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

Abstract

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