This paper addresses a task assignment problem encountered by check-in counter personnel at airports. The problem consists of assigning multiskilled agents to a sequence of tasks in check-in counters. Because each task’s ending time is fixed to comply with the flight schedule, its processing time depends on the arrival of the assigned agents. The article proposes a mixed-integer program and a branch-and-price algorithm to solve this problem. It exploits the problem structure to efficiently formulate the pricing problems and improve computation time. Using real-world data from a German ground-handling agency, the team conducted numerical studies to evaluate the performance of the proposed solutions.