Mathematical models and heuristics for the home health care routing and scheduling problem

Mohammed Bazirha

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arXiv · 2312.08032

Mathematical models and heuristics for the home health care routing and scheduling problem

Mohammed Bazirha

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Abstract

This thesis addressed the HHCRSP, which is a class of workforce scheduling problems. The HHCRSP is an extension of the VRPTW to which the constraints related to the HHC context are added. It aims to provide care services to patients at their homes instead of going to the hospital. We dealt with three different problems from the optimization viewpoint. In the first one, we considered a deterministic model to tackle the HHCRSP with multiple time windows, multiple services, their synchronization if they are required to be simultaneous and skill requirements. We proposed a new mathematical to solve this problem along with a GVNS based heuristic to solve large instances. In the second problem, we extended the deterministic model to cope with uncertainties in terms travel and service times. We proposed two SPR models. In the first SPR model, we defined the recourse as a penalty cost for the tardiness of services and a remuneration for caregivers' overtime. In the second SPR model, we defined the recourse as skipping patients if their time windows should be violated. We embedded Monte Carlo simulation, which is used to estimate the expected value of recourse, into a GA based heuristic to solve SPR models. In the last problem, we kept the multi-objective aspect of the deterministic model without aggregating its objective functions, and we used algorithms based on Pareto dominance to find the non-dominated solutions and then involve the decision-maker to select which one he prefers. Two approaches, Pareto and decomposition based, with multi-objective evolutionary algorithms are adopted to solve the HHCRSP. Three algorithms are implemented: NSGA-II, MOEA/D and a hybrid NSGA-II with MOEA/D (hybrid) algorithm.

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BibTeX RIS

Mohammed Bazirha. 2023-12-13. Mathematical models and heuristics for the home health care routing and scheduling problem. https://arxiv.org/abs/2312.08032

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