Multi-Cycle Assignment Problems with Rotational Diversity

Multi-cycle assignment problems address scenarios where a series of general assignment problems has to be solved sequentially. Subsequent cycles can differ from previous ones due to changing availability or creation of tasks and agents, which makes an upfront static schedule infeasible and introduces uncertainty in the task-agent assignment process. We consider the setting where, besides profit maximization, it is also desired to maintain diverse assignments for tasks and agents, such that all tasks have been assigned to all agents over subsequent cycles. This problem of multi-cycle assignment with rotational diversity is approached in two sub-problems: The outer problem which augments the original profit maximization objective with additional information about the state of rotational diversity while the inner problem solves the adjusted general assignment problem in a single execution of the model. We discuss strategies to augment the profit values and evaluate them experimentally. The method's efficacy is shown in three case studies: multi-cycle variants of the multiple knapsack and the multiple subset sum problems, and a real-world case study on the test case selection and assignment problem from the software engineering domain.