Optimisation of a multilevel logistics network for prepositioned warehouses under an omni-channel retail model

The paper addresses the surge in online agricultural product purchases in China since 2020 and the consequent need for highly efficient logistics, especially for perishable goods. Prepositioned warehouses—small facilities located near consumers—enable rapid (within hours) delivery and can integrate offline stores to offer omni-channel services. Key characteristics considered are: complex logistics nodes; diverse consumer shopping behaviours (online and offline); critical importance of freshness for perishables; and stringent delivery-time constraints (often within one hour). Existing networks have shown deficiencies (e.g., suboptimal siting, freshness loss, delayed deliveries). Literature has not jointly considered omni-channel demand shifts, freshness dynamics, and cost–time trade-offs in one model. The paper poses two research questions: (1) How to optimise a three-level logistics network with prepositioned warehouses under omni-channel retailing? (2) What is the impact of key parameters (offline shopping preference, freshness penalty cost, and time–cost weights) on outcomes? The study develops a multi-objective mixed-integer planning model (LRIP) to minimise cost and time and validates it with data from Haidian District, Beijing, followed by sensitivity analysis.

The review covers: (1) Omni-channel retailing: origins, integrated consumer experiences, and logistics implications, including models for distribution under omni-channel contexts, vehicle routing, siting problems for prepositioned warehouses, and inventory models across channels. (2) Prepositioned warehouses: characterized as small, consumer-proximate facilities; research spans supply strategies, siting via center-of-gravity, and location–routing problems allowing replenishment. Prior work typically considers two nodes (regional distribution centers and prepositioned warehouses). (3) Agricultural logistics networks: objectives often minimise cost and time, incorporate customer satisfaction, and address perishability via freshness penalty costs, constraints on freshness-related inventory limits, and spoilage-integrated inventory models. (4) Location–routing–inventory problems (LRIP) in city logistics: joint optimisation of facility location, inventory, and routing is necessary; assumptions include deterministic demand, facility/vehicle capacities, single-visit service, and homogeneous fleets. Gaps identified: limited omni-channel-specific characteristics for prepositioned warehouses, lack of perishability integration in LRIP, and insufficient consideration of time alongside cost in e-commerce logistics.

Model context: A three-echelon network of suppliers → regional distribution centres (RDCs) → prepositioned warehouses (PWs) → consumer groups. PWs enable both online delivery and offline in-store purchases; demand is dense and clustered. Stage 1 (RDC→PW) uses small cold-chain trucks; Stage 2 (PW→consumers) uses electric bicycles. Objectives: minimise total daily cost and total delivery time. Key assumptions beyond standard LRIP: (1) Direct transport from RDCs to PWs; itinerant distribution from PWs to consumer groups. (2) A PW provides online and may also provide offline service but not offline-only. (3) Consumers within a radius of a PW may purchase in-store; if multiple PWs are nearby, a consumer chooses one for offline purchase. (4) PW inventory follows the EOQ model. (5) Freshness penalty occurs only during storage at PWs (as a daily penalty cost). (6) Out-of-stock, delayed delivery, and returns are not modelled. Decision framework: Sets for RDCs, candidate PWs, consumer groups, vehicles for each stage; parameters include facility and vehicle capacities, demands, distances, speeds, fixed dispatch costs, per-distance transport costs, siting cost, replenishment cost, holding cost, freshness penalty, and offline purchase radius and share (β). Decision variables include replenishment quantity Qi, cycle Ti, PW daily demand Di, vehicle flows and loads, siting variables zi, assignment variables xai, route variables y, and offline shopping choice sij. Inventory (EOQ) at PWs: Qi = sqrt(720 RC Di / HC) and Ti = Qi / Di; inventory costs per day comprise replenishment, holding (HC Qi/2), and freshness penalty (Cf Qi/2). Site selection cost aggregates construction and operating costs (LC zi). Transportation costs include fixed dispatch and distance-based variable costs for both stages; stage frequencies reflect Ti (RDC→PW) and daily delivery (PW→consumers). Total cost Z = cost_site + cost_inventory + cost_transport. Total time aggregates routing times for PW→consumer deliveries. Constraints ensure: each selected PW served by exactly one RDC; PW demand equals online plus offline components; capacity limits for PWs and vehicles; flow conservation and path continuity; each consumer group is served once; vehicle load constraints; load–unload relationships (also eliminating sub-tours); offline shopping assignment constraints (each consumer group visits at most one PW; PWs cannot be offline-only); and integrality/binary restrictions. Multi-objective handling: Normalisation plus linear weighting with weights αt (time) and αc (cost), αt + αc = 1, to form a single objective. Solution approach: Two-stage solving using Gurobi: first invoke built-in heuristics to obtain high-quality initial feasible solutions; then use branch-and-bound to refine to an exact or near-optimal solution. Empirical setting: Haidian District, Beijing, with 10 candidate PW sites, 40 demand points, RDCs located in suburban districts; vehicles: 2.6 m small cold-chain trucks (RDC→PW) and e-bikes (PW→consumer). Parameter values are based on literature, field investigation, and expert input.

Numerical results (Haidian District case):

• Optimal total cost: ¥112,228.14 per day; total time: 18.8; weighted objective Z: 0.098.
• Cost breakdown: site selection cost ¥80,000; inventory cost ¥21,380.97; transportation cost ¥10,847.17.
• Selected PW sites: 4 (IDs 1, 3, 6, 10). Required vehicles: 4 cold-chain trucks (RDC→PW) and 26 e-bikes (PW→consumers).
• Inventory strategy (examples): average daily demand and EOQ-derived policies yield frequent replenishments (mostly ≤2 days). Illustrative values: PW1 Di=376 kg, Qi=581.72 kg, Ti=1.55 days; PW3 Di=378 kg, Qi=583.27 kg, Ti=1.54 days; PW6 Di=140 kg, Qi=354.96 kg, Ti=2.54 days; PW10 Di=319 kg, Qi=535.82 kg, Ti=1.68 days.
• Routing: Consumer demand in southeast Haidian is partitioned into four service regions around the selected PWs. Two suburban RDCs replenish the two nearest PWs each. Most e-bike routes are designed to keep travel within 1 hour (with e-bike speed limit 15 km/h), except a route serving a distant northwest demand point. Average loading rates exceed 85% (all RDC→PW trucks ≥60%; PW→consumer vehicles ≥70%). Sensitivity analysis:
• Offline shopping share (β in [0.1, 0.9]): Increasing β reduces both total cost and total time, as more demand is met via in-store purchases, lowering delivery needs.
• Freshness penalty cost (Cf in [1, 5]): Total cost increases with Cf, while total time changes insignificantly, reflecting that storage-quality penalties affect costs more than routing.
• Time weight (αt in [0.1, 0.9]): As αt increases, total time decreases (better time performance) while total cost increases, indicating a clear cost–time trade-off.

The model addresses the research questions by jointly optimising PW siting, EOQ-based inventory policies, and last-mile routing, explicitly incorporating omni-channel behaviour (online delivery plus offline in-store purchases) and perishability via a storage freshness penalty. Results demonstrate that a four-PW layout with frequent small replenishments and carefully designed e-bike routes can achieve low total cost and near-instant delivery, aligning with operational goals for prepositioned warehouses. Sensitivity findings yield managerial insights: (1) Locating PWs where offline propensity is higher reduces both cost and time; (2) Quality control to reduce freshness-loss penalties is crucial since higher penalties directly increase costs; (3) Time–cost weighting reflects a trade-off—prioritising time improves service speed but raises cost—so firms must choose weights consistent with service-level goals and budget constraints. The approach is applicable to urban fresh-agri logistics and supports decisions in regions with dense demand and strict delivery-time expectations.

The study develops a mixed-integer LRIP model for omni-channel prepositioned warehouses that integrates EOQ-based inventory with siting and routing, jointly minimising cost and time. Freshness penalties during storage and offline shopping behaviour are explicitly modelled. A normalised linear-weighting transformation yields a tractable single-objective problem solved via a heuristic-initialised exact approach using Gurobi. Empirical results from Beijing’s Haidian District show that four PWs with frequent replenishment and optimised e-bike routing can achieve low total cost and rapid delivery. Sensitivity analyses confirm that greater offline shopping reduces logistics cost and time, higher freshness penalties increase cost with little time effect, and prioritising time reduces delivery time at the expense of higher cost. Future work should incorporate logistics organisation and information networks, supplier-side considerations, product categorisation, and time-varying freshness penalty functions.

The study focuses on physical network layout and does not model logistics organisation structures or information platforms; it primarily considers the demand side rather than suppliers; products are not categorised; and the freshness penalty is treated as a constant over time rather than a time-varying function.