Affiliations: School of Business, Renmin University of China, Beijing, China. E-mail: xiaofang.wang@gmail.com | European Space Operations Centre, European Space Agency, Darmstadt, Germany. E-mail: nicola.policella@esa.int | The Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, USA. E-mail: sfs@cs.cmu.edu | ISTC-CNR, Institute for Cognitive Science and Technology, National Research Council of Italy, Rome, Italy. E-mail: angelo.oddi@istc.cnr.it
Note: [] Corresponding author.
Abstract: A project network composed of discretionary tasks typically exists in service professions, such as journalism, clinic, software development or financial analysis, where the quality (or value) of a task increases with the time spent on it. Since a longer task duration consumes more resources (i.e., workers' time), the project manager must strike a balance between quality and time by scheduling tasks and setting their durations while respecting the project deadline, precedence and resource constraints. We formulate this problem, give a polynomial-time optimal algorithm for the single capacity case and prove the NP-completeness of the general multiple capacity case. Then we develop two hybrid solution procedures integrating linear optimization and an AI search procedure – precedence constraint posting – for the general case. Our results verify the effectiveness of these procedures and show there exists a potential synergy between objectives of maintaining temporal flexibility and maximizing quality, which implies that existing techniques in building flexible schedules can be adapted to solve this new class of problems.
Keywords: Scheduling, constraint programming, discretionary service
