The falling tide algorithm: A new multi-objective approach for complex workforce scheduling

• Published in: Omega (Oxford) 2012-06, Vol.40 (3), p.283-293
• Main Authors: Li, Jingpeng, Burke, Edmund K., Curtois, Tim, Petrovic, Sanja, Qu, Rong
• Format: Article
• Language: English
• Subjects: Algorithms; Applied sciences; Decision theory. Utility theory; Exact sciences and technology; Firm modelling; Goal programming; Heuristic; Heuristics; Mathematical programming; Multi-criteria; Operational research and scientific management; Operational research. Management science; Scheduling; Scheduling Goal programming Heuristics Multi-criteria; Scheduling, sequencing; Studies; Workforce planning
• ISSN: 0305-0483; 1873-5274
• DOI: 10.1016/j.omega.2011.05.004

We present a hybrid approach of goal programming and meta-heuristic search to find compromise solutions for a difficult employee scheduling problem, i.e. nurse rostering with many hard and soft constraints. By employing a goal programming model with different parameter settings in its objective function, we can easily obtain a coarse solution where only the system constraints (i.e. hard constraints) are satisfied and an ideal objective-value vector where each single goal (i.e. each soft constraint) reaches its optimal value. The coarse solution is generally unusable in practise, but it can act as an initial point for the subsequent meta-heuristic search to speed up the convergence. Also, the ideal objective-value vector is, of course, usually unachievable, but it can help a multi-criteria search method (i.e. compromise programming) to evaluate the fitness of obtained solutions more efficiently. By incorporating three distance metrics with changing weight vectors, we propose a new time-predefined meta-heuristic approach, which we call the falling tide algorithm, and apply it under a multi-objective framework to find various compromise solutions. By this approach, not only can we achieve a trade off between the computational time and the solution quality, but also we can achieve a trade off between the conflicting objectives to enable better decision-making. ► Presenting a new approach called the falling tide algorithm for multi-objective optimization. ► Offering high quality solutions and enough flexibility in handling various types of constraints. ► The approach is easy to implement and just has a few intuitive parameters understandable to users. ► It could be adapted to other domains with different types and a different number of constraints.