Social insects are classic examples of cooperation and coordination. For instance, laboratory studies of colony relocation, or house-hunting, have investigated how workers coordinate their efforts to swiftly move the colony to the best nesting site available while preserving colony integrity, i.e. avoiding a split. However, several studies have shown that, in some other contexts, individuals may use private rather than social information and may act solitarily rather than in a coordinated way. Here, we study resource allocation by a mature ant colony when it reproduces by fissioning into several colonies. This is a very different task than house-hunting in that colony fission seeks the split of the colony. We develop a simple individual-based model to test if colony fission and resource allocation may be carried out by workers acting solitarily with no coordination. Our model reproduces well the pattern of allocation observed in nature (number and size of new colonies). This does not show that workers do not communicate nor coordinate. Rather, it suggests that independent decision making may be an important component of the process of resource allocation.