A Selective Many-to-Many Pickup and Delivery Problem With Handling Cost in the Omni-Channel Last-Mile Delivery

This paper introduces a selective many-to-many pickup and delivery problem with handling cost (SMMPDPH) arising in the omni-channel last-mile delivery. In SMMPDPH, each request is associated with multiple pickup and delivery nodes, which provide or require commodities. A request is to load commodities from the pickup nodes and transport them to the delivery nodes. Since the total supply is greater than the total demand, we need to determine the selected subset of pickup nodes to visit for each request. Based on the loading and unloading policy, we take into account the handling cost incurred by additional operations. SMMPDPH aims to obtain a routing plan with the minimum total cost, including the travel cost and handling cost, for a fleet of homogeneous vehicles with limited capacity and driving mileage to satisfy the requests. We present two mixed integer programming formulations of the problem and propose two algorithms, including an iterated local search (ILS) and a memetic algorithm (MA), with specially designed move operators to solve the problem. Experiments on small instances clearly indicate the effectiveness of the two heuristic methods. With a comparison of efficiency on large-scale instances, we find that MA outperforms ILS in terms of both the best and average solution quality.