Knowing the real costs of a project, correctly estimating them and identifying the risks involved in resource allocation for projects such as the construction of a petrochemical unit whose resources are expensive or difficult to access, is of particular importance. By using costing methods in conditions of risk and uncertainty, more reliable cost information can be obtained. By examining past studies and researches in the field of costing, it was found that their focus was mostly on carrying out activities, and less attention was paid to the risk factor. In this article, the use of the ABC approach, which focuses on identifying activities and cost centers, has been discussed in the form of a mathematical model whose purpose is to minimize the risk of resource allocation to activity centers based on the desired limitations in costs and resources. Due to the fact that the numerical values of the parameters in the general model, such as cost and time, have uncertainty, risk-based resource allocation modeling has been considered. To test the proposed model, the main activities of the construction and installation stage of a petrochemical unit were considered, and after collecting the necessary data, the steps of the compiled model for resource allocation and the steps of the activity-based costing approach have been implemented. The results show that there is a difference between the costs calculated based on the allocation of resources of the proposed model for the activity centers and the costs estimated according to the past data.