Reconstruction projects in the aftermath of events such as natural disasters require proper allocation of scarce resources to multiple projects that need to run concurrently according to a planned schedule. Project deadlines are specified based on the urgency and importance of the infrastructure being rebuilt. Construction companies within the locality of the site may have insufficient capacity to cope with all the reconstruction projects. In such cases, external construction companies from other regions supplement local reconstruction efforts. Use of such external resources incurs environmental penalties (e.g., greenhouse gas emissions) due to the transport of heavy equipment, material supplies, and workers, over greater distances. It is necessary to assign companies suitably to minimize the carbon footprint of accomplishing the tasks. A multi-period source-sink model is developed to optimize the assignment of construction companies to multiple projects along a planned time horizon, using earliest finish time during reconstruction campaign. The model is formulated as a Mixed Integer Linear Program whose objective function is to minimize total carbon footprint during reconstruction while taking into account company size and classification, as well as project deadlines. A case study on urban reconstruction in the southern Philippines is solved using the model.