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 sub-problems 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.
Highlights
Home healthcare planning (HHC) is a type of workforce scheduling and routing problem (Castillo-Salazar et al 2014)
We propose two improved decomposition methods: Geographical Decomposition with Conflict Repair (GDCR), and Repeated Decomposition and Conflict Repair (RDCR) which will be described in Sects. 5 and 6 respectively
Table presents percentage of heuristic assignment made in GDCR, objective value from using GDCR, the number of iterations used in RDCR, objective value from using RDCR and percentage differences between the two solutions Bold text presents better solution Positive percentage difference refers to the case that RDCR provides better solution Negative percentage difference refers to the case that GDCR provides better solution
Summary
Home healthcare planning (HHC) is a type of workforce scheduling and routing problem (Castillo-Salazar et al 2014). We propose here an improved decomposition technique, called Geographical Decomposition with Conflict Repair (GDCR), where the solving sequence is no longer required This method allows conflicting assignments to happen which are repaired later to produce a valid solution. The main contribution of this paper is to present two improved decomposition techniques to tackle real-world instances of the home healthcare planning (HHC) problem in the UK. These techniques are the Geographical Decomposition with Conflict Repair (GDCR) and the Repeated Decomposition and Conflict Repair (RDCR), which harness the power of modern mixed-integer programming solvers in order to produce high-quality solutions in practical computation time.
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