Jonathan Patrick | Searcharxiv

arXiv2026

A Relaxation-Based Decomposition Approach for Solving a Supported-Evacuation Problem in Wildfires

This study addresses the critical yet under researched area of supported evacuation for vulnerable populations during wildfires, such as hospital patients and long term care residents, by developing a two stage stochastic optimization model that optimizes facility location, fleet sizing, and vehicle routing under strict time windows. To overcome the problem NP hard complexity, the authors propose an innovative solution methodology leveraging Logic Based Benders Decomposition, featuring Combinatorial Benders Cuts and logic based inequalities. Extensive numerical experiments and real world data from a community wildfire drill in Roxborough Park, Colorado, demonstrate that the proposed approach yields high quality solutions, significantly improving shelter placement, vehicle utilization, and overall evacuation efficiency compared to alternative policies.

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arXiv2024

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

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. Since 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.

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