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Minimizing the distribution time in supply chain networks is critical. By minimizing the total time of distribution in the network we can reduce the cost as well as decrease the product wastage for goods with fast approaching expiration date such as dairy products. In real-world the traveling time in supply chain network is not deterministic most of the time and uncertainties in the form of randomness are not avoidable. For this reason, for finding the optimal path of distributor vehicles in the distributionnetwork that has the lowest travel time, a probabilistic dynamic optimization model has been used in this study and the results of a numerical example are discussed.