Parallel system scheduling with general worker learning and forgetting

Learning and forgetting models available in the literature are generally not intended for math programming formulations, thus their incorporation within worker-task assignment problem models leads to non-linearity in the objective function, producing a Mixed Integer Nonlinear Program (MINLP) that is difficult to solve. Even though Dynamic Programming and other alternate approaches have been implemented to solve assignment problems in production systems with independent stations and independent jobs while maximizing output, such solutions are generally not optimal. In this paper, we develop results that reveal the form of the optimal solution, which allows us to solve the problem as a Mixed Integer Linear Program (MILP), rather than the more complex MINLP. We examine the effectiveness of this information to reduce the time complexity of the problem. As the presented methodology is independent of the productivity model, it has general application, irrespective of the specific learning/forgetting models employed. The approach is relevant in the context of a set of tasks with some task similarity, learning and forgetting among the workforce, and equal or unequal numbers of workers and tasks.