Abdalrahman Algendi

• Algendi, Abdalrahman; Urrutia, Sebastián & Hvattum, Lars Magnus (2025). A matheuristic for the home healthcare routing and scheduling problem with ferry-dependent travel times. Computers & Operations Research. ISSN 0305-0548. 188(2026)(April ). doi: 10.1016/j.cor.2025.107372. Full text in Research Archive Show summary

  Home healthcare in coastal regions of Norway presents unique operational challenges, as caregivers must combine road driving with scheduled ferry trips to reach certain patients. Unlike conventional time-dependent travel, fixed ferry timetables impose strict synchronization requirements, where a missed departure may lead to prolonged idle times, cascading delays, or even unserved patients. Despite its practical significance, this integration of driving and ferry transportation has not been examined in the home healthcare routing and scheduling literature, leaving a gap between research and practice. To address this gap, we formulate a mixed-integer linear programming model that incorporates patient and caregiver time windows, skill matching requirements, and synchronization constraints, including those induced by ferry-dependent travel. Given the complexity of the problem, we propose a two-phase matheuristic. Phase I constructs a feasible solution through a sequential graph expansion strategy that employs either classical or weighted proximity search, while Phase II refines this solution using the same search method. Computational tests on 20 realistic instances derived from two Norwegian healthcare centers demonstrate that the proposed method with weighted proximity search outperforms direct model solving and the classical proximity search in terms of feasibility, optimality, and solution quality. In particular, the method solves instances with up to 30 patients (50 visits) to proven optimality and identifies high-quality feasible solutions for instances with up to 80 patients (135 visits) within a 3600-second time limit. [Available online 18 December 2025]

• Algendi, Abdalrahman; Urrutia, Sebastián; Hvattum, Lars Magnus & Melo, Rafael A. (2025). Nested logic-based Benders decomposition for an integrated home healthcare problem. European Journal of Operational Research. ISSN 0377-2217. 328(2026)(1), p. 32–48. doi: 10.1016/j.ejor.2025.06.006. Full text in Research Archive Show summary

  In this study, we apply nested logic-based Benders decomposition to solve an integrated home healthcare staffing, assignment, routing, and scheduling problem with application in Norway. The proposed method operates at two decomposition levels. Consequently, the entire problem is decomposed into three hierarchical sub-problems: the staffing problem, the assignment problem, and the routing and scheduling problem. These sub-problems are interrelated through two levels of logic-based Benders cuts. Computational experiments on 40 test instances demonstrate the superior performance of nested logic-based Benders decomposition compared to directly solving a mixed-integer linear programming model available in the literature. Specifically, the proposed solution method achieved proven optimality in 28 instances and provided feasible solutions for the remaining 12 instances. In contrast, directly solving the mixed-integer linear programming model yielded proven optimality in 16 instances, provided feasible solutions for 20 instances, and failed to find feasible solutions for 4 instances within the same computational time limit.

• Algendi, Abdalrahman; Urrutia, Sebastián; Hvattum, Lars Magnus & Helgheim, Berit (2024). Home healthcare staffing, routing, and scheduling problem with multiple shifts and emergency considerations. Networks: An International Journal. ISSN 0028-3045. 85(2), p. 223–242. doi: 10.1002/net.22260. Full text in Research Archive Show summary

  Effective planning of human resources is critical in designing an efficient home healthcare system. In this study, we present a novel home healthcare staffing, routing, and scheduling problem inspired by a real-world application. The proposed problem addresses a set of patients, with varying daily visit requirements, being served by a set of caregivers with different qualification levels over a multi-day multi-shift planning horizon. The problem aims to minimize the number of extra shifts for caregivers, maximize the allocation of caregivers to emergencies, and minimize the sum of route durations over the planning horizon. These objectives are optimized hierarchically while considering a set of restrictions, including time windows, skill matching, synchronization, care continuity, and labor regulations. To tackle the problem, we introduce a mixed-integer linear programming model. The model is then extended and two sets of valid inequalities are incorporated to enhance its tightness. Computational experiments are conducted on a set of 20 instances. The results highlight the efficiency of the proposed extension in increasing both the number of instances that can be solved to optimality and the number of instances for which a feasible solution is found.

• Algendi, Abdalrahman; Urrutia, Sebastián & Hvattum, Lars Magnus (2022). Optimizing production levels in maritime inventory routing with load-dependent speed optimization. Flexible Services and Manufacturing Journal. ISSN 1936-6582. 35(1), p. 111–141. doi: 10.1007/s10696-022-09460-z. Full text in Research Archive Show summary

  Maritime inventory routing problems with load-dependent speed optimization involves determining optimal routes, as well as vessel speeds and loads at these routes, so that inventory limits are satisfied at both production and consumption ports. This paper considers a variant where production rates can be selected from several available alternative production levels, as opposed to the normal situation where production rates are chosen a priori. In both cases, production rates remain constant for the duration of the planning horizon. The effect on transportation costs when considering production levels as decision variables is evaluated. The resulting solutions are compared with solutions obtained when production rates are considered as fixed parameters. Computational experiments on a set of benchmark instances from the literature confirm that the process of determining the optimal production levels plays a crucial role in improving the solutions to maritime inventory routing problems with load-dependent speed optimization. Optimizing the production levels can reduce transportation costs by up to 35%.

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• Algendi, Abdalrahman (2026). Optimization methods for integrated home healthcare routing and scheduling problems in a Norwegian context. Høgskolen i Molde - Vitenskapelig høgskole i logistikk. ISSN 9788279624103. Full text in Research Archive
• Algendi, Abdalrahman; Urrutia, Sebastián; Hvattum, Lars Magnus & Helgheim, Berit (2024). Home health care staffing, routing, and scheduling problem with multiple shifts and emergency considerations. Høgskolen i Molde - Vitenskapelig høgskole i logistikk. ISSN 9788279623625. Full text in Research Archive Show summary

  Effective planning of human resources is critical in designing an efficient home healthcare system. In this study, we present a novel home healthcare staffing, routing, and scheduling problem inspired by a real-world application. The proposed problem addresses a set of patients, with varying daily visit requirements, being served by a set of caregivers with different qualification levels over a multi-day multi-shift planning horizon. The study aims to achieve three objectives: minimizing the number of additional shifts, maximizing the allocation of caregivers to emergencies, and minimizing the sum of route lengths. These objectives are optimized hierarchically while considering a set of restrictions, including time windows, skill matching, synchronicity, care continuity, and labor regulations. To tackle the problem, we introduce a mixed-integer linear programming model. The model is then extended and two sets of valid inequalities are incorporated to enhance its tightness. Computational experiments are conducted on a set of 20 instances. The results highlight the efficiency of the proposed extension in increasing both the number of instances that can be solved to optimality and the number of instances for which a feasible solution is found. Keywords: Mixed-integer programming; Valid inequalities; Home healthcare; Human resource planning; Multiple shifts; Synchronization.

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