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

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

Towards facilitated optimisation

Optimisation modelling in healthcare has addressed a diverse range of challenges inherent to decision-making and supports decision-makers in determining the best solution under a variety of constraints. In contrast, optimisation models addressing planning and service delivery issues in mental healthcare have received limited attention. Mental healthcare services in England are routinely facing issues relative to scarcity of available resources, inequities in their distribution, and inefficiencies in their use. Optimisation modelling has the potential to support decision making and inform the efficient utilisation of scare resources. Mental healthcare services are a combination of several subsystems and partnerships comprising of numerous stakeholders with a diversity of interests. However, in optimisation literature, the lack of stakeholder involvement in the development process of optimisation models is increasingly identified as a missed opportunity impacting the practical applicability of the models and their results. This thesis argues that simulation modelling literature offers alternative modelling approaches that can be adapted to optimisation modelling to address the shortcoming highlighted. In this study, we adapt PartiSim, a multi-methodology framework to support facilitated simulation modelling in healthcare, towards facilitated optimisation modelling and test it using a real case study in mental healthcare. The case study is concerned with a Primary Care Mental Healthcare (PCMH) service that deploys clinicians with different skills to several General Practice (GP) clinics. The service wanted support to help satisfy increasing demand for appointments and explore the possibility of expanding their workforce. This research puts forward a novel multimethodology framework for participatory optimisation, called PartiOpt. It explores the adaptation and customisation of the and PartiSim framework at each stage of the optimisation modelling lifecycle. The research demonstrates the applicability and relevance of a 'conceptual model' to optimisation modelling, highlighting the potential of facilitated optimisation as a methodology. This thesis argues for the inclusion of conceptual modelling in optimisation when dealing with real world practice-based problems. The thesis proposes an analytics-driven optimisation approach that integrates descriptive, predictive, and prescriptive analytics stages. This approach is utilised to construct a novel multi-skill multi-location optimisation model. By applying the analytics-driven optimisation approach to the case study, previously untapped resource potential is uncovered, leading to the identification of various strategies to improving service efficiency. The successful conceptualisation of an optimisation model and the quantitative decision support requirements that emerged in the initial stages of the study drive the analytics-driven optimisation. Additionally, this research also presents a facilitative approach for stakeholder participation in the validation, experimentation, and implementation of a mathematical optimisation model. Reflecting on the adaptation and subsequent amendments to the modelling stages, the final PartiOpt framework is proposed. It is argued that this framework could reduce the gap between theory and practice for optimisation modelling and offers guidance to optimisation modellers on involving stakeholders in addressing real world problems