Joint column generation and Lagrangian relaxation technique for incident respondent location and allocation

Incident response operations require effective planning of resources to ensure timely clearance roadways and avoidance secondary incidents. This study formulates a mixed-integer linear program minimize the total expected travel time maximize demand covered. The model accounts for location, severity, frequency incidents, dispatching locations, availability incident respondents. An integrated methodology that includes column generation Lagrangian relaxation with density-based clustering technique defines hot spots is proposed. hybrid approach applied an empirical case in Raleigh, NC. A network instance 10,672 sites, clustered search distance (ε) 5 min, solved efficiently optimality gap 1.37% 2 min. Benders decomposition implemented conduct benchmark analyses. numerical results suggest proposed algorithm can solve problem outperform solutions.