A vehicle routing problem with multiple overlapped batches

•A real vehicle routing problem with backhaul, time window and multiple batches is considered.•The problem includes vehicle assignment to overlapped batches and vehicle routing in batch.•We develop two tabu search algorithms to handle the problem.•We study the algorithm efficiency, tradeoff between traveling cost and customer service.

This paper considers a vehicle routing problem faced by an express company which tackles complicated operations involving time window constraints, multiple delivery and pick-up customer visits per day, multiple trips per vehicle, and latency cost for each delivery. It is challenging in that it involves multiple delivery and pick-up batches and the time spans of the batches are overlapped. We formally define the problem and develop two tabu search algorithms. By computational experiments, we find one algorithm outperforms the other by getting better solution in much shorter time. Moreover, our approach produces a significant cost saving for the company.