The Lagrangian Relaxation Approach for Home Health Care Problems

Lagrangian Relaxation for Mixed-Integer Linear Programming: Importance, Challenges, Recent Advancements, and Opportunities

“…MILP has multiple applications in problems of importance to society: ambulance relocation (Lee et al, 2022), balanced item placement (Gasse et al, 2022), cost-sharing for ride-sharing (Hu et al, 2021), drop box location (Schmidt and Albert, 2022), efficient failure detection in large-scale distributed systems (Er-Rahmadi and Ma, 2022), home healthcare routing (Dastgoshade et al, 2020), home service routing and appointment scheduling (Tsang and Shehadeh, 2022), inventory control under demand and lead time uncertainty (Thorsen and Yao, 2017), job-shop scheduling (Liu et al, 2021), facility location (Basciftci et al, 2021), flow-shop scheduling (Hong et al, 2019;Balogh et al, 2022;Öztop et al, 2022), freight transportation (Archetti et al, 2021), location and inventory prepositioning of disaster relief supplies (Shehadeh and Tucker, 2022), machine scheduling with sequence-dependent setup times (Yalaoui and Nguyen, 2021), maritime inventory routing (Gasse et al, 2022), multi-agent path finding with conflict-based search (Huang et al, 2021), multi-depot electric bus scheduling (Gkiotsalitis et al, 2023), multi-echelon/multi-facility green reverse logistics network design (Reddy et al, 2022), optimal physician staffing (Prabhu et al, 2021), optimal search path with visibility (Morin et al, 2023), oral cholera vaccine distribution (Smalley et al, 2015), outpatient colonoscopy scheduling (Shehadeh et al, 2020), pharmaceutical distribution (Zhu and Ursavas, 2018), plant factory crop scheduling (Huang et al, 2020), post-disaster blood supply (Hamdan and Diabat, 2020;Kamyabniya et al, 2021), real assembly line balancing with human-robot collaboration (Nourmohammadi et al, 2022), reducing vulnerability to human trafficking (Kaya et al, 2022), restoration planning and crew routing (Morshedlou et al, 2021)...…”