An important class of tasks that is underexplored in current human computation systems are complex tasks for which the solutions demand a set of global constraints to be met. One example of such a task is itinerary planning, where solutions consist of a sequence of activities that meet the requirements specified by the requester. In this paper, we focus on the joint formulation of such plans as a case study of constraint-based human computation task and introduce a collaborative planning system called Mobi. Mobi presents a single interface that enables participants to view the current solution context and make appropriate contributions based on current needs during the progression of collaboration. We conduct experiments that show the end-to-end usability of Mobi, and that explain how the system enables a crowd to effectively and collaboratively resolve global constraints.