Dynamic Home Care Routing and Scheduling with Uncertain Number of Visits per Referral

Danial Khorasanian (), Jonathan Patrick () and Antoine Sauré ()
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Danial Khorasanian: Telfer School of Management, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
Jonathan Patrick: Telfer School of Management, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
Antoine Sauré: Telfer School of Management, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

Transportation Science, 2024, vol. 58, issue 4, 841-859

Abstract: Despite the rapid growth of the home care industry, research on the scheduling and routing of home care visits in the presence of uncertainty is still limited. This paper investigates a dynamic version of this problem in which the number of referrals and their required number of visits are uncertain. We develop a Markov decision process (MDP) model for the single-nurse problem to minimize the expected weighted sum of the rejection, diversion, overtime, and travel time costs. Because optimally solving the MDP is intractable, we employ an approximate linear program (ALP) to obtain a feasible policy. The typical ALP approach can only solve very small-scale instances of the problem. We derive an intuitively explainable closed-form solution for the optimal ALP parameters in a special case of the problem. Inspired by this form, we provide two heuristic reduction techniques for the ALP model in the general problem to solve large-scale instances in an acceptable time. Numerical results show that the ALP policy outperforms a myopic policy that reflects current practice, and is better than a scenario-based policy in most instances considered.

Keywords: dynamic home care routing and scheduling; uncertain number of visits; approximate linear program (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:58:y:2024:i:4:p:841-859

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