A Modified Benders Decomposition Algorithm for a Last-Mile Network with Flexible Delivery Options

The purpose of this paper is to introduce an integrated and specialized approach to tackling a challenging issue, known as “Last-mile Transportation”. This issue, which is classified in terms of the decision-making level at the tactical level, is a model of the operational and application processes of prominent businesses in online commerce in developed countries, while it has attracted little attention from an operation-research aspect. This is a single-echelon network that includes a central distributor, parcel lockers, and customers, allowing customers to take advantage of three flexible product delivery options after purchasing the product. In the first option, the parcels are delivered at the door and in the time window specified by the customer; In the second option, customers pick up the parcels from the desired lockers with a discount, and in the third option, customers leave the choice of delivery type to the company under gaining an attractive discount. Offering online targeted discounts based on a selected option to encourage as many customers as possible for cooperation with the company and the guarantee of gradual development of the parcel-locker network by a management lever are other innovations of this study. To solve this model, a Benders decomposition algorithm has been modified by variable neighborhood search (VNS) and local branching strategies. The results obtained from the analysis of parameters related to problem innovations indicate the efficiency and validity of this presented model in different scenarios and the proposed solution algorithm in large-sized instances.