An important class of tasks that are underexplored in current human computation systems are complex tasks with global constraints. One example of such a task is itinerary planning, where solutions consist of a sequence of activities that meet requirements specified by the requester. In this paper, we focus on the crowdsourcing of such plans as a case study of constraint-based human computation tasks and introduce a collaborative planning system called Mobi that illustrates a novel crowdware paradigm. Mobi presents a single interface that enables crowd participants to view the current solution context and make appropriate contributions based on current needs. We conduct experiments that explain how Mobi enables a crowd to effectively and collaboratively resolve global constraints, and discuss how the design principles behind Mobi can more generally facilitate a crowd to tackle problems involving global constraints.