We present a centralized auction algorithm to solve the Multi-Depot Rural Postman Problem with Rechargeable and Reusable Vehicles (MD-RPP-RRV), focusing on rescheduling arc routing after vehicle failures. The problem involves finding heuristically obtained best feasible routes for multiple rechargeable and reusable vehicles with capacity constraints capable of performing multiple trips from multiple depots, with the possibility of vehicle failures. Our algorithm auctions the failed trips to active (non-failed) vehicles through local auctioning, modifying initial routes to handle dynamic vehicle failures efficiently. When a failure occurs, the algorithm searches for the best active vehicle to perform the failed trip and inserts the trip into that vehicle's route, which avoids a complete rescheduling and reduces the computational effort. We compare the algorithm's solutions against offline optimal solutions obtained from solving a Mixed Integer Linear Programming (MILP) formulation using the Gurobi solver; this formulation assumes that perfect information about the vehicle failures and failure times is given. The results demonstrate that the centralized auction algorithm produces solutions that are, in some cases, near optimal; moreover, the execution time for the proposed approach is much more consistent and is, for some instances, orders of magnitude less than the execution time of the Gurobi solver. The theoretical analysis provides an upper bound for the competitive ratio and computational complexity of our algorithm, offering a formal performance guarantee in dynamic failure scenarios.

This paper addresses the Capacitated Arc Routing Problem (CARP) using an Ant Colony Optimization scheme. Ant Colony schemes can compute solutions for medium scale instances of VRP. The proposed Ant Colony is dedicated to large-scale instances of CARP with more than 140 nodes and 190 arcs to service. The Ant Colony scheme is coupled with a local search procedure and provides high quality solutions. The benchmarks we carried out prove possible to obtain solutions as profitable as CARPET ones can be obtained using such scheme when a sufficient number of iterations is devoted to the ants. It competes with the Genetic Algorithm of Lacomme et al. regarding solution quality but it is more time consuming on large scale instances. The method has been intensively benchmarked on the well-known instances of Eglese, DeArmon and the last ones of Belenguer and Benavent.