Multi-Depot arc routing problems (MDARP) extend classical arc routing problems to the case in which there are several depots instead of only one. These problems combine two types of decisions: the allocation of required edges to depots and the planning of routes. The aim is to construct a minimum cost set of routes traversing each required edge of the graph, where each route starts and ends at the same depot. Applications of MDARPs arise in a wide variety of practical cases, namely garbage collection, road maintenance, mail delivery, snow plowing or pipelines inspection.
We present a worst-case analysis for the comparison with the case of one single depot. We also present compact integer linear programming formulations containing only binary variables, as well as a polyhedral analysis. Results from an exact branch-and-cut algorithm that includes several new exact and heuristic separation procedures are presented and analyzed. Instances involving up to four depots, 744 vertices, and 1315 edges can be solved to optimality.
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