In the oil production distribution network, there are three main nodes, namely the supply node, the transshipment node, and the demand node. The pattern of distribution of oil production from the supply node to the demand node is very diverse and can affect the costs to be incurred. Therefore, a company must be able to determine the right distribution pattern, so that the costs incurred are optimal. This paper intends to conduct a study of how to determine and calculate the distribution patterns and the minimum total costs incurred, using the primal-dual linear program method. Based on the results of the case analysis, it is known that the number of supply commodities will be the same as the number of demand commodities, but the distribution from each source does not necessarily have the same capacity and costs. Therefore, the distribution pattern is determined based on the existing cost and capacity, so that cost optimization can be achieved.