The establishment of contracts pursues the efficient fulfillment of supply chain members' needs. However, this is not always possible due to market features and, more interestingly, the additional constraints that such mechanisms impose. Trust relationships, that we define as the absence of contracts, appear as a mean to deal with situations where contracts block decision making. Although trust enhances production/management activities, it is not clear how the absence of contracts impact on delivery times, which we investigate in this paper. We analyze a decentralized supply chain where a manufacturer needs an intermediate input, but typical suppliers that have a contract with the manufacturer do not provide it; so, he establishes a non-contractual relationship with an "external" provider. We model this interaction as a two-stage game and show necessary and sufficient condition to guarantee the existence and uniqueness of the Sub-game perfect Nash equilibria. Also, we show the relationship between delivery times and input's requisition, at equilibrium, with exogenous variables like production costs and base revenue. We find that intuitive relationships hold when the requisition cost is higher than a third of the manufacturer's revenue.