## 3 The F-Channel Platform
### Coordination Module
#### 3.2.4. Auction Wizard and Bid Submission Wizard  
After the FSP successfully completes the prequalification process and the related tests and their addition to the unified FSP register, they are allowed to participate in the auctions organized for responding to the needs spotted in the system. However, those auctions can be quite confusing tasks, especially if there is more than one auction taking place at the same time. Since each of those auctions would probably be either for different timeframes or for different products, it is understandable how this could overwhelm not only the FSPs but the SOs and MOs as well. To make this less tiresome, the F-channel platform's Coordination module also includes an auction wizard submodule. In addition, towards simplifying the auction process for the users, the F-channel platform also makes the submission of the bids for those auctions rather easy via the section called \"Bid Submission Wizard\". This part of the platform incorporates three consecutive steps, out of which the first is the confirmation of the general information on the user that exists on the platform. After all participants submit their bids and the window for the submission of bids closes, there is a need to select those bids that will participate in the auction in question. This is commonly performed by conducting the optimization procedure. This procedure must be performed for each of the products that are supported by the platform. The goal of the optimization is to maximize the total welfare of all participants, with the welfare being defined as the difference between the total cost that the SOs would be prepared to pay for the required services and the amount that the FSPs would like to receive for those same services. The optimization needs to take place across all markets and all trade intervals. The objective function for the process could be written as given in Equation (1):  
\[\max\sum_{\tau\in T}\left\{\sum_{n=1}^{N}k_{n,\tau}^{BUY}\cdot c_{n,\tau}^{ BUY}-\sum_{m=1}^{M}k_{m,\tau}^{SELL}\cdot c_{m,\tau}^{SELL}+\lambda\cdot \left(\sum_{n=1}^{N}k_{n,\tau}^{BUY}+\sum_{m=1}^{M}k_{m,\tau}^{SELL}\right)\right\} \tag{1}\]  
In this expression, the symbols have the following meanings:  
\(c_{n,\tau}^{BUY}\): Price that, by the \(n\)-th buy bid, SOs would be willing to pay for the product in interval \(\tau\);  
\(c_{m,\tau}^{SELL}\): Price that, by the \(m\)-th sell bid, FSP would require for the product in interval \(\tau\);  
\(k_{n,\tau}^{BUY}\): Total accepted amount from the \(n\)-th buy bid in interval \(\tau\);  
\(k_{m,\tau}^{SELL}\): Total accepted amount from the \(m\)-th sell bid in interval \(\tau\);  
\(M\) and \(N\): Respectively, total numbers of sell and buy bids in interval \(\tau\);  
\(T\): Set of all time intervals \(\tau\) in the period that the auction envelops;  
\(\lambda\): Small constant value (could be, for instance, in the range from \(10^{-6}\) to \(10^{-5}\)). Out of these, the total accepted volumes per each bid (buy and sell) would be treated as the decision variables, whereas all other parts of Equation (1) could be seen as the constants that are essential for the optimization to take place. The part of the objective function multiplied by the small constant \(\lambda\) is there to guarantee that the maximum total number of bids is accepted, if the objective function's value is not harmed by those bids being accepted. The constraints that are considered in this process are given by the set of expressions (2), (3), and (4), as follows:  
\[\forall(n,\tau)\ \Big{|}\ k_{n,\tau}^{BUY}\leq K_{n,\tau}^{BUY} \tag{2}\]  
\[\forall(m,\tau)\ \Big{|}\ k_{m,\tau}^{SELL}\leq K_{m,\tau}^{SELL} \tag{3}\]\[\forall(\tau)\ \Big{|}\sum_{m=1}^{N}k_{n,\tau}^{BUY}-\sum_{m=1}^{M}k_{m,\tau}^{ SELL}=0 \tag{4}\]  
The first two constraints describe in a mathematical form that the accepted volume of the bid (either buy or sell) cannot exceed the total offered (in case of the sell bids) or requested volume of the specified product (in case of the buy bids).