Assigning Team Tasks and Multiple Activities to Fixed Work Shifts

In the service industry, the multi‐activity and task assignment problem consists of assigning various activities and tasks to given work shifts. An activity has a time‐dependent continuous demand (number of employees required to service the customers) and is interruptible, i.e., an employee assigned to it can be relieved at any time. At the opposite, a task has a specific duration, is performed once by a single employee, and is uninterruptible. In this paper, we consider an extension of this problem, called the multi‐activity and team task assignment problem where the tasks can be undertaken in different ways by several employees simultaneously. We propose a mixed integer programming formulation and a two‐module approach to find solutions to this problem. In the first module, an approximation model for assigning tasks without activities is solved by a mixed integer programming solver. The second module consists of a column generation model for assigning activities by allowing task reassignments during the process. These modules are used within a variable neighborhood descent heuristic. We have performed extensive computational experiments to validate our approach.