61 Advances in Production Engineering & Management ISSN 1854-6250 Volume 20 | Number 1 | March 2025 | pp 61–74 Journal home: apem-journal.org https://doi.org/10.14743/apem2025.1.527 Original scientific pape Independent vs. collaborative blockchain Research and Development: Operational decisions in food supply chains Kang, Y.X. a,b , Feng, J.Y. a,c,* , Zhang, W.J. a a School of Economics and Management, Beijing Jiaotong University, Beijing, P.R. China b China Center for Information Industry Development, Beijing, P.R. China c Ministry of Industry and lnformation Technology, Equipment Industry Development Center, Beijing, P.R. China A B S T R A C T A R T I C L E I N F O As blockchain increasingly demonstrates advantages in enhancing consumer trust and reducing collaborative production costs in food supply chains, more food companies are developing blockchain-based supply chain management platforms. However, in a complex and competitive supply chain environment, food companies face critical operational management challenges in selecting appropriate blockchain R&D approaches and determining optimal R&D levels. This study examines two competing food companies deciding on their optimal food production and blockchain R&D levels. We first established a benchmark model without blockchain adoption. Then, we constructed supply chain opera- tion models for both independent and collaborative blockchain R&D scenarios. By comparing equilibrium decisions across different models, we derived the optimal blockchain R&D model and operational strategies in food supply chains. Furthermore, we extended our analysis to consider asymmetric food substitution scenarios. Our findings revealed that independent blockchain R&D tends to increase equilibrium food production and is more suitable for pre- mium food supply chains. Conversely, collaborative blockchain R&D signifi- cantly enhanced overall supply chain profitability. As spillover effects increase, food companies are likely to favor independent blockchain R&D to achieve higher R&D levels and stronger market competitiveness. Additionally, we demonstrated that blockchain R&D levels are influenced by food substitutabil- ity and quality credibility. Keywords: Blockchain adoption; Food supply chains; Game theory; Competitive collaboration; Operation strategy; Spillover effects *Corresponding author: fengjiayi@eidc.org.cn (Feng, J.Y.) Article history: Received 1 October 2024 Revised 31 March 2025 Accepted 7 April 2025 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction With the increasing popularity and advancement of blockchain technology, stakeholders in the food supply chain have begun to recognize its value. Food manufacturers, retailers, and blockchain firms are actively engaging in blockchain R&D aimed at enhancing the management and oversight of information across various stages of food production, processing, storage, transportation, and distribution. The primary objective of these initiatives is to establish a decentralized, tamper- proof, and transparent system that improves the integrity and efficiency of the food supply chain. The benefits of blockchain for the food supply chain are increasingly apparent. For consumers, the adoption of blockchain by food companies enhances engagement by showcasing robust food safety systems, improving brand perception, and fostering confidence in product quality. This in- creased transparency can stimulate consumer demand by allowing individuals to make more in- formed purchasing decisions. For food companies, a blockchain network facilitates collaboration between upstream and downstream stakeholders within the supply chain. A distributed ledger maintains comprehensive information on food raw materials, production, processing, storage, Kang, Feng, Zhang 62 Advances in Production Engineering & Management 20(1) 2025 logistics, supplier transfers, and retail operations, thereby enabling mutual oversight. Enhanced information sharing across different stages allows companies to quickly assess overall supply chain performance, improve operational efficiency, and make informed decisions while minimiz- ing communication costs. For example, β€œBlockchain + Vegetables” innovation project in Weifang City, where the Yukesong Digital Agriculture Industry Park developed a digital agricultural man- agement platform that integrates vegetable planting, logistics, storage, processing, and sales. This initiative not only enhanced the quality of agricultural products within the park but also achieved over a 10 % reduction in water and fertilizer usage and a labor cost reduction exceeding 15 %. Additionally, blockchain R&D has certain positive externalities that can bring multiple benefits to the blockchain industry and society. Firstly, blockchain R&D can promote innovation and ad- vancement in blockchain technology, improving its functionality, performance, and security, thus bringing more value and benefits to the blockchain industry and society. Secondly, it can drive the standardization and normalization of blockchain technology, reducing R&D and operational costs and risks, enhancing credibility and interoperability, and thereby bringing more order and vitality to the blockchain ecosystem and food market. Thirdly, it can facilitate the integration and expan- sion of blockchain technology with other emerging information technologies such as 5G, IoT, and AI, creating an innovative "Blockchain +" model that supports the food industry in exploring new business operation models and management solutions. Given the numerous advantages of blockchain, many food companies have begun to invest in blockchain R&D. Common approaches include: (1) Independent R&D, where some food compa- nies choose to develop or customize blockchain solutions to meet their specific business needs. The advantage of independent R&D is that it allows for tailored blockchain solutions based on distinct requirements and scenarios, thereby improving system flexibility and adaptability. How- ever, it requires significant investments in human, material, and financial resources and presents challenges related to immature technology and a lack of standards. (2) Collaborative R&D, where some food companies choose to develop and utilize blockchain solutions in partnership with other organizations to facilitate cross-organization data sharing and collaboration. For instance, global food retailers such as Walmart and NestlΓ© have partnered with IBM to develop a blockchain-based service system, establishing a global food safety alliance aimed at enhancing the efficiency and transparency of the food supply chain. The advantage of collaborative R&D lies in leveraging the technology and resources of partners, which reduces development and operational costs and risks while increasing system credibility and interoperability. However, it necessitates the coordination of interests and the resolution of issues related to data privacy and security. Moreover, the R&D costs represent a major obstacle for food companies in adopting blockchain services. For example, in terms of software, blockchain adoption requires selecting or developing an appropriate blockchain platform, writing smart contracts, and integrating data verification functions. This process necessitates substantial investments in human, material, and financial re- sources while facing challenges related to immature technology and a lack of standardization. Ad- ditionally, blockchain solutions must integrate with the existing systems of brand owners, ad- dressing discrepancies in system architecture, data standards, and data exchange protocols, which adds to the complexity and overall cost of R&D. In terms of hardware, blockchain solutions need to be deployed on servers, networks, and storage devices, requiring investments in equip- ment, physical space, and considerations of performance, security, and stability. Furthermore, the adoption of blockchain solutions necessitates the use of coding and reading devices for processing food information, which involves purchasing or leasing the necessary equipment while consider- ing factors such as cost, efficiency, and compatibility. This paper explores the issues related to the supply chain operation management of food companies in the context of blockchain R&D and dis- cusses the following questions: (1) In the highly competitive food industry, what motivates members of the food supply chain to conduct blockchain R&D? Additionally, how does blockchain impact operational deci- sions within the food supply chain? (2) When comparing blockchain independent R&D to collaborative R&D, which model is more advantageous for operational decisions? Furthermore, how do operational decisions in the food supply chain differ between two R&D scenarios? Independent vs. collaborative blockchain Research and Development: Operational decisions in food supply chains Advances in Production Engineering & Management 20(1) 2025 63 (3) In a more complex food market environment (e.g., the asymmetric substitute foods), will the choice of blockchain R&D model change? To the best of our knowledge, this paper is one of the pioneering analytical operations manage- ments (OM) studies that explore operational decision-making strategies related to blockchain R&D, providing theoretical insights for food companies in selecting appropriate blockchain R&D models. Addressing the issue of poor information communication within food supply chains, we compre- hensively consider the advantages of blockchain platforms in enhancing operational efficiency and reducing production costs. We conduct a comparative analysis of the operational decision-making differences between independent and collaborative R&D blockchain platform models and propose optimal choices for blockchain R&D models at different stages of development. We organize the paper as follows. Section 2 provides a comprehensive review of related studies to identify gaps in the literature and appropriately position our contribution. In Section 3, we de- fine the problem, outline its assumptions, and develop the model. Section 4 analyzes the value of blockchain R&D in the food supply chain. Section 5 further explores operational decisions for food supply chains under different Blockchain R&D models based on the context of asymmetric substi- tute foods and provide targeted management insights. 2. Literature review 2.1 Blockchain in supply chains Numerous investigations have explored the potential advantages of distributed ledger technology for various sectors and enterprises within supply chain ecosystems [1, 2]. The implementation of this innovative technology in supply chain operations management is becoming increasingly prev- alent. For instance, it has been applied to enhance supply chain transparency and verify product authenticity [3-6]. Furthermore, it has demonstrated its capacity to promote supply chain sustain- ability [7-9] and even revolutionize lean manufacturing practices within supply chains [10, 11]. Notably, the body of research examining the integration of distributed ledger technology with food supply chain management continues to expand rapidly. The application of distributed ledger systems in supply chain management has seen a signifi- cant surge in interest. Numerous researchers have employed diverse methodologies to investigate the potential implementation of this technology in supply chain operations. For instance, Wu et al. took an analytical approach to examine strategies for adopting a distributed ledger technology system (DLTS) in fresh product supply chains (FPSC). They compared scenarios without this tech- nology to three different situations where various FPSC members led the DLTS implementation. Their research yielded optimal conditions for DLTS deployment in FPSC and proposed a two-part tariff contract to coordinate DLTS construction [12]. Bumblauskas et al. utilized a case study ap- proach to investigate the deployment of this technology in egg distribution. Their findings demon- strated how it can enhance accuracy and transparency in product movement throughout supply chains [13]. Kamble et al. adopted a hybrid methodology, combining Interpretive Structural Mod- eling and Decision-Making Trial and Evaluation Laboratory, to explore strategies for implement- ing distributed ledger systems in agricultural supply chains, with a focus on ensuring food safety and sustainability [14]. Wang et al. has examined blockchain's impact on pricing strategies in dual- channel supply chains, revealing how this technology incentivizes dynamic pricing adjustments across sales periods while accounting for strategic consumer behavior [15]. As the advantages of distributed ledger technology become increasingly apparent, researchers have begun to delve into specific operational challenges within this framework. For instance, Mangla et al. utilized system dynamics modeling to examine the implementation of distributed ledger tech- nology in a sustainable dairy supply chain. This study showcased how technology could be lever- aged to address sustainability concerns in a complex, perishable goods supply chain [16]. In the context of food supply networks, Rogerson and Parry employed case study methodologies to em- pirically demonstrate the capacity of distributed ledger systems to enhance supply chain visibility. Their research highlighted the transformative potential of this technology in improving transpar- ency across the entire supply chain [17]. Taking a different approach, Behnke and Janssen conducted Kang, Feng, Zhang 64 Advances in Production Engineering & Management 20(1) 2025 an empirical investigation into the requisite modifications of supply chain organizational structures and the importance of persuading supply chain participants to dismantle information silos [18]. Yang and Zhang proposed a blockchain-based production scheduling and control optimization (PSCO-PC) strategy for intelligent manufacturing. By introducing adaptive difficulty mechanisms and improving simulation model flexibility, the research addressed data throughput and consensus challenges. Experimental results validated the strategy's effectiveness in optimizing production re- source control and enhancing matching rationality in manufacturing systems [19] . Existing studies have explored blockchain technology adoption in various supply chains, pri- marily using methods like case analyses, empirical research, and interpretive structural modeling. However, game-theoretic analytical approaches remain scarce in this area. Our study differs by comparing operational decision-making between independent and collaborative blockchain R&D approaches. We also suggest optimal blockchain R&D strategies for different developmental stages. By comparing independent and collaborative blockchain R&D models, we provide theoret- ical insights that guide food companies in their strategic decision-making. Our analysis considers various factors, including food substitutability, quality credibility, and spillover effects, to deter- mine optimal R&D levels and production strategies. This holistic approach allows us to propose tailored solutions for different supply chain scenarios, contributing to the overall effectiveness of food supply chains in an increasingly competitive landscape. 2.2 Competitive collaboration in supply chain Research on competitive collaboration in supply chains has also gained significant attention. Vari- ous studies have explored different aspects of this phenomenon. For instance, an investigation into e-commerce channels examined optimal decisions and profits for online retailers and manufactur- ers across four service channel types, highlighting revenue sharing as a crucial factor [20]. In the fresh produce sector, a study on supplier competition revealed that freshness preservation efforts and retailer's information disclosure level significantly influence supply channel dynamics [21]. An- other research focused on a manufacturer's service selection between competing module suppliers, suggesting that leveraging diverse pricing and service strategies from both suppliers could be more beneficial than relying on a single superior supplier [22]. The timing of pricing and marketing deci- sions in manufacturer-led supply chains has also been analyzed. Through a series of game-theoretic models, researchers identified optimal decision timing by comparing equilibrium outcomes across different supply chain configurations [23]. Furthermore, Deng employed machine learning-en- hanced agent-based modeling to examine retailer price competition under consumer learning be- havior and supplier competition. The study utilized fuzzy logic, genetic algorithms, reinforcement learning, and swarm intelligence to simulate market dynamics. Results showed that different con- sumer learning behaviors lead to varied retailer competition patterns, while supplier price compe- tition affects the intensity of retailer price competition. The study provides a simulated market model for future research on price competition among supply chain actors [24]. In the context of blockchain application, Liu et al. investigated blockchain service provision in supply chains with downstream competition. Using game theory, they analyzed the optimal strat- egies for a manufacturer and two competing retailers. Their work explored how blockchain im- pacts market dynamics, economic outcomes, and service performance in competitive supply chain settings. These studies underscore the potential of blockchain to reshape competitive collabora- tion in modern supply chains [25]. Similarly, Song et al. examined how blockchain affects infor- mation sharing decisions among rival e-commerce sellers. Their research on a two-competitor market revealed that blockchain adoption becomes universal when consumer trust in information is low or implementation costs are minimal. This highlights how blockchain can foster collabora- tion even in competitive environments [26]. Yan et al. compared blockchain-based and traditional approaches to supply chain information coordination. They developed a three-level supply chain model incorporating retailer information sensitivity. Their study revealed that blockchain tech- nology can effectively reduce operating costs. Interestingly, they found that moderate levels of information-sensitive retailers optimize blockchain value, as extreme levels may increase privacy concerns among supply chain companies [27]. Independent vs. collaborative blockchain Research and Development: Operational decisions in food supply chains Advances in Production Engineering & Management 20(1) 2025 65 Our research builds upon previous studies by offering a comprehensive analysis of block- chain's role in food supply chains, focusing on operational efficiency and production costs. Unlike earlier work that primarily examined competitive dynamics and information disclosure, we in- vestigate the critical choice between independent and collaborative blockchain R&D approaches. This study addresses the unique challenges in food supply chains, such as consumer trust and collaborative production costs. 3. The model This paper considers the operational decision-making issues of two food companies in the context of a duopoly market. Food companies 𝑖𝑖 ( 𝑖𝑖 = 1, 2) each sell similar types of food with a certain de- gree of substitutability. As blockchain technology begins to be applied in various food segments, both companies are aware that blockchain R&D can enhance market demand potential, increase consumer trust in food quality, and reduce food production costs. The food production and sales price of company are denoted as π‘žπ‘ž 𝑖𝑖 and 𝑝𝑝 𝑖𝑖 , respectively, while the blockchain R&D effort is de- noted as 𝑠𝑠 𝑖𝑖 , the higher intensity of blockchain R&D, the more production costs the company can save, and consumer trust in the food will also increase. To improve the readability, Table 1 sum- marizes all abbreviations and definitions of important variables involved. Table 1 Notation used in this paper Notation Definition π‘žπ‘ž 𝑖𝑖 Production of food company 𝑖𝑖 𝑠𝑠 𝑖𝑖 The blockchain R&D effort level(the level of blockchain services) 𝑝𝑝 𝑖𝑖 The sales price of food company 𝑖𝑖 πœ‹πœ‹ 𝑖𝑖 The profit of food company 𝑖𝑖 𝑄𝑄 Total production of the food supply chain πœƒπœƒ Market demand potential under blockchain adoption 𝛼𝛼 Market demand potential without blockchain adoption 𝛽𝛽 Food substitutability coefficient 𝑐𝑐 Unit production cost of food companies without blockchain adoption 𝐢𝐢 𝑖𝑖 Total production cost of food companies with blockchain adoption 𝛾𝛾 The coefficient of blockchain R&D spillover effect π‘₯π‘₯ Food quality 𝑑𝑑 The credibility of food’s quality 3.1 Without considering blockchain R&D As the benchmark model, we first consider the scenario where blockchain technology is con- ducted in the food supply chain. Without considering the blockchain R&D, the two food companies do not engage in collaborative R&D. Followed the previous studies [28-31], the respective inverse demand functions of can be expressed as follows: 𝑝𝑝 𝑖𝑖 𝑁𝑁𝑁𝑁 = 𝛼𝛼 βˆ’ π‘žπ‘ž 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ’ 𝛽𝛽 π‘žπ‘ž 3 βˆ’ 𝑖𝑖 𝑁𝑁𝑁𝑁 + π‘₯π‘₯ 𝑑𝑑 (1) where 𝛼𝛼 represents the market demand potential without blockchain technology. The market de- mand potential is normalized to 1 ( 𝛼𝛼 = 1). This assumption is consistent with the research hy- pothesis of Niu et al. (2021) and does not affect the main results. 𝛽𝛽 represents the food substitut- ability coefficient (0 < 𝛽𝛽 < 1); π‘₯π‘₯ denotes the food quality. Premium food typically refers to prod- ucts of superior quality, high nutritional value, and fine processing, such as organic or imported foods. Ordinary food refers to products of average quality and lower processing levels, like every- day groceries; 𝑑𝑑 represents consumer trust in food quality (0 ≀ 𝑑𝑑 < 1). When 𝑑𝑑 = 0, it indicates that consumers have no trust in the information described on food packaging and completely dis- trust the stated food quality. In this case, only consumers who are entirely insensitive to food quality will choose to purchase, deciding solely based on price. Clearly, as consumer trust in food quality increases, they will be willing to pay a higher price for the food. In the blockchain context, 𝑑𝑑 also reflects consumer adoption of verification tools - higher 𝑑𝑑 implies not only greater trust but also more consumers actively using blockchain verification, which directly enhances the market value of blockchain investment. Kang, Feng, Zhang 66 Advances in Production Engineering & Management 20(1) 2025 The profit functions for the two food companies can be expressed as follows: πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 = 𝑝𝑝 𝑖𝑖 𝑁𝑁𝑁𝑁 π‘žπ‘ž 𝑖𝑖 βˆ’ 𝑐𝑐 π‘žπ‘ž 𝑖𝑖 𝑁𝑁𝑁𝑁 = ( 𝛼𝛼 βˆ’ π‘žπ‘ž 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ’ 𝛽𝛽 π‘žπ‘ž 3 βˆ’ 𝑖𝑖 𝑁𝑁𝑁𝑁 + π‘₯π‘₯ 𝑑𝑑 βˆ’ 𝑐𝑐 ) π‘žπ‘ž 𝑖𝑖 𝑁𝑁𝑁𝑁 (2) where 𝑐𝑐 represents the unit production cost of food (0 < 𝑐𝑐 < 𝛼𝛼 + π‘₯π‘₯ 𝑑𝑑 ). Under equilibrium condi- tions, the optimal quantity for each food company and the total production of the food supply chain can be expressed as: π‘žπ‘ž 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— = 1 + 𝑑𝑑 π‘₯π‘₯ βˆ’ 𝑐𝑐 2 + 𝛽𝛽 (3) 𝑄𝑄 𝑁𝑁𝑁𝑁 βˆ— = 2(1 + 𝑑𝑑 π‘₯π‘₯ βˆ’ 𝑐𝑐 ) 2 + 𝛽𝛽 (4) The optimal profit for each food company can be expressed as: πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— = (1 βˆ’ 𝑐𝑐 + 𝑑𝑑 π‘₯π‘₯ ) 2 (2 + 𝛽𝛽 ) 2 (5) 3.2 Independent blockchain R&D When both food companies decide to develop blockchain services, firstly, the addition of block- chain technology to food products will attract more consumers, thereby increasing the potential demand for such products in the market. Secondly, because information about the entire process from production to distribution will be recorded and verified in their respective blockchain ser- vices, consumer trust in the quality and safety of the food will be strengthened. Additionally, the reduction in food production waste and improvement in production efficiency will lower the pro- duction costs for the companies. Therefore, when food companies choose to conduct blockchain R&D independently, the following applies: 𝑝𝑝 𝑖𝑖 𝑁𝑁𝑁𝑁 = πœƒπœƒ βˆ’ π‘žπ‘ž 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ’ 𝛽𝛽 π‘žπ‘ž 3 βˆ’ 𝑖𝑖 𝑁𝑁𝑁𝑁 + π‘₯π‘₯ ( 𝑑𝑑 + 𝑠𝑠 𝑖𝑖 𝑁𝑁𝑁𝑁 ) (6) 𝐢𝐢 𝑁𝑁𝑁𝑁 = οΏ½ 𝑐𝑐 βˆ’ 𝑠𝑠 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ’ 𝛾𝛾 𝑠𝑠 3 βˆ’ 𝑖𝑖 𝑁𝑁𝑁𝑁 οΏ½ π‘žπ‘ž 𝑖𝑖 𝑁𝑁𝑁𝑁 (7) πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 = 𝑝𝑝 𝑖𝑖 𝑁𝑁𝑁𝑁 π‘žπ‘ž 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ’ 𝐢𝐢 𝑁𝑁𝑁𝑁 βˆ’ 𝑠𝑠 𝑖𝑖 𝑁𝑁𝑁𝑁 2 2 (8) In the above formula, 𝛾𝛾 represents the spillover effect of blockchain R&D (0 < 𝛾𝛾 < 1). As an in- novation activity that enhances production efficiency, the blockchain R&D may have positive spill- over effects on other companies in the market that undertake similar R&D actions. For the pro- duction process, blockchain technology greatly ensures the credibility and security of food pro- duction and distribution data, and the adoption of blockchain can reduce the data verification and audit costs for both parties involved in the transaction. For the transaction process, if both food companies use smart contract features of blockchain technology to simplify and automate market transactions, the risk of transaction defaults and time costs will decrease. From an industry development perspective, blockchain R&D by any food company will drive the digital transformation of the entire industry supply chain, promoting improvements in pro- duction efficiency across the industry. Therefore, it can be inferred that the external effects of a food company's R&D activities will lower the unit production costs of its competitors. It is also worth noting that, in practice, regulatory and data-sharing constraints significantly influence the magnitude of spillover effects. In regions with relaxed regulatory environments, in- ter-firm technology exchange and data sharing are more convenient, resulting in relatively higher 𝛾𝛾 values. However, in jurisdictions with strict data protection regulations, information sharing be- tween companies faces more legal restrictions, leading to lower 𝛾𝛾 values. Thus, 𝛾𝛾 reflects not only technological knowledge diffusion but also the impact of institutional environments on collabora- tive R&D feasibility. Additionally, the relationship between R&D expenditure and returns is modeled using a quad- ratic function to reflect the diminishing returns of R&D investment. Thus, given 𝑠𝑠 𝑖𝑖 𝑁𝑁𝑁𝑁 , the equilib- rium production quantities for the two food companies can be expressed as: Independent vs. collaborative blockchain Research and Development: Operational decisions in food supply chains Advances in Production Engineering & Management 20(1) 2025 67 οΏ½ π‘žπ‘ž 1 𝑁𝑁𝑁𝑁 ( 𝑠𝑠 1 𝑁𝑁𝑁𝑁 , 𝑠𝑠 2 𝑁𝑁𝑁𝑁 ) βˆ— = πœƒπœƒ +𝑑𝑑𝑑𝑑 βˆ’ 𝑐𝑐 2 + 𝛽𝛽 + 𝑠𝑠 1 𝑁𝑁𝑁𝑁 ( 2 + 2 𝑑𝑑 βˆ’ 𝛽𝛽𝛽𝛽 ) 4 βˆ’ 𝛽𝛽 2 + 𝑠𝑠 2 𝑁𝑁𝑁𝑁 ( 2 𝛽𝛽 βˆ’ 𝛽𝛽 βˆ’ 𝑑𝑑𝛽𝛽 ) 4 βˆ’ 𝛽𝛽 2 π‘žπ‘ž 2 𝑁𝑁𝑁𝑁 ( 𝑠𝑠 1 𝑁𝑁𝑁𝑁 , 𝑠𝑠 2 𝑁𝑁𝑁𝑁 ) βˆ— = πœƒπœƒ +𝑑𝑑𝑑𝑑 βˆ’ 𝑐𝑐 2 + 𝛽𝛽 + 𝑠𝑠 1 𝑁𝑁𝑁𝑁 ( 2 𝛽𝛽 βˆ’ 𝛽𝛽 βˆ’ 𝑑𝑑𝛽𝛽 ) 4 βˆ’ 𝛽𝛽 2 + 𝑠𝑠 2 𝑁𝑁𝑁𝑁 ( 2 + 2 𝑑𝑑 βˆ’ 𝛽𝛽 𝛽𝛽 ) 4 βˆ’ 𝛽𝛽 2 (9) Based on this, the total market demand for food in the production phase can be expressed as: 𝑄𝑄 𝑁𝑁𝑁𝑁 ( 𝑠𝑠 1 𝑁𝑁𝑁𝑁 , 𝑠𝑠 2 𝑁𝑁𝑁𝑁 ) βˆ— = 2 πœƒπœƒ +𝑑𝑑𝑑𝑑 βˆ’ 𝑐𝑐 2 + 𝛽𝛽 + 𝑠𝑠 1 𝑁𝑁𝑁𝑁 ( 2 βˆ’ 𝛽𝛽 )( 1 + 𝑑𝑑 + 𝛽𝛽 ) 4 βˆ’ 𝛽𝛽 2 + 𝑠𝑠 2 𝑁𝑁𝑁𝑁 ( 2 βˆ’ 𝛽𝛽 )( 1 + 𝑑𝑑 + 𝛽𝛽 ) 4 βˆ’ 𝛽𝛽 2 = 2 𝑅𝑅 2 + 𝛽𝛽 + π‘Œπ‘Œ 2 + 𝛽𝛽 Β· 2 𝑠𝑠 𝑖𝑖 𝑁𝑁𝑁𝑁 (10) For simplicity in the formula, let π‘Œπ‘Œ = 1 + π‘₯π‘₯ + 𝛾𝛾 , which can be understood as the positive impact of the R&D spillover effect on the level of R&D; let 𝑅𝑅 = πœƒπœƒ + 𝑑𝑑 π‘₯π‘₯ βˆ’ 𝑐𝑐 , which can be understood as the marginal revenue per unit of food. In the expression for total food market demand in the produc- tion phase, the first term 2𝑅𝑅 (2 + 𝛽𝛽 ) ⁄ represents the sum of the equilibrium quantities of the two food companies without R&D; the second term π‘Œπ‘Œ (2 + 𝛽𝛽 ) ⁄ represents the positive impact factor of R&D level on total demand. The numerator reflects the impact of the R&D spillover effect, with a larger 𝛾𝛾 indicating a stronger spillover effect and thereby increasing total demand. The denomi- nator 𝛽𝛽 reflects the sensitivity of market demand to food substitutability, with a larger 𝛽𝛽 indicat- ing more intense market homogenization and thus reducing total demand. By substituting π‘žπ‘ž 1 𝑁𝑁𝑁𝑁 ( 𝑠𝑠 1 𝑁𝑁𝑁𝑁 , 𝑠𝑠 2 𝑁𝑁𝑁𝑁 ) βˆ— and π‘žπ‘ž 2 𝑁𝑁𝑁𝑁 ( 𝑠𝑠 1 𝑁𝑁𝑁𝑁 , 𝑠𝑠 2 𝑁𝑁𝑁𝑁 ) βˆ— into πœ‹πœ‹ 1 𝑁𝑁𝑁𝑁 and πœ‹πœ‹ 2 𝑁𝑁𝑁𝑁 , and calculating the sec- ond derivative of the profit expressions for the two food companies, it can be determined that maximum profit occurs when (2 + 2π‘₯π‘₯ βˆ’ 𝛽𝛽𝛾𝛾 ) (4 βˆ’ 𝛽𝛽 2 ) ⁄ < √2 2 ⁄ . Thus, the optimal R&D level for food companies under independent blockchain R&D is: 𝑠𝑠 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— = 2𝑁𝑁𝑅𝑅 𝐡𝐡 𝐡𝐡 β€² βˆ’ 2π‘π‘π‘Œπ‘Œ (11) where 𝑁𝑁 = 2 + 2π‘₯π‘₯ βˆ’ 𝛽𝛽𝛾𝛾 , which can be understood as the negative impact of the R&D spillover effect on the level of R&D; π‘π‘π‘Œπ‘Œ can represent the complementarity between the R&D levels of the two companies. When the R&D spillover effect 𝛾𝛾 is large, this value is smaller, indicating that the R&D levels of the two companies mutually enhance each other, thus increasing total demand. When 𝛾𝛾 is small, this value is larger, indicating that the R&D levels of the two companies counter- act each other, thus reducing total demand; 𝐡𝐡 = 4 βˆ’ 𝛽𝛽 2 , 𝐡𝐡 β€² = 2 + 𝛽𝛽 , and 𝐡𝐡 Β· 𝐡𝐡 β€² can be understood as the negative impact of food substitutability on the level of R&D. Under independent blockchain R&D model, the optimal food production quantities for each food company and the total food production can be expressed as: π‘žπ‘ž 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— = 𝐡𝐡𝑅𝑅 𝐡𝐡 𝐡𝐡 β€² βˆ’ 2π‘π‘π‘Œπ‘Œ (12) 𝑄𝑄 𝑁𝑁𝑁𝑁 βˆ— = 2𝐡𝐡𝑅𝑅 𝐡𝐡 𝐡𝐡 β€² βˆ’ 2π‘π‘π‘Œπ‘Œ (13) The optimal profit for each food company can be expressed as: πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 = 𝑅𝑅 2 ( 𝐡𝐡 2 βˆ’ 2 𝑁𝑁 2 ) ( 𝐡𝐡 𝐡𝐡 β€² βˆ’ 2π‘π‘π‘Œπ‘Œ ) 2 (14) 3.3 Collaborative blockchain R&D This model examines the scenario in which two food companies engage in collaborative efforts during the blockchain R&D phase. When these companies opt for cooperative R&D initiatives, the extent and sophistication of blockchain R&D are collectively determined through the combined efforts and resources of both companies, so 𝑠𝑠 𝐢𝐢 𝑅𝑅𝑁𝑁 = 𝑠𝑠 1 𝐢𝐢 𝑅𝑅𝑁𝑁 = 𝑠𝑠 2 𝐢𝐢 𝑅𝑅𝑁𝑁 . First, using the same calculation methods as in the previous section, we calculate the optimal profit for each food company. Accordingly, under blockchain R&D collaboration, the joint profit function for the two food companies can be expressed as: Kang, Feng, Zhang 68 Advances in Production Engineering & Management 20(1) 2025 πœ‹πœ‹ 𝐢𝐢 𝑅𝑅𝑁𝑁 = πœ‹πœ‹ 1 𝐢𝐢 𝑅𝑅𝑁𝑁 + πœ‹πœ‹ 2 𝐢𝐢𝑅𝑅 𝑁𝑁 (15) Accordingly, in the production phase, given 𝑠𝑠 𝐢𝐢 𝑅𝑅𝑁𝑁 , the equilibrium production quantities for the two food companies can be expressed as: π‘žπ‘ž 𝑖𝑖 𝐢𝐢𝑅𝑅 𝑁𝑁 ( 𝑠𝑠 𝐢𝐢 𝑅𝑅𝑁𝑁 ) βˆ— = 𝑅𝑅 + π‘Œπ‘Œ 𝑠𝑠 𝐢𝐢 𝑅𝑅𝑁𝑁 2 + 𝛽𝛽 = 2 𝑅𝑅 2 + 𝛽𝛽 + π‘Œπ‘Œ 2 + 𝛽𝛽 Β· 2 𝑠𝑠 𝑖𝑖 𝑁𝑁𝑁𝑁 (16) When π‘Œπ‘Œ (2 + 𝛽𝛽 ) ⁄ < 1 √2 ⁄ , the food companies achieve maximum profit. Thus, the optimal R&D level for the two food companies under independent blockchain R&D is: 𝑠𝑠 𝐢𝐢 𝑅𝑅𝑁𝑁 βˆ— = 2π‘…π‘…π‘Œπ‘Œ 𝐡𝐡 β€² 2 βˆ’ 2 π‘Œπ‘Œ 2 (17) π‘žπ‘ž 𝑖𝑖 𝐢𝐢𝑅𝑅 𝑁𝑁 βˆ— = 𝑅𝑅 𝐡𝐡 β€² 𝐡𝐡 β€² 2 βˆ’ 2 π‘Œπ‘Œ 2 (18) πœ‹πœ‹ 𝑖𝑖 𝐢𝐢 𝑅𝑅𝑁𝑁 βˆ— = 𝑅𝑅 2 𝐡𝐡 β€² 2 βˆ’ 2 π‘Œπ‘Œ 2 (19) 4. The value of blockchain R&D in food supply chain By comparing the equilibrium quantities under three scenariosβ€”no blockchain adoption, inde- pendent blockchain R&D, and collaborative blockchain R&D, the following conclusions can be drawn: Proposition 1: (1) π‘žπ‘ž 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— < π‘žπ‘ž 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— ， π‘žπ‘ž 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— < π‘žπ‘ž 𝑖𝑖 𝐢𝐢𝑅𝑅 𝑁𝑁 βˆ— ; (2) when 2𝛾𝛾 βˆ’ (1 + π‘₯π‘₯ ) 𝛽𝛽 > 0, then π‘žπ‘ž 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— < π‘žπ‘ž 𝑖𝑖 𝐢𝐢 𝑅𝑅𝑁𝑁 βˆ— ; when 2𝛾𝛾 βˆ’ (1 + π‘₯π‘₯ ) 𝛽𝛽 < 0，then π‘žπ‘ž 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— > π‘žπ‘ž 𝑖𝑖 𝐢𝐢 𝑅𝑅𝑁𝑁 βˆ— . Proposition 1 indicates that (1) The food supply chain can improve its optimal production quantity by conducting blockchain R&D. (2) The impact of the blockchain R&D model on the equi- librium production quantity of the food supply chain is influenced jointly by the blockchain R&D spillover effect ( 𝛾𝛾 ), food quality ( π‘₯π‘₯ ), and food substitutability ( 𝛽𝛽 ). To illustrate the findings of Proposition 1 more clearly, we perform calculations with assigned values for the relevant variables. Assume πœƒπœƒ = 1.2, 𝑐𝑐 = 0.8, 𝑑𝑑 = 0.9. The effect of variations in 𝛾𝛾 , π‘₯π‘₯ , and 𝛽𝛽 within their respective ranges on the difference in food supply chain production quantities is shown in Fig. 1. Firstly, by comparing the feasible region where π‘žπ‘ž 𝑖𝑖 𝐢𝐢 𝑅𝑅𝑁𝑁 βˆ— > π‘žπ‘ž 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— , it is observed that the independ- ent R&D model is more likely to achieve higher equilibrium food production quantities compared to the collaborative R&D model. Secondly, as food quality increases, the region where collaborative R&D blockchain can achieve higher food production quantities becomes increasingly constrained. This suggests that high- quality food is typically a key product for food companies with high commercial value. If the two food companies collaborate on blockchain R&D, the sales data and flow information of high-qual- ity food are likely to be acquired by competitors, leading to a gradual reduction in their optimal production quantity. However, if the two food companies develop blockchain R&D independently, each can maintain its own data and information, better protect its commercial secrets and com- petitive advantage, and adjust its production and sales strategies more flexibly to meet consumer demands and preferences, thereby increasing its market share. Independent vs. collaborative blockchain Research and Development: Operational decisions in food supply chains Advances in Production Engineering & Management 20(1) 2025 69 Fig.1 Evolution of the dominant region between π‘žπ‘ž 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— and π‘žπ‘ž 𝑖𝑖 𝐢𝐢 𝑅𝑅𝑁𝑁 βˆ— Proposition 2: (1) when πœƒπœƒ > πœƒπœƒ β€² ， πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— < πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— ; (2) when πœƒπœƒ < πœƒπœƒ β€² ， πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— > πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— ; (2) πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— < πœ‹πœ‹ 𝑖𝑖 𝐢𝐢 𝑅𝑅𝑁𝑁 βˆ— οΌŒπœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— < πœ‹πœ‹ 𝑖𝑖 𝐢𝐢 𝑅𝑅𝑁𝑁 βˆ— . Proposition 2 indicates that the adoption of blockchain does not necessarily lead to profit in- creases for members of the food supply chain. When food companies choose to independently conduct blockchain R&D, it is only more profitable for food companies to opt for independent blockchain R&D if the blockchain significantly enhances the potential demand for the food supply chain. Assuming π‘₯π‘₯ = 0.2 and keeping the other parameters constant, Fig. 2 illustrates the range of profit differences between choosing to develop and not to conduct blockchain R&D in the food supply chain. It can be observed that, firstly, under different settings of potential market demand for food, the area where πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— < πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— is always larger than the area where πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— > πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— . This suggests that, although there are instances where not conducting blockchain R&D yields higher profits, choosing independent R&D is more likely to result in greater economic benefits. Secondly, as the blockchain increases the potential market demand for food, represented by πœƒπœƒ , the feasible area for πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— < πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— expands accordingly, indicating that the economic incentive for food companies to conduct blockchain R&D also strengthens. While our model treats consumer trust 𝑑𝑑 as a con- stant parameter, in reality, trust in blockchain systems can be undermined by misinformation or security breaches. Such trust erosion would effectively reduce 𝑑𝑑 , thereby raising the profitability threshold πœƒπœƒ in Proposition 2. This means even greater market demand enhancement would be required to justify blockchain investment. For instance, a security breach that reduces 𝑑𝑑 could shift a company from the profitable region (where πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— < πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— ) to the unprofitable region, highlight- ing why maintaining blockchain integrity is crucial for sustained profitability. However, if food companies choose to collaborate on blockchain R&D, the profit level of the food supply chain can be significantly enhanced compared to the other two blockchain develop- ment models mentioned above. Thus, choosing collaborative R&D is a more economically viable operational strategy. Fig. 2 Evolution of the dominant region between πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— and πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— Proposition 3: (1) when 𝛾𝛾 < ( 1 + 𝑑𝑑 ) 𝛽𝛽 2 , 𝑠𝑠 𝑖𝑖 𝐢𝐢 𝑅𝑅𝑁𝑁 βˆ— > 𝑠𝑠 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— ; (2) when 𝛾𝛾 > ( 1 + 𝑑𝑑 ) 𝛽𝛽 2 , 𝑠𝑠 𝑖𝑖 𝐢𝐢 𝑅𝑅𝑁𝑁 βˆ— < 𝑠𝑠 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— . πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— < πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝐡𝐡 βˆ— πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— > πœ‹πœ‹ 𝑖𝑖 𝑁𝑁𝐡𝐡 βˆ— πœƒπœƒ = 1.1 𝛽𝛽 𝛾𝛾 πœƒπœƒ = 1.3 𝛽𝛽 𝛾𝛾 πœƒπœƒ = 1.5 𝛽𝛽 𝛾𝛾 Kang, Feng, Zhang 70 Advances in Production Engineering & Management 20(1) 2025 Proposition 3 indicates that when the spillover effect level of blockchain R&D is below a certain threshold, a collaborative R&D model enables the food supply chain to achieve a higher level of R&D effort. Conversely, when the spillover effect level is higher, an independent R&D model can achieve a higher level of R&D effort. Specifically, when the blockchain R&D spillover effect is rela- tively low, it implies that the application of blockchain technology is not yet widespread and deep enough. In such cases, deeper integration with other technologies like the IoT, big data, and AI is required, which increases the complexity and cost of technology development and maintenance. If a company opts for a collaborative R&D model, it can coordinate and integrate the technical resources and advantages of other companies within the supply chain, thus reducing the difficulty and risk of technology development and maintenance. This approach can help achieve a higher level of blockchain R&D in the food supply chain. On the other hand, when the blockchain R&D spillover effect level is high, it indicates that blockchain technology is already quite mature and stable. In such a scenario, food companies can customize the blockchain services according to the specific characteristics of their supply chain, achieving a higher level of blockchain service appli- cation. This not only helps to protect their trade secrets and competitive advantages but also en- hances their market competitiveness. Fig. 3 illustrates the variation in the difference between the level of blockchain collaborative R&D and independent R&D under different levels of R&D spillover effects. As 𝛾𝛾 increases, the fea- sible region where the collaborative R&D model achieves a higher R&D level gradually expands and moves towards the upper left region of the graph. This suggests that when the spillover effect of R&D is low, food companies lack sufficient motivation and resources to engage in R&D collabo- ration. However, as the spillover effect of R&D increases, the production efficiency of food compa- nies is significantly enhanced with the help of blockchain services, prompting them to have a stronger incentive to engage in collaborative R&D and improve the level of blockchain services. On the other hand, this move may also intensify competition in the food market (as shown in the graph by the increase in the food substitutability rate, 𝛽𝛽 ). Furthermore, implementation time lags in blockchain deployment create additional strategic considerations, as early collaborative inves- tors must balance the immediate costs against delayed spillover benefits, potentially moderating the attractiveness of collaboration even in high-spillover environments. Fig. 3 Evolution of the dominant region between 𝑠𝑠 𝑖𝑖 𝐢𝐢 𝑅𝑅𝑁𝑁 βˆ— and 𝑠𝑠 𝑖𝑖 𝑁𝑁𝑁𝑁 βˆ— 5. Extended analysis 5.1 Asymmetric substitute foods This section expands the research background to include asymmetric substitute food supply chains, considering supply chain operational decisions within the more complex context of block- chain R&D collaboration. Asymmetric substitute foods refer to cases in the food market where two or more types of food exist, and their substitutability is not mutual but rather one-directional. For example, soy milk can serve as a substitute for cow's milk, catering to the needs of individuals who are lactose intolerant or follow a vegetarian diet. However, cow's milk cannot completely replace the nutritional value and health benefits of soy milk. Based on these industry observations, this subsection assumes that the food product of Company 1 is superior to that of Company 2. Thus, the former can be considered a perfect substitute for the latter, but not vice versa. In the 𝛾𝛾 = 0.05 𝛾𝛾 = 0.5 𝛾𝛾 = 0.7 𝑠𝑠 𝑖𝑖 𝐢𝐢 𝑅𝑅𝐡𝐡 βˆ— > 𝑠𝑠 𝑖𝑖 𝑁𝑁𝐡𝐡 βˆ— 𝑠𝑠 𝑖𝑖 𝐢𝐢 𝑅𝑅𝐡𝐡 βˆ— < 𝑠𝑠 𝑖𝑖 𝑁𝑁𝐡𝐡 βˆ— 𝛽𝛽 𝛽𝛽 𝛽𝛽 π‘₯π‘₯ π‘₯π‘₯ π‘₯π‘₯ Independent vs. collaborative blockchain Research and Development: Operational decisions in food supply chains Advances in Production Engineering & Management 20(1) 2025 71 remaining content of this subsection, the product of Company 1 will be referred to as the β€œsuperior food”, while the product of Company 2 will be referred to as the β€œinferior food”. To simplify the modeling process, this subsection assumes that Ξ²_2=1 and Ξ²_1=Ξ²<1. Therefore, under independ- ent R&D, the inverse demand function for the food supply chain can be rewritten as follows: 𝑝𝑝 1 𝐴𝐴𝑁𝑁 𝑁𝑁 = πœƒπœƒ βˆ’ π‘žπ‘ž 1 𝐴𝐴𝑁𝑁 𝑁𝑁 βˆ’ 𝛽𝛽 π‘žπ‘ž 2 𝐴𝐴𝑁𝑁 𝑁𝑁 + π‘₯π‘₯ ( 𝑑𝑑 + 𝑠𝑠 1 𝐴𝐴𝑁𝑁 𝑁𝑁 ) (20) 𝑝𝑝 2 𝐴𝐴𝑁𝑁 𝑁𝑁 = πœƒπœƒ βˆ’ π‘žπ‘ž 2 𝐴𝐴 𝑁𝑁𝑁𝑁 βˆ’ π‘žπ‘ž 1 𝐴𝐴 𝑁𝑁𝑁𝑁 + π‘₯π‘₯ ( 𝑑𝑑 + 𝑠𝑠 2 𝐴𝐴𝑁𝑁 𝑁𝑁 ) (21) Furthermore, under collaborative R&D, the inverse demand function for the food supply chain can be rewritten as follows: 𝑝𝑝 1 𝐴𝐴𝐢𝐢 𝑁𝑁 = πœƒπœƒ βˆ’ π‘žπ‘ž 1 𝐴𝐴𝐢𝐢 𝑁𝑁 βˆ’ 𝛽𝛽 π‘žπ‘ž 2 𝐴𝐴𝐢𝐢 𝑁𝑁 + π‘₯π‘₯ ( 𝑑𝑑 + 𝑠𝑠 1 𝐴𝐴𝐢𝐢 𝑁𝑁 ) (22) 𝑝𝑝 2 𝐴𝐴𝐢𝐢 𝑁𝑁 = πœƒπœƒ βˆ’ π‘žπ‘ž 2 𝐴𝐴𝐢𝐢 𝑁𝑁 βˆ’ π‘žπ‘ž 1 𝐴𝐴 𝐢𝐢𝑁𝑁 + π‘₯π‘₯ ( 𝑑𝑑 + 𝑠𝑠 2 𝐴𝐴𝐢𝐢 𝑁𝑁 ) (23) Referring to similar calculation steps from the previous text, the equilibrium decision results for the two food companies in the asymmetric substitute food supply chain, under both independ- ent and collaborative blockchain R&D scenarios, can be easily derived. 5.2 Comparison of R&D levels in asymmetric substitute food companies By comparing the equilibrium R&D levels of asymmetric substitute food companies under inde- pendent blockchain R&D model, the following conclusions can be drawn: Proposition 4: when 𝛽𝛽 > 4( √2 βˆ’ 1 βˆ’ π‘₯π‘₯ ) ( √2 βˆ’ 2𝛾𝛾 ) οΏ½ or 𝛽𝛽 < 4( √2 βˆ’ 1 βˆ’ π‘₯π‘₯ ) ( √2 βˆ’ 2𝛾𝛾 ) οΏ½ and 3 √2 + 2𝛾𝛾 β‰₯ 4 + 4π‘₯π‘₯ , 𝑠𝑠 1 𝐴𝐴𝑁𝑁 𝑁𝑁 βˆ— < 𝑠𝑠 2 𝐴𝐴𝑁𝑁 𝑁𝑁 βˆ— ; Otherwise 𝑠𝑠 1 𝐴𝐴𝑁𝑁 𝑁𝑁 βˆ— > 𝑠𝑠 2 𝐴𝐴𝑁𝑁 𝑁𝑁 βˆ— . Fig. 4 Evolution of the dominant region between 𝑠𝑠 1 𝐴𝐴 𝑁𝑁𝑁𝑁 βˆ— and 𝑠𝑠 2 𝐴𝐴 𝑁𝑁𝑁𝑁 βˆ— Proposition 4 indicates that the relative sizes of food quality levels, food substitutability rates, and blockchain R&D spillover effects collectively determine the R&D levels of the two food com- panies. When R&D spillover effects are low, the inferior food company may have a higher R&D level than the superior food company under lower market competition or higher food quality lev- els. This suggests that, under lower market competition, superior food companies may lack the motivation to invest in blockchain R&D, as they already hold a significant market share. In con- trast, inferior food companies need to invest in blockchain R&D to enhance their market position and increase their revenue and profit. At higher food quality levels, superior food companies al- ready possess high quality and reputation, so there is less need to invest in blockchain services to further enhance their brand image. Meanwhile, inferior food companies need to use blockchain services to demonstrate that their products are also of high quality and reliability, thereby attract- ing more high-end consumers. Using the same parameter settings as in the previous subsection, and setting 𝛾𝛾 to 𝛾𝛾 = 0.05, 0.25, 0.8 respectively, Fig. 4 illustrates the comparative results of R&D levels for asymmetric substitute food companies under independent blockchain R&D. The figure shows that, under var- ious R&D spillover parameter settings, the feasible domain where 𝑠𝑠 1 𝐴𝐴𝑁𝑁 𝑁𝑁 βˆ— > 𝑠𝑠 2 𝐴𝐴𝑁𝑁 𝑁𝑁 βˆ— is significantly larger than the domain where 𝑠𝑠 1 𝐴𝐴𝑁𝑁 𝑁𝑁 βˆ— < 𝑠𝑠 2 𝐴𝐴𝑁𝑁 𝑁𝑁 βˆ— . This indicates that superior food companies are more likely to set higher blockchain R&D levels to maintain their dominant position in the market. 𝛾𝛾 = 0.25 𝛾𝛾 = 0.8 𝑠𝑠 1 𝐴𝑁𝑁 𝐡𝐡 βˆ— < 𝑠𝑠 2 A 𝑁𝑁𝐡𝐡 βˆ— 𝑠𝑠 1 𝐴𝑁𝑁 𝐡𝐡 βˆ— > 𝑠𝑠 2 A𝑁𝑁𝐡𝐡 βˆ— 𝛽𝛽 𝛽𝛽 π‘₯π‘₯ π‘₯π‘₯ 𝛾𝛾 = 0.05 𝛽𝛽 π‘₯π‘₯ Kang, Feng, Zhang 72 Advances in Production Engineering & Management 20(1) 2025 5.3 Value of R&D collaboration for asymmetric substitute food supply chains By comparing the optimal production quantities and optimal profits of the two food companies in the context of independent blockchain R&D for asymmetric substitute foods, the following con- clusions can be drawn: Proposition 5: (1) 𝑄𝑄 𝐴𝐴𝑁𝑁 𝑁𝑁 βˆ— < 𝑄𝑄 𝐴𝐴𝐢𝐢 𝑁𝑁 βˆ— ; (2) πœ‹πœ‹ 𝐴𝐴𝑁𝑁 𝑁𝑁 βˆ— < πœ‹πœ‹ 𝐴𝐴𝐢𝐢 𝑁𝑁 βˆ— . Proposition 5 indicates that in an asymmetric substitute food supply chain, collaborative block- chain R&D can lead to higher overall consumer demand and total profit in the food market. Com- paring this with the conclusions from Proposition 1, it is evident that, when food substitutability is asymmetric, the food production under collaborative R&D will be strictly higher than under independent R&D. For members of the food supply chain, this asymmetric substitutability means that the impact of collaborative R&D on blockchain services differs between companies. For Company 1, collabo- rative R&D can enhance the advantages of its food products, thereby consolidating its market leadership, capturing a larger market share, and increasing its profit levels. For Company 2, col- laborative R&D can help compensate for the disadvantages of its food products, thereby improv- ing its market competitiveness, attracting more consumers, and boosting its profit levels. 6. Conclusion This paper explores the blockchain R&D decision-making issues faced by food companies in the context of the increasing application of blockchain technology in food supply chain management. It focuses on two competing food companies simultaneously developing blockchain services on their self-built blockchain platforms. The paper examines the motivations for developing block- chain services, the impact of blockchain services on supply chain operational decisions, differ- ences in supply chain operational decisions under independent and collaborative R&D models, and changes in R&D model choices in more complex food market environments (such as asym- metric substitute foods). To address these issues, the paper establishes several models: Supply chain operational decisions without blockchain R&D collaboration (Benchmark Model), supply chain operational decisions with collaborative blockchain R&D (Collaborative R&D Model), and supply chain operational decisions under the context of asymmetric substitute foods (Asymmetric Substitute Foods Model). By comparing optimal operational decisions for food companies under three modelsβ€”no blockchain R&D, independent R&D, and collaborative R&Dβ€”the paper derives the optimal model and operational strategy for blockchain R&D collaboration in food supply chains. Additionally, the paper revisits operational decision schemes under different R&D models in the context of asym- metric substitute foods to test the robustness of the benchmark model results and provide more targeted management insights: From the perspective of food supply chain production, (1) Independent blockchain R&D tends to achieve higher market equilibrium production compared to collaborative R&D. This is because independent R&D better protects food companies' trade secrets and competitive advantages, whereas collaborative R&D may lead to information leakage and imitation by competitors. (2) High-value premium food supply chains are more suited for independent blockchain R&D, while ordinary food supply chains are better suited for collaborative R&D. Premium foods have higher commercial value and competitive advantages, giving supply chain members a stronger incentive and ability to protect their trade secrets and intellectual property, thus reducing the risk of infor- mation leakage and imitation. Ordinary foods, being more homogeneous, benefit more from col- laboration to reduce R&D costs and risks. From the perspective of food supply chain profit: The application of blockchain does not nec- essarily increase profits for food supply chain members. For independent R&D, it is only profitable when the blockchain's potential demand enhancement effect reaches a certain level. For collabo- rative R&D, the profit level of the food supply chain can be significantly higher compared to the Independent vs. collaborative blockchain Research and Development: Operational decisions in food supply chains Advances in Production Engineering & Management 20(1) 2025 73 other two blockchain R&D models. Therefore, choosing collaborative R&D is a more economical operational strategy. From the perspective of blockchain R&D, both independent and collaborative model of block- chain R&D can achieve relatively higher equilibrium R&D levels. The level of blockchain R&D spill- over effects reflects the stage of blockchain service application in the food market. When block- chain technology is not yet widely and deeply applied, the R&D spillover effect level is lower, mak- ing collaborative R&D a better choice. As the adoption of blockchain and R&D progress, the spill- over effect level increases, and food companies will gradually shift towards independent R&D model to achieve higher levels of blockchain service and stronger market competitiveness. Addi- tionally, when considering further asymmetric food R&D contexts, it is found that the R&D levels of blockchain under independent and collaborative models are also influenced by the level of food differentiation and food quality. Inferior goods may set higher R&D levels in independent R&D to prove their food quality and attributes to consumers. We propose several avenues for future research. First, exploring how consumer trust in block- chain affects the adoption of independent versus collaborative R&D models could provide valua- ble insights into strategic decision-making in food supply chains. Second, future studies should investigate the role of blockchain R&D in enhancing sustainability practices within food supply chains, particularly regarding transparency and traceability. Lastly, examining the long-term im- pact of blockchain R&D on competitive advantage will be crucial as companies transition from collaborative to independent models in response to market dynamics. Acknowledgement This work was supported by the [National Natural Science Foundation of China] under Grant [72401283]. References [1] Gurtu, A., Johny, J. (2019). Potential of blockchain technology in supply chain management: A literature review, International Journal of Physical Distribution & Logistics Management, Vol. 49, No. 9, 881-900, doi: 10.1108/ IJPDLM-11-2018-0371. [2] Wang, Y., Singgih, M., Wang, J., Rit, M. (2019). Making sense of blockchain technology: How will it transform supply chains?, International Journal of Production Economics, Vol. 211, 221-236, doi: 10.1016/j.ijpe.2019.02.002. [3] Choi, T.-M. (2019). Blockchain-technology-supported platforms for diamond authentication and certification in luxury supply chains, Transportation Research Part E: Logistics and Transportation Review, Vol. 128, 17-29, doi: 10.1016/j.tre.2019.05.011. [4] ČuΕ‘-Babič, N., Rebolj, D., Nekrep-Perc, M., Podbreznik, P. (2014). Supply-chain transparency within industrialized construction projects, Computers in Industry, Vol. 65, No. 2, 345-353, doi: 10.1016/j.compind.2013.12.003. [5] Pun, H., Swaminathan, J.M., Hou, P. (2021). Blockchain adoption for combating deceptive counterfeits, Production and Operations Management, Vol. 30, No. 4, 864-882, doi: 10.1111/poms.13348. [6] Sunny, J., Undralla, N., Pillai, V.M. (2020). Supply chain transparency through blockchain-based traceability: An overview with demonstration, Computers & Industrial Engineering, Vol. 150, Article No. 106895, doi: 10.1016/ j.cie.2020.106895. [7] Bai, C., Sarkis, J. (2020). A supply chain transparency and sustainability technology appraisal model for blockchain technology, International Journal of Production Research, Vol. 58, No. 7, 2142-2162, doi: 10.1080/00207543. 2019.1708989. [8] Saberi, S., Kouhizadeh, M., Sarkis, J., Shen, L. (2019). Blockchain technology and its relationships to sustainable supply chain management, International Journal of Production Research, Vol. 57, No. 7, 2117-2135, doi: 10.1080/ 00207543.2018.1533261. [9] Dong, Y., Song, L., Fu, L., Zhang, G. (2024). Humanitarian supply chain agility: A blockchain integration perspective, Tehnički Vjesnik – Technical Gazette, Vol. 31, No. 5, 1660-1667, doi: 10.17559/TV-20230425000568. [10] Chang, J.A., Katehakis, M.N., Shi, J.J., Yan, Z. (2021). Blockchain-empowered newsvendor optimization, Interna- tional Journal of Production Economics, Vol. 238, Article No. 108144, doi: 10.1016/j.ijpe.2021.108144. [11] Choi, T.-M., Luo, S. (2019). Data quality challenges for sustainable fashion supply chain operations in emerging markets: Roles of blockchain, government sponsors and environment taxes, Transportation Research Part E: Lo- gistics and Transportation Review, Vol. 131, 139-152, doi: 10.1016/j.tre.2019.09.019. [12] Wu, X., Fan, Z., Cao, B. (2021). An analysis of strategies for adopting blockchain technology in the fresh product supply chain, International Journal of Production Research, Vol. 61, No. 11, 3717-3734, doi: 10.1080/00207543. 2021.1894497. Kang, Feng, Zhang 74 Advances in Production Engineering & Management 20(1) 2025 [13] Bumblauskas, D., Mann, A., Dugan, B., Rittmer, J. (2020). A blockchain use case in food distribution: Do you know where your food has been?, International Journal of Information Management, Vol. 52, Article No. 102008, doi: 10.1016/j.ijinfomgt.2019.09.004. [14] Kamble, S.S., Gunasekaran, A., Sharma, R. (2020). Modeling the blockchain enabled traceability in agriculture sup- ply chain, International Journal of Information Management, Vol. 52, Article No. 101967, doi: 10.1016/j.ijinfo- mgt.2019.05.023. [15] Wang, G., Cao, E., Weng, J., Xie, S. (2024). Dynamic pricing in a blockchain-enabled dual-channel supply chain, Tehnički Vjesnik – Technical Gazette, Vol. 31, No. 3, 753-773, doi: 10.17559/TV-20230726000830. [16] Mangla, S.K., Kazancoglu, Y., Ekinci, E., Liu, M., Γ–zbiltekin, M., Sezer, M.D. (2021. Using system dynamics to analyze the societal impacts of blockchain technology in milk supply chainsrefer, Transportation Research Part E: Logistics and Transportation Review, Vol. 149, Article No. 102289, doi: 10.1016/j.tre.2021.102289. [17] Rogerson, M., Parry, G.C. (2020). Blockchain: Case studies in food supply chain visibility, Supply Chain Management: An International Journal, Vol. 25, No. 5, 601-614, doi: 10.1108/SCM-08-2019-0300. [18] Behnke, K., Janssen, M.F.W.H.A. (2020). Boundary conditions for traceability in food supply chains using block- chain technology, International Journal of Information Management, Vol. 52, Article No. 101969, doi: 10.1016/ j.ijinfomgt.2019.05.025. [19] Yang, S.Y., Zhang, M.F. (2023). Blockchain-driven optimization in intelligent manufacturing, International Journal of Simulation Modelling, Vol. 22, No. 2, 350-361, doi: 10.2507/IJSIMM22-2-CO10. [20] Shen, J., Qian, J., Shao, X. (2022). Service channel choice for supply chain under online marketplace, International Transactions in Operational Research, Vol. 29, No. 4, 2401-2422, doi: 10.1111/itor.13095. [21] Chen, Z., Dan, B., Ma, S., Tian, Y. (2022). Demand information sharing of fresh produce supply chain considering competing suppliers' freshness-keeping effort, International Transactions in Operational Research, Vol. 31, No. 2, 1206-1231, doi: 10.1111/itor.13177. [22] Liu, L., Zhao, L., Lee, C. (2021). Competing product service in an OEM supply chain with upstream module suppliers as service providers, International Transactions in Operational Research, Vol. 28, No. 6, 3364-3393, doi: 10.1111/ itor.12980. [23] Karray, S., MartΓ­n-HerrΓ‘n, G. (2021). The effects of decision timing for pricing and marketing efforts in a supply chain with competing manufacturers, International Transactions in Operational Research, Vol. 31, No. 1, 568-615, doi: 10.1111/itor.13094. [24] Deng, G.F. (2023). Dynamic price competition market for retailers in the context of consumer learning behavior and supplier competition: Machine learning-enhanced agent-based modeling and simulation, Advances in Produc- tion Engineering & Management, Vol. 18, No. 4, 434-446, doi: 10.14743/apem2023.4.483. [25] Liu, J., Zhao, H., Lyu, Y., Yue, X. (2022). The provision strategy of blockchain service under the supply chain with downstream competition, Annals of Operations Research, Vol. 327, 375-400, doi: 10.1007/s10479-022-05034-2. [26] Song, Y., Liu, J., Zhang, W., Li, J. (2022). Blockchain's role in e-commerce sellers' decision-making on information disclosure under competition, Annals of Operations Research, Vol. 329, 1009-1048, doi: 10.1007/s10479-021- 04276-w. [27] Yan, K., Cui, L., Zhang, H., Liu, S., Zuo, M. (2022). Supply chain information coordination based on blockchain tech- nology: A comparative study with the traditional approach, Advances in Production Engineering & Management, Vol. 17, No. 1, 5-15, doi: 10.14743/apem2022.1.417. [28] Yang, S.Y., Tan, C. (2022). Blockchain-based collaborative management of job shop supply chain, International Journal of Simulation Modelling, Vol. 21, No. 2, 364-374, doi: 10.2507/IJSIMM21-2-CO10. [29] Hu, H., Li, Y., Li, M. (2024). Dual-channel supply chain coordination considering the consumer's perception of qual- ity, Economic Computation and Economic Cybernetics Studies and Research, Vol. 58, No. 2, 198-216, doi: 10.24818/ 18423264/58.2.24.12. [30] Wang, Y., Yang, L., Chen, J.H., Li, P. (2023). Supply chain game analysis based on mean-variance and price risk aversion under different power structures, Advances in Production Engineering & Management, Vol. 18, No. 1, 104- 115, doi: 10.14743/apem2023.1.460. [31] Wang, S.L., Zhang, Y., Sheng, X., Luo, X.Y. (2023). Blockchain in supply chain collaboration: A quantitative study, International Journal of Simulation Modelling, Vol. 22, No. 3, 532-543, doi: 10.2507/IJSIMM22-3-CO15.