Crowdsourcing is important paradigm in humanproblem solving using the Web. When they face a workload outburst, businesses may choose outsource certain or all of process tasks to the crowd in order to not compromise the quality of service promised for their customers. This may occur in situations like crisis management, when organization are overloaded by a sudden event breakout. These tasks are generally difficult to implement as solution based on software service only. So, the use of crowdsourcing platform seems enticing. To ensure efficient and wise use of resources, decision making aids methods need to be developed in which the aim is to assist businesses in choosing the most knowledgeable workers. In this paper we address the resource allocation problem in crisis context by defining a delegation approach based on crowd-sourcing as resource provider. Firstly, we propose a mathematical model for business process execution in crowd-sourcing context and an exact optimization algorithm. Secondly, as the problem addressed here is NP-complete, we propose an efficient algorithm, as shown by a series of experiments, to deal with the considered problem. Furthermore, to overcome the limitations of existing works we take here the fact that business process tasks are dependent while optimizing the overall execution time of a given business process instance under budget constraint.