## 2 Demand-Side Management Classifications and Their Roles in Cost Minimization
### Cost Minimization by Employing Efficient DSM Schemes
#### 2.2.1 Game Theoretic and Real-Time Pricing Approaches in Cost Minimization  
Cost minimization can be achieved by utilizing the various approaches mentioned in the literature. The game theoretic and real-time pricing approaches are the most prominent approaches available in the literature and are presented in the following text. Cost Minimization Using the Game Theoretic Approach  
Game theory is one of the mathematical tools used in the literature to model different DSM schemes that is valuable both for consumers as well as for suppliers. In [140; 141; 142; 143; 140; 141; 61], the authors introduced autonomous DSM schemes based on game theory. In the first one of these articles, the authors proposed a scheme in which each consumer schedules his/her own energy usage in a time slot with a low price by participating in the game, thus reducing his/her electricity bills. The energy cost is minimized by achieving the Nash equilibrium point. The PAPR is reduced by using the distributed DSM in [61]. The formulation is based on the non-cooperative game theory, where the consumers act as players and the utility companies as strategies. Similarly, the authors in [140; 141; 142], used the multiple leader multiple follower Stackelberg game to maximize the profits of the micro-grid. In [81], the authors considered a scenario with multiple suppliers connected to a central DSM center as well as with the consumers through the communication link and power line, as shown in Figure 7.  
Each of the suppliers has to submit a bid to the DSM center through the communication link, where the DSM center calculates the electricity price on the basis of these bids and on the information provided by the consumers in terms of an aggregated load. The proposed framework is based on the non-cooperative game theory. The objective of the framework is to maximize the supplier's profit as well as to maximize the consumers' satisfaction in terms of bill reductions. The mathematical formulation is done for the supplier and consumer sides independently and is given as follows. \[\max\ \ profit=S_{j,t}(b_{t},Q_{t})Pe(b_{t},Q_{t})-C_{j}(S_{j,t}(b_{t},Q_{t})) \tag{1}\]  
where \(S_{j,t}(. )\) is the generated electricity by the \(j\)th supplier at time \(t\), which is a function of the bid vector of all suppliers and the aggregated load of consumers. \(Pe(b_{t},Q_{t})\) is the electricity price calculated by the DSM center, and \(C(. )\) is the generated electricity cost. On the consumer side, the problem is formulated as  
\[\max\sum_{t\in T}\bigg{(}U_{i}(L_{i}^{sh}(t)+L_{i}^{b}(t))-(L_{i}^{sh}(t)+L_{i} ^{b}(t))\bigg{)}\frac{\sum_{i\in N}(L_{i}^{sh}(t)+L_{i}^{b}(t))}{\sum_{r\in S }b_{r,t}} \tag{2}\]where \(U_{i}(. )\) represents the utility function for consumer \(i\) which shows the satisfaction of consumer \(i\) with their electricity consumption. The utility is a function of the consumers' shiftable and base loads represented by \(L_{i}^{sh}(t)\) and \(L_{i}^{b}(t)\). In Equation (2), \(N\) is the total number of consumers and \(T\) is total number of time slots. Similarly, in [77], [PERSON] suggested an auction game-based algorithm to schedule consumer energy consumption. In this paper, the authors solved the problem of cost minimization in two different scenarios; the first one was the minimization of the utility cost of generation, and the second one was the maximization of consumer welfare. The authors achieved their objectives by first dividing the consumers' load into flexible and essential loads and then minimizing the flexible load for different intervals of time. In [117] presented a profit maximization problem based on risk constrained demand responses. The proposed framework is composed of a micro-grid aggregator and a scheduler, where the aggregator procures electricity from different sources and sells it to the consumers. The scheduler in the proposed framework offers different scheduling contracts to the consumers in order to minimize the consumers' bills and to reduce the demand on the micro-grid during peak hours.