Decomposition techniques with mixed integer programming and heuristics for home healthcare planning

Laesanklang, Wasakorn; Landa-Silva, Dario

Abstract

We tackle home healthcare planning scenarios in the UK using decomposition methods that incorporate mixed integer programming solvers and heuristics. Home healthcare planning is a difficult problem that integrates aspects from scheduling and routing. Solving real-world size instances of these problems still presents a significant challenge to modern exact optimization solvers. Nevertheless, we propose decomposition techniques to harness the power of such solvers while still offering a practical approach to produce high-quality solutions to real-world problem instances. We first decompose the problem into several smaller sub-problems. Next, mixed integer programming and/or heuristics are used to tackle the sub-problems. Finally, the sub-problem solutions are combined into a single valid solution for the whole problem. The different decomposition methods differ in the way in which subproblems are generated and the way in which conflicting assignments are tackled (i.e. avoided or repaired). We present the results obtained by the proposed decomposition methods and compare them to solutions obtained with other methods. In addition, we conduct a study that reveals how the different steps in the proposed method contribute to those results. The main contribution of this paper is a better understanding of effective ways to combine mixed integer programming within effective decomposition methods to solve real-world instances of home healthcare planning problems in practical computation time.

Citation

Laesanklang, W., & Landa-Silva, D. (2017). Decomposition techniques with mixed integer programming and heuristics for home healthcare planning. Annals of Operations Research, 256(1), 93-127. https://doi.org/10.1007/s10479-016-2352-8

• Journal Article Type: Article
• Acceptance Date: Oct 5, 2016
• Online Publication Date: Oct 24, 2016
• Publication Date: Sep 30, 2017
• Deposit Date: Oct 27, 2016
• Publicly Available Date: Oct 27, 2016
• Journal: Annals of Operations Research
• Print ISSN: 0254-5330
• Electronic ISSN: 1572-9338
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 256
• Issue: 1
• Pages: 93-127
• DOI: https://doi.org/10.1007/s10479-016-2352-8
• Keywords: Home healthcare planning; workforce scheduling and routing; mixed integer programming; problem decomposition; heuristic decomposition
• Public URL: https://nottingham-repository.worktribe.com/output/885664
• Publisher URL: http://link.springer.com/article/10.1007%2Fs10479-016-2352-8