This paper first presents a formal model of the transactions activated in a blockchain used to manage a supply chain composed by Small-Mid Enterprises (SME). Such a formal model is based on a correspondence between the decision to be taken by a SME each time a new order is arrived from a downstream stage of the supply chain, and the formulation of a transaction in a blockchain. Based on this correspondence, a model of the blockchain management of all SMEs included in a supply chain is formulated according to the basic concepts of an event-driven production scheduling problem. The resulting blockchain model can be represented by a table showing the interactions between a provider and a consumer in terms of smart contract, thus connecting two stages of the supply chain. The transaction security is assured by secret codes of both the contract and the two actors, namely the provider and the consumer. Applications of blockchain to two SMEs operating in the agro-food sector is briefly described, thus showing the real impact of blockchain-based management in practice situations.