In several companies such as large retail stores, the employees perform different activities (e.g., cashier or clerk in a specific department) to respond to a customer demand for each activity that varies over the planning horizon and must be fulfilled as soon as possible. For a given time period, this demand translates into an ideal number of employees required for the corresponding activity. During a work shift, an employee can be assigned to several activities that are interruptible at any time and subject to operational constraints (required skills, minimum and maximum assignment durations). Given work shifts already assigned to the employees, the multi-activity assignment problem (MAAP) consists of assigning activities to the shifts such that the activity demands are satisfied as best as possible over the planning horizon. In this paper, we propose three integer programming models for the MAAP and develop various heuristics based on mathematical programming techniques. Computational results obtained on randomly generated MAAP instances show that a heuristic column generation method embedded into a rolling horizon procedure provides the best results in general.