Shipper Transportation Design Problem

• STDP is a family of integrated shipper-side models that consolidate, route, and schedule shipments under capacity and cost constraints in global logistics.
• It employs diverse network representations such as time-space, two-layer, and hub-compressed graphs to manage consolidation and timing effectively.
• Operational objectives blend cost minimization, emission control, and capacity planning while addressing uncertainties and service regularity.

The explicit label Shipper Transportation Design Problem (STDP) appears in shipper-side inbound transportation planning for Renault’s global supply chain, where the problem integrates consolidation, routing, and regularity constraints over a six-month horizon (Brichet et al., 9 Sep 2025). Closely related formulations in courier transportation networks, hinterland less-than-container-load planning, daily package shipment on transit center networks, multimodal inbound logistics, hyperconnected relay transportation, shipment rerouting, and choice-driven service network design optimize analogous shipper-side decisions: how shipments are routed, consolidated, timed, priced, outsourced, and assigned to vehicles or services under cost, capacity, and service commitments (Lin, 2018, Jost et al., 2022, Wang et al., 2022, Camur et al., 2022, Li et al., 2024, Li et al., 9 Jan 2025, Nicolet et al., 2023). This suggests that STDP is best understood as a family of integrated shipper-side network design models rather than as a single canonical formulation.

1. Problem scope and planning perspective

In the Renault formulation, the decision maker is the shipper itself rather than a carrier or third-party operator. The planning problem decides which routes each part shipment should follow, whether to ship directly or consolidate through intermediate platforms, how often recurring flows should be sent, and how shipments should be packed into trucks or containers. The reported industrial scale is world-wide: more than 3,000 sites, 40 industrial sites, 100 logistics platforms, more than 40,000 distinct parts, 700,000 commodities, around 9,000,000 packages, and approximately 20,000,000 m$^3$ of volume (Brichet et al., 9 Sep 2025).

Other formulations instantiate the same shipper-side logic at different operational levels. In courier transportation network design, the courier enterprise determines the transportation organization mode for each origin–destination flow, allowing either direct transportation or a transfer chain through local distribution centers, airports, railway stations, and transfer/sorting centers (Lin, 2018). In hinterland LCL planning for DB Schenker, the planner jointly chooses origin ports, inland consolidation hubs, and direct-versus-hub routing for branch-to-port flows before ocean transport (Jost et al., 2022). In the daily package shipment problem on a transit center network, the enterprise must decide each day which vehicles to dispatch, which paths they should follow, how packages should flow on those paths, and how much demand should be outsourced, with instances involving more than 10,000 OD pairs at the whole-network level and a practical solution deadline of within one hour (Wang et al., 2022). In GE Gas Power’s inbound logistics setting, the design is multi-period and multimodal, with decisions over FCL, LCL, air, and ground transportation under delivery windows, booking lead times, and storage limits (Camur et al., 2022). In hyperconnected relay transportation, a logistics platform opens short-haul services and contracts truckers before demand is known, then assigns capacity and routes freight after demand realization (Li et al., 2024).

The planning horizon varies substantially across formulations. Renault’s STDP is tactical and strategic over six months (Brichet et al., 9 Sep 2025); the Chinese package-express model is daily and operational (Wang et al., 2022); the GE model is dynamic and multi-period (Camur et al., 2022); the relay-transportation model uses a five-day horizon with 6-hour time discretization (Li et al., 2024). A plausible implication is that the STDP concept is structurally stable across horizons, but its dominant constraints shift from daily dispatch and outsourcing to regularity, consolidation, and network-wide capacity design as the horizon expands.

2. Network representations and decision layers

A defining feature of STDP formulations is the use of network representations tailored to consolidation and timing. The Renault model begins with a static directed graph

$D=(V,A), \qquad V=S\cup P\cup U,$

where $S$ are suppliers, $P$ platforms, and $U$ industrial sites. The arc set is partitioned into supplier-to-platform collection arcs, platform-to-platform arcs, platform-to-unit delivery arcs, and direct supplier-to-unit arcs. It is then lifted to two time-expanded structures: a time-space graph $\mathcal{D}=(\mathcal{V},\mathcal{A})$ for actual timing, and a travel-time graph $\mathscr{D}=(\mathscr{V},\mathscr{A})$ for regularity and flexible delivery timing. Commodities are further aggregated into orders and bundles, with all orders in the same bundle required to use the same sequence of nodes (Brichet et al., 9 Sep 2025).

Other models compress or restructure the network differently. The localized package shipment on a transit center network introduces a two-layer graph: first-layer destinations shipped by the origin itself, and second-layer destinations handled via partial outsourcing from assigned first-layer transit centers (Wang et al., 2022). The LCL hinterland model uses a tripartite network of branches $B$, origin ports $S$, and destination ports $T$, with the practical restriction that for each pair $D=(V,A), \qquad V=S\cup P\cup U,$0, at most one inland hub may be used (Jost et al., 2022). The shipment rerouting problem reduces an underlying transportation network $D=(V,A), \qquad V=S\cup P\cup U,$1 to a complete digraph over hubs,

$D=(V,A), \qquad V=S\cup P\cup U,$2

where each arc represents a shortest path between hubs in the original network (Li et al., 9 Jan 2025). The mixed-transport collaboration problem assumes a metric space $D=(V,A), \qquad V=S\cup P\cup U,$3 over transportation bases and a database of lanes $D=(V,A), \qquad V=S\cup P\cup U,$4; a mixed transport $D=(V,A), \qquad V=S\cup P\cup U,$5 loads in the order $D=(V,A), \qquad V=S\cup P\cup U,$6 and unloads in reverse order because of the LIFO property of truck beds (Kira et al., 31 Mar 2025).

The choice of network representation determines which design layers are explicit. Static supplier–platform–plant graphs emphasize consolidation and regularity (Brichet et al., 9 Sep 2025). Time-space graphs emphasize departure times, due times, and service schedules (Li et al., 2024). Two-layer graphs make outsourcing endogenous rather than exogenous (Wang et al., 2022). Hub-compressed digraphs reduce route design to sequencing and capacity allocation over hubs (Li et al., 9 Jan 2025). Metric-space lane models emphasize geometric compatibility between collaborating shippers (Kira et al., 31 Mar 2025). This suggests that STDP models are best classified by the operational mechanism they encode—consolidation, timing, relay, pricing, or collaboration—rather than by a single graph template.

3. Objective structures and operational constraints

The objective functions in STDP formulations are integrated cost models rather than pure transportation-cost minimizations. In courier network design, the objective minimizes total cost including the accumulation cost, the transportation cost and the transfer cost, with transportation modes and types of transport carriers taken into account. The model also imposes capacities of transfer and sorting centers and delivery dates predefined (Lin, 2018). The accumulation component captures waiting while shipments accumulate for dispatch; transportation cost captures direct service movement; transfer cost captures handling, waiting, and operation at transfer or sorting centers (Lin, 2018).

In the DB Schenker LCL model, the integrated objective includes hub opening cost, hub consolidation cost, port consolidation cost, hinterland transportation cost, hub-to-port transportation cost, and sea transportation cost. Inland and sea costs are volume-dependent and reflect containerization structure. Early modeling choices therefore affect not only route length but also consolidation economies on both inland and ocean legs (Jost et al., 2022). In GE Gas Power’s model, the objective minimizes total transportation cost plus total FCL fixed-booking cost. The practical motivation is explicitly asymmetric in time: early delivery is undesirable because it creates inventory carrying cost and unloading/resource constraints, while late delivery can disrupt assembly and incur major operational penalties (Camur et al., 2022).

The Renault STDP objective combines transport cost on consolidated arcs, outsourcing cost on outsourced arcs, CO$D=(V,A), \qquad V=S\cup P\cup U,$7 / emission-related cost, platform handling and overload costs, and capital cost in transit (Brichet et al., 9 Sep 2025). Hyperconnected relay transportation instead minimizes expected total cost composed of first-stage driver-contracting cost, second-stage hauling-capacity rental cost, and outsourcing cost under demand scenarios (Li et al., 2024). Choice-driven service network design adds a revenue layer: the upper-level operator maximizes profit, whereas the lower level allocates demand according to utility over cost, time, frequency, accessibility, and, in stochastic variants, unobserved attributes and heterogeneity (Nicolet et al., 2023).

The constraint structures are equally heterogeneous but share several recurring motifs. Service-quality constraints include hard delivery deadlines in courier and package-shipment models (Lin, 2018, Wang et al., 2022), earliest/latest acceptable delivery times in GE’s inbound problem (Camur et al., 2022), and entry-time/due-time constraints in relay transportation (Li et al., 2024). Capacity constraints appear at sorting centers, hubs, service legs, trucks, FCL bookings, and platforms (Lin, 2018, Jost et al., 2022, Nicolet et al., 2023, Camur et al., 2022, Brichet et al., 9 Sep 2025). Design consistency constraints are also central: Renault imposes bundle-level path regularity across time (Brichet et al., 9 Sep 2025), while the relay-transportation model imposes strong consistency across repeated services in different cycles (Li et al., 2024). In the rerouting problem, indivisibility, pickup-before-delivery, route contiguity, and prefix capacity constraints couple sequencing and packing on each truck route (Li et al., 9 Jan 2025).

4. Representative mathematical formulations

A basic courier-network design formulation uses binary routing variables $D=(V,A), \qquad V=S\cup P\cup U,$8 for direct shipment and $D=(V,A), \qquad V=S\cup P\cup U,$9 for selection of first transfer node $S$0. Its core exclusivity condition is

$S$1

which enforces that each courier flow chooses exactly one organization mode—either direct or transfer-based (Lin, 2018). The same paper emphasizes that flows are unsplittable, so a flow may use road, rail, and air links in different combinations, but it cannot be split among multiple paths or modes (Lin, 2018).

A different but equally canonical STDP formulation appears in mixed transportation for shipper collaboration. For a mixed transport $S$2, the efficiency metric is the reduction rate

$S$3

with threshold $S$4. The design problem is: for a given anchor lane $S$5, find all partner pairs $S$6 such that the mixed transport $S$7 has reduction rate $S$8 (Kira et al., 31 Mar 2025). This formulation is not a classical flow model; it is an exact lane-matching and collaboration-enumeration problem over a logistics database.

At world scale, Renault’s STDP is formulated over bundle paths, time-space commodity flows, and explicit bin usage. Bundle-path flow conservation on the travel-time graph is written as

$S$9

while the bin-packing constraints on consolidated arcs are

$P$0

These equations encode the decisive modeling choice of the paper: consolidation is represented through an explicit one-dimensional bin-packing model rather than through aggregate capacity only (Brichet et al., 9 Sep 2025).

Service network design and pricing extends the formulation space further by using a bilevel model. The upper level chooses fleet allocation $P$1, service frequency $P$2, and OD prices $P$3; the lower level allocates total demand $P$4 between the operator and competing alternatives according to utility-maximizing behavior. The model is reformulated to a single-level MILP using KKT conditions and strong duality, with complementarity linearized by big-$P$5 binary variables (Nicolet et al., 2023). This shifts STDP from pure physical design to joint design-and-demand modeling.

5. Algorithms and computational evidence

The algorithmic literature around STDP is correspondingly diverse. In related logistics service network design, an exact Meta Partial Benders Decomposition strengthens the master problem with information derived from aggregating subproblem data and dynamically switches among master problems by changing both the amount of subproblem information included and the way it is aggregated; an extensive computational study shows that it outperforms existing benchmark methods (Belieres et al., 2020). In the Chinese daily package-shipment problem, the model is proved Strongly NP-hard, and a column-generation algorithm iteratively adds profitable paths, then strengthens the formulation with problem-specific cutting planes and variable bound tightening; on realistic instances from a major Chinese package express company, the model yields daily economic cost reduction up to 1 million CNY for the whole TCN and solves substantially faster than CPLEX (Wang et al., 2022).

For database-scale collaboration recommendation, the mixed-transport paper derives four pruning inequalities that are mathematically proven necessary for the reduction-rate threshold. The resulting algorithm is exact rather than heuristic and can be extended to a top-$P$6 version with a binary heap. On real anonymized Japanese lane data with approximately $P$7 and $P$8, and on 1000 matching requests, the total time at $P$9 is reported as 124230.3 seconds for brute force, 563.2 seconds for pruning, and 17.1 seconds for the $U$0-best method; the paper states more than 7,000 times faster than brute force at $U$1 and more than 400,000 times faster at $U$2 (Kira et al., 31 Mar 2025).

Large industrial multimodal problems have motivated hybrid exact-heuristic methods. GE’s multi-period network-flow model is solved by Gurobi and by a rolling-horizon knapsack heuristic that focuses on FCL timing and composition. Across baseline test cases, the heuristic is on average 9.1% more expensive than the best feasible IP solution, but its average runtime is 54.4 seconds against 2524.4 seconds for the IP. In the no-FCL scenario, both the IP and heuristic return optimal solutions for every instance, with average runtimes of 19 seconds and 3.3 seconds respectively (Camur et al., 2022). Renault’s world-scale STDP instead uses a tailored Iterated Local Search combining shortest-path insertion, re-packing, consolidation neighborhoods, and MILP-based perturbations with giant-container approximations. On world instances with roughly 625,166–724,454 commodities and 1,192,022–1,198,366 arcs in the time-space graph, the ILS achieves an average gap of 7.9% to the best available lower bound and improves Renault’s current planning solutions by 23.2% (Brichet et al., 9 Sep 2025).

Alternative computational paradigms have also been tested. The shipment rerouting problem is modeled both as a classical mixed-integer formulation and as a constrained quadratic model for quantum annealing. On six real transportation networks, classical CPLEX runtimes for SRP grow from 0.0285 s to 101.2672 s, whereas the hybrid quantum runtimes remain around 3.03–3.10 s; on Sioux Falls, the total costs reported for SRP and QA match exactly at 18, 30, 44, 46, 61 for $U$3 (Li et al., 9 Jan 2025). These results do not imply a universal dominance of one paradigm, but they do show that STDP instances can be structured to exploit very different algorithmic architectures.

6. Uncertainty, behavior, regularity, and interpretation

A substantial branch of the literature treats STDP under uncertainty rather than under deterministic demand and cost. The interval transportation problem replaces exact supplies, demands, and unit costs by intervals $U$4, $U$5, and $U$6. It distinguishes weak and strong feasibility and optimality, gives a polynomial-time test for weak optimality, and studies the best optimal value and the worst finite optimal value, the latter being NP-hard for the balanced interval transportation problem (Garajová et al., 2023). In hyperconnected relay transportation, uncertainty is modeled by a scenario-based two-stage stochastic program. On an automotive-delivery case study in the Southeast USA, the deterministic design has total expected cost \$U$7422,985</strong>, implying a <strong><a href="https://www.emergentmind.com/topics/visual-semantic-salience-vss" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">VSS</a> of \$133,509 and about 24% savings; the deterministic design yields a 10.3% outsourcing rate, whereas the stochastic design achieves 0% outsourcing (Li et al., 2024).

Behavioral modeling further enlarges the STDP concept. In choice-driven service network design and pricing, the benchmark assumption is that shippers are pure cost-minimizers. The alternative formulation models shipper decisions by utility maximization with observed attributes such as cost, time, frequency, and accessibility, and with stochastic variants based on MNL and Mixed Logit. The deterministic choice-driven model yields actual profits more than 2.5 times those of the benchmark, and the stochastic variants produce roughly an additional 40% gain over the deterministic model. The Mixed Logit specification is reported to give the best prevision of realized demand and profit because it captures heterogeneity in cost sensitivity (Nicolet et al., 2023). This shows that STDP need not be limited to physical routing and consolidation; it can also include endogenous demand response.

Integrated planning is another recurrent theme. In the LCL hinterland study, integrated modeling of hub opening, port selection, routing, and consolidation has several advantages over partitioned planning, although it requires more computational effort. The integrated model routes about 20.79% to 49.65% of total shipment volume via hubs, with an average of 38.29% (Jost et al., 2022). Renault’s analysis further states that accurate bin-packing models are essential for realistic consolidation and that highly regular plans offer the best balance between cost and operational stability (Brichet et al., 9 Sep 2025). The relay-transportation study similarly finds that daily consistency can reduce total expected cost relative to weekly consistency in its setting, even though it increases contracted hours and truck-rental hours (Li et al., 2024).

Several common oversimplifications are therefore contradicted by the published formulations. STDP is not merely a shortest-path assignment problem; it often requires explicit consolidation, service design, and timing (Brichet et al., 9 Sep 2025, Camur et al., 2022). It is not always enough to optimize routing separately from facility or service decisions; integrated formulations repeatedly outperform partitioned ones (Jost et al., 2022). Nor is outsourcing a universally dominant remedy: the Chinese package-shipment model finds that partial outsourcing can reduce cost when co-optimized with local shipment design, whereas the Renault study reports that outsourcing is only attractive in low-volume contexts and that large-scale networks benefit from in-house planning (Wang et al., 2022, Brichet et al., 9 Sep 2025). Taken together, these results suggest that the economic value of outsourcing, regularity, and consolidation is strongly contingent on shipment density, temporal structure, and the fidelity of the underlying packing and service models.