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

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.

Bicriteria Vehicle Routing Problem with Preferences and Timing Constraints in Home Health Care Services

“…TW Simu Pre f Q Prec Reg [45] × × [46] × × × [47] × × × [48] × × [49] × × × [50] × × [47] × × × [48] × × [49] × × × [50] × × [51] × × × [52] × [53] × × × [54] × × × [55] × × [56] × × [57] × Table 4 shows that time windows and qualification are considered in the majority of the reviewed papers. However, some characteristics such as simultaneous synchronization, precedence synchronization, and periodicity have attracted less interest in the literature.…”

“…Cont. [21] × × × [22] × × × [23] × × × [24] × × × × [25] × × × [26] × [27] × [28] × [29] × [30] × [31] × [32] × [33] × × [34] × × [35] × × [36] × × [37] × × × [38] × × [39] × × × [1] × × [40] × × [41] × × [42] × [43] × [44] × [45] × [46] × [47] × × × [48] × [49] × [50] × × × [51] × × × [52] × [53] × [54] × × × [55] × × [56] × [57] × As shown in the last table, the objective of minimizing traveling costs, waiting costs, or patient preferences is undoubtedly the most widespread in the literature. However, when multiple objective functions are handled, they are often considered within a single criterion as a weighted sum.…”

Selecting Genetic Operators to Maximise Preference Satisfaction in a Workforce Scheduling and Routing Problem

“…The problem instances used in this study were also tackled in (Laesanklang and Landa-Silva, 2016;Pinheiro et al, 2016). This work seeks to identify effective combinations of genetic operators for tackling preference constraints in WSRP instances to then inform the design of competitive GAs to tackle this difficult problem.…”

“…See (Laesanklang and Landa-Silva, 2016) for details of the MIP model of this WSRP. Note that in (Laesanklang and Landa-Silva, 2016), unassigned visits constraint is considered as a soft constraint. However, here this is a hard constraint, hence all visits must be assigned.…”

“…However, here this is a hard constraint, hence all visits must be assigned. Additionally, in this paper, time-conflict constraint is introduced, while the study by (Laesanklang and Landa-Silva, 2016) avoided conflicts. The decomposition method divided a problem into sub-problems, then available workers were updated so that no conflicting assignments exists.…”