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<p>Order fulfillment in omni-channel (OC) drug retailing necessitates the integrated optimization of order allocation and delivery routing. This integration is particularly challenging, as it requires collaboration among multiple pharmacies to fulfill online orders. To address this issue, we propose a novel variant of the pickup and delivery problem, namely the <i>Unpaired Multi-Pickup and Delivery Problem with Time Windows</i> (UM-PDPTW). This problem is distinguished by the incorporation of item-level allocation decisions that determine the sourcing pharmacy for each item in an order into vehicle routing decisions, together with item-flow decisions under multiple pickups per order. The UM-PDPTW is computationally intractable using existing algorithms or solvers, as it incorporates three interrelated NP-hard sub-problems: item allocation for multi-item orders, multi-commodity flow, and delivery routing. To solve this complex problem, we develop a decomposition-iteration-based algorithm, the <i>Iterative Allocation and Routing algorithm with Commodity Flow Matching</i> (IAR-CFM). IAR-CFM leverages the partial decoupling between item allocation and delivery routing decisions by duplicating the multi-commodity flow variables. It iteratively solves the sub-problems using tailored algorithms and coordinates them into a feasible solution to the primal problem. This coordinated solution is then further improved via an improved variable neighborhood search algorithm. Computational results indicate that IAR-CFM achieves optimal solutions for small-scale instances and near-optimal solutions for large-scale cases, surpassing the upper bounds provided by CPLEX by up to 41.96%. A comprehensive sensitivity analysis based on real-world omni-channel drug retailing scenarios yields managerial insights on delivery time commitments, capacity constraints, assortment compositions, and stocking modes. These findings offer practical guidance for optimizing operations in drug retailing and other similar fulfillment and delivery operations, especially those involving multiple fulfillment centers and synchronized visits.</p>

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Collaborative order fulfillment in omni-channel retailing: Unpaired multi-pickup and delivery problem with time windows

  • 期刊论文

  • 发表日期：

    2026年3月5日

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  • Mengqi Yu,
  • Mu Du,
  • Jennifer Shang,
  • Xiangpei Hu

摘要

Order fulfillment in omni-channel (OC) drug retailing necessitates the integrated optimization of order allocation and delivery routing. This integration is particularly challenging, as it requires collaboration among multiple pharmacies to fulfill online orders. To address this issue, we propose a novel variant of the pickup and delivery problem, namely the Unpaired Multi-Pickup and Delivery Problem with Time Windows (UM-PDPTW). This problem is distinguished by the incorporation of item-level allocation decisions that determine the sourcing pharmacy for each item in an order into vehicle routing decisions, together with item-flow decisions under multiple pickups per order. The UM-PDPTW is computationally intractable using existing algorithms or solvers, as it incorporates three interrelated NP-hard sub-problems: item allocation for multi-item orders, multi-commodity flow, and delivery routing. To solve this complex problem, we develop a decomposition-iteration-based algorithm, the Iterative Allocation and Routing algorithm with Commodity Flow Matching (IAR-CFM). IAR-CFM leverages the partial decoupling between item allocation and delivery routing decisions by duplicating the multi-commodity flow variables. It iteratively solves the sub-problems using tailored algorithms and coordinates them into a feasible solution to the primal problem. This coordinated solution is then further improved via an improved variable neighborhood search algorithm. Computational results indicate that IAR-CFM achieves optimal solutions for small-scale instances and near-optimal solutions for large-scale cases, surpassing the upper bounds provided by CPLEX by up to 41.96%. A comprehensive sensitivity analysis based on real-world omni-channel drug retailing scenarios yields managerial insights on delivery time commitments, capacity constraints, assortment compositions, and stocking modes. These findings offer practical guidance for optimizing operations in drug retailing and other similar fulfillment and delivery operations, especially those involving multiple fulfillment centers and synchronized visits.