## 3 Methodology  
### Model Overview  
For our model we chose a mixed-integer problem (MIP) as the mathematical basis to be able to model the linear optimization of transportation and storage and include the binary decision of building optional interim storage facilities at different locations. The given problem is a transportation problem and can be modeled as a network consisting of four kinds of nodes. * The first kind are the NPPs that produce the HLW, which also store amounts of HLW in independent spent fuel storage installations (ISFSI) until further transportation. * From here on, the waste can be transported either directly to the final repository or to an CISF. The model has the option to build these facilities when needed, at predefined locations. * There are two nodes representing two hot cells (hot cells are shielded nuclear radiation containment chambers. They protect operators from radiation by providing a safe containment box in which they can open the casks containing SNF and either refill it into other casks or extract it for reprocessing purposes (Engineering360. Hot Cells Information, 2018. Accessed via the Internet on 29.01.2018 at [[http://www.globalspec.com/learnmore/lab_equipment_scientific_instruments/lab_safety/hot_cells](http://www.globalspec.com/learnmore/lab_equipment_scientific_instruments/lab_safety/hot_cells)]([http://www.globalspec.com/learnmore/lab_equipment_scientific_instruments/lab_safety/hot_cells](http://www.globalspec.com/learnmore/lab_equipment_scientific_instruments/lab_safety/hot_cells))), to which HLW can be transported either from the reactors or from the interim storages. * Once in the final repository the waste can not be accessed again. Each type of node had a given storage capacity with specific storage costs. The storage costs in the final repository were neglected, as we were only considering the costs of the process until the waste is in the final repository. All existing transportation routes were included with their respective distance and type of transport which is either rail or road (truck). The model chose the type of transport, also taking into account the NRC's regulation on some routes. The intermediate repositories can be built at nine different given locations (Grantsville (Utah), Barstow (California), Watkins (Colorado), Rayne (Louisiana), Barnesville (Georgia), Lucas (Iowa), Lasalle (Illinois), Newville (Pennsylvan), Old Chatham (New York)). These were chosen exogenously at interceptions of main possible transport routes. The model decides endogenously whether the capacity of those facilities is needed and in what year they are built. The facilities built are identical, with the exact same capacity as well as the same building cost. This decision is modeled using a binary variable. The model differentiates between three types of waste. * First of all there was the SNF from the NPPs. * The second type was waste that has been vitrified, after the original SNF has been reprocessed and thereby its volume has been decreased. It was important to mention that during the vitrification process, the waste has to be refilled into a new cask. * Likewise, the third type was waste that had simply been refilled into a new cask within a hot cell as the casks containing the suffer from decay. Therefore the HLW had to be refilled into a new cask when the old casks expire after their lifetime. Figure 3 portrays the most important parts and the general build up of the model. Exogenous input in form of collected data and the framework scenarios are given and bound by several constraints that are mostly based on technological assumptions. The model then endogenously decided on which transport routes to take, which CISF to build and whether or not reprocessing is an cost-efficient alternative. Finally the output data such as costs, transportation amounts and storage levels are given. A total of six scenarios concerning the long-term waste management options are considered for this model and the results are then compared.