reserve level that minimizes costs. A critical threshold exists for the second-hand platform selling price: when the actual selling price exceeded this threshold, the optimal reserve level increased while costs decreased. Conversely, if the price was below the threshold, the reserve level decreased and costs rose. This finding provides a theoretical basis for governments to formulate more economical reserve strategies.

Various parameters impact reserve levels. The determination of the government’s optimal reserve level was positively influenced by the probability of disasters and the success rate of sales. As these parameters increased, the government was more inclined to augment reserves to sell at higher prices on the second-hand platform, thus enhancing revenue while reducing the costs associated with excessive reserves. Additionally, the government’s optimal reserve strategy was adjusted in response to increases in purchase prices or changes in costs due to the urgency and difficulty of storage.

Blockchain technology has a significant impact by enhancing the traceability of supplies, boosting government confidence in successfully selling these supplies on the second-hand E-commerce platform, which leads to an increase in stored reserves. Under the blockchain “second-hand platform” consignment strategy, supply chain coordination was unaffected by transaction fees but was primarily influenced by the timestamp-based consignment costs of the platform. The study indicated that higher costs lead to reduced optimal reserve levels and lower supply chain profits. These findings optimize emergency supplies’ management strategies and offer new insights into the application of blockchain technology to enhance the efficiency of supply chain coordination.

6.2. Limitations and Future Directions

In summary, this research advances government decision-making regarding emergency supplies reserves and introduced innovative approaches for managing supply chains within a second-hand platform model. Despite its contributions, the study presented certain limitations that should be acknowledged. One critical limitation is the research’s reliance on assumptions that may not hold in real-world emergency scenarios. These include the use of second-hand E-commerce platforms for supply procurement and the implementation of traceability mechanisms through blockchain technology, which may not be realistic or currently feasible due to various practical constraints. Additionally, while this study addressed the storage and rotation of emergency supplies, it did not fully consider potential supply chain variabilities, such as disruptions or regulatory changes, which are essential for effective disaster response. Future studies should explore these impacts on reserve strategies more comprehensively. Furthermore, the research primarily focused on isolated government reserve strategies, and future investigations should expand to include diversified approaches, such as cross-jurisdictional collaborations and multi-level network reserves. There is also a significant opportunity to integrate advanced technologies, such as artificial intelligence, to enhance management and responsiveness. Overall, more research is needed to develop a comprehensive analytical framework that includes these broader considerations for emergency supply reserves.