Discrete firefly algorithm with compound neighborhoods for asymmetric multi-depot vehicle routing problem in the maintenance of farm machinery

We introduce a new variant of the vehicle routing problem, that is, the asymmetric multi-depot vehicle routing problem in the maintenance of farm machinery. When providing door-to-door service for farm machinery maintenance, there exists not only node service, (e.g., part replacement), but also directed arc service, (e.g., pulling the breakdown farm machinery from the farm location to the specified maintenance station). In the problem, there are multiple constraints, including the customer’s time window, maximum repairman working duration, fleet size, and vehicle capacity, etc. A mathematical programming model is formulated with the minimum total costs by transforming the problem into the asymmetric multi-depot vehicle routing problem with time windows. Discrete firefly algorithm with compound neighborhoods, presenting new neighborhood methods, is proposed to solve it. New procedures to evaluate the duration infeasibility are suggested with the reduced additional computational complexity. Computational results demonstrate that the proposed approach performs better than CPLEX solver, especially for large designed instances. Moreover, the proposed approach is superior to the other algorithms on solving benchmark instances of multi-depot vehicle routing problem with time windows. This study can provide decision support to door-to-door service for the maintenance of farm machinery.