G-2025-40
Learning-to-optimize for consolidation and transshipment in multi-store order delivery
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This study investigates multi-store order delivery services where customers can order from multiple stores for home delivery. We first consider separated-order delivery, where orders from different stores are processed and delivered individually. To improve customer convenience and operational efficiency, we introduce consolidated-order delivery, enabling customers to place a single order across stores and receive all items in one combined delivery. While this enhances convenience, it can increase delivery times due to additional routing for visiting multiple stores. To mitigate this shortcoming, we propose a consolidated-order delivery system with transshipment, allowing drivers to transfer orders at transshipment nodes for higher efficiency. We develop a mixed-integer linear program for the multi-store order problem that models different delivery systems, including separated-order delivery and consolidated-order delivery with or without transshipment. Due to computational challenges arising from routing decisions and time variables, we adopt a learning-to-optimize approach that integrates machine learning and optimization. Four methods are implemented for learning driver allocation decisions: Nearest Driver Allocation, Driver Assignment Neural Network (DANN), Driver Classification Neural Network (DCNN), and Graph-based Neural Network (GNN). Our experimental study reveals that GNN consistently performs the best in terms of accuracy, optimality gap, efficiency, and scalability to larger problem instances beyond the training set. The DCNN and DANN are effective with sufficiently large training sets and perform well when the instance scale in the testing set aligns with the training set. We conduct experiments across four U.S. regions using the learning-to-optimize method in a realistic setting with dynamic customer arrivals. We find that consolidated-order delivery with transshipment, coupled with a short-duration waiting strategy, consistently delivers superior performance, yielding shorter order completion times and reduced driver travel times through effective spatial and temporal consolidation. Waiting longer to batch more customers is advantageous under conditions of frequent customer arrivals and limited driver availability.
Published June 2025 , 35 pages
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