Mixed integer linear programming model for a multi-depot arc routing problem with different arc types and flexible assignment of end depot

This article addresses a street sweeping problem that extends the class of multi-depot arc routing problem by integrating a flexible assignment of end depot for each working shift. A unique team of specialized vehicles starts each shift from a depot, visits the required arcs and returns at the end of each shift to a depot. The service in the next shift should start from the end depot of the previous one. An additional new constraint imposes that the highway arcs must be serviced during a night shift while all others arcs (boulevard, street, etc.) can be swept during both day and night. The aim of this arc routing problem is to find optimal shifts that satisfy these two practical aspects, along with other constraints such as maximum shift duration. The problem is motivated by a real-world application that has not been previously studied in the literature. A mixed integer linear programming model is formulated with the objective of minimizing the total travel time and tested on newly generated instances based on Cordeau's multi-depot vehicle routing problem instances. The results show a generation of total travel time savings up to 12 % compared to the single depot arc routing problem.