Introducing a mathematical model in supply chain by adding trust flow

These day, supply chains (SCs) have become more and more complicated and have extensively expanded and due to these complexities, the supply chain management (SCM) has encountered several uncertainties, and, as a result, trust and assurance between members in SCs has become essential for a successful SCM. Although trust is an inevitable component in nearly all fields in SCs, like cooperation, coordination and management. As Trust increases the sense of security among members and cuts back on the losses, this research attempts to introduce a mathematical model that is able to utilize trust as a main element in a two-echelon SC. Defining trust is difficult since it is analyzed from different perspectives, and it is used in a wide range of situations. Therefore, the aim of this study is to propose an appropriate definition for this concept according to SCs, and to present a two-echelon SC, including a retailer and a supplier. The supplier and the retailer play Stackelberg game in newsvendor framework. The order quantity and stock, as the best sections for proposing the definition of trust, is developed for retailer and supplier. In addition, Beta model is presented for calculating trust and finally in order to verify the quality and efficiency of the proposed model, a numerical example is also offered.