## 1 Introduction  
### Motivation  
Power distribution grids are becoming more intelligent due to the opportunities that are provided by today's information and communication technologies [1]. These so-called smart grids consist of several parts, features and functions. A smart outage management system is an essential part of smart power distribution grids [2]. Distributed Generations (DGs) play an important role in outage management. In a time of crisis, the outage management system can effectively use the output power of the DGs to restore the power more effectively, to minimize the affected area and, consequently, to decrease the cost of the outage. For this, the output power of DGs should be dispatched by the outage management system considering economic aspects. Moreover, the integrated distribution system is divided into multiple areas [3]. In some areas, the customers' demand is not satisfied with the output power of DGs. Consequently, the Distribution System Operator (DSO) is inevitably forced to choose load shading to balance the generation and demand of consumers. The load shading is costly; therefore, DSOs prefer not to go for such a solution unless it is necessary. In this regard, if the sum of the generation power capacity is lower than the sum of the demand of each area, then load shedding is chosen.  
To address this issue, the Emergency Demand Response Program (EDRP) contract can be used to decrease the load shading cost by the DSO [4]. The EDRP is an incentive type of demand response program. There are three types of demand response, namely, an emergency demand response, economic demand response and ancillary service demand response. An emergency demand response is employed to avoid involuntary service interruptions during times of supply scarcity (such as outages in the power system). An economic demand response is employed to allow electricity customers to curtail their consumption when the productivity or convenience of consuming that electricity is worth less to them than paying for the electricity. An ancillary service demand response consists of a number of specialty services that are needed to ensure the secure operation of the transmission grid and which have traditionally been provided by generators. In summary, the demand response programs can be implemented in optimal energy management or other operation problems without any outage occurrence in the power system.  
The EDRPs can be an effective solution for reducing the operation cost of the power system when the energy market price of the deregulated power market is high [4]. Furthermore, the main target of the EDRP contracts is in crisis times.  
In a crisis time, crews of each depot try to repair the outages of the distribution system. The operation performance of each crew affects the load restoration time and the value of the pickup loads. The topology of the power system will be changed in each repair time interval. Furthermore, the optimal output power of each DG and the number of EDRPs in each load point and repair time interval depend on the performance of the crews. Hence, an optimal outage management system is needed to integrate the DG dispatch problem, reduce the EDRP cost, minimize the operation time of crews and minimize the load shading cost.