Section Montréal de la SCRO- Double séminaire sur les applications de la RO
Home care aims at providing personalized medical care and social support to patients within their own home. It allows patients to avoid unnecessary hospital costs and either prevents or postpones long-term institutionalization. Since 2014, it has been the fastest-growing US industry attending to more than 14 million patients per year. In this work we propose a dynamic scheduling framework to assist in the assignment of patients to home care practitioners (or HPs). An HP attends to the individual for the entirety of their care (continuity of care requirement) and must travel to their homes in order to serve them. We formulate the assignment of patients to HPs within a home care agency as a discrete-time Markov decision process (MDP). We consider the amount of service each HP provides per period, the expected number of remaining visits a patient will need with an HP, and the total time an HP spends in-transit serving their patient panel. Due to the curse of dimensionality and the complex underlying combinatorial structure of the problem, we propose a one-step policy improvement heuristic that builds upon the agencies existing assignment strategy. Specifically, we apply machine-learning techniques to learn different probabilistic policies from historical data, and formulate the one-step improvement problem as an exponentially-sized mathematical programming model. Such a model can be solved using a Benders decomposition approach that simultaneously provides upper and lower bounds at each iteration. It can also be stopped at any desired optimality gap. We derive a new relaxation to speed-up the convergence of our method and show sufficient conditions under which this relaxation is solved efficiently. Several extensions account for patients that return for service, multiple HP assignments per patient, and patients who need periodic service are also provided. We test the quality of our solution methodology with data from a Canadian home health care provider to assess the service improvement as compared to their existing policies.
2e séminaire : Mid and long-term passenger demand forecast: The Kenza approach
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