This work examines the scheduling and adaptive re-scheduling of energy usage in in-home applications. And the work can expand to the specific power usage region such as in home case, in company or in community. In this work, the discussion can be divided into two parts. First, we try to formulate the practical power scheduling issue under the assumption that we know the scheduling information in advance. To be more precise, we know the day ahead information about power usage and the cost information, and we try to rearrange those power usage jobs optimally. We proposed an algorithm to schedule those jobs which can be predicted from history data. From simulation result, we claim that our proposed CREPES(Convex Relaxation Based Energy Pre-Scheduling) algorithm is quasioptimal. When we apply our algorithm in the scenario of community. The fairness occurs. Since if we try to schedule our job greedily for every member in the community, the optimality for the community can’t be achieved. We can achieve the optimality if all the members in the community try to cooperate. This will result in the deviation of optimality for individual from the whole community. Therefore, we also introduce the fairness index in the off-line scheduling case, which is a index to judge the deviation from the performance of individual scheduling from cooperation scheduling, which motivates us to minmax the fairness index to confirm our system costs each user fairly. In the second part of our work we try to extend our system with PHEVs, that is, we take battery of PHEVs into consideration. And we also permit our job to be executed with tolerable delay. We try to take an online action for i the scheduling system. The resulting problem is a stochastic dynamic programming for cost optimization problem. The standard way to solve this kind of problem is Lypunov optimization procedure. In the online scheduling system, in some case we can find that the electricity energy is relatively cheap at that time and then who can buy the power becomes an issue. That is, what is the most fair scheduling way in the online scheduling system becomes a problem we concern. This motivates us to introduce the concept of proportional fairness in our online scheduling system, which is a standard way to allocate resource in wireless communication system.