By Scott Elliott, Principal Transportation Systems Architect at Strong Tower Consulting, LLC. Founded in Minnesota in 2008, Strong Tower Consulting has served motor carriers and freight brokerages for more than 18 years. Phone: 763-244-1373.
Motor carriers operating regional and national networks routinely encounter trailer supply imbalances. Manufacturing and distribution hubs generate consistent outbound loads that rapidly consume available empty trailers, while inbound freight returns equipment to other locations at a different rate. Without proactive intervention, these imbalances lead to yard starvation at high-volume origins and excess inventory at destinations, increasing deadhead miles and driver downtime.
Modern enterprise Transportation Management Systems (TMS) address this challenge by modeling empty trailer repositioning as a minimum-cost network flow problem. This technical guide examines the mathematical foundations, solver implementations, database schemas, integration patterns, and operational workflows required to deploy dynamic empty trailer redistribution engines inside production TMS platforms.
The Empty Trailer Imbalance Challenge
Network dispatchers at truckload and dedicated fleets monitor hundreds of terminals and customer facilities daily. A typical Midwest manufacturing shipper may require 40-60 trailers per day while returning only 10-15. The resulting deficit must be covered by either:
Empty (deadhead) movements from surplus locations
Substitution with power-only moves when equipment is unavailable
Third-party trailer rentals (increasing per diem expense)
Manual repositioning decisions become intractable as network size grows. Dispatchers must simultaneously consider:
Current and forecasted trailer inventory at every node
Driver hours-of-service (HOS) availability and restart cycles
Opportunity cost of using a driver for an empty move versus revenue freight
Linehaul cost, fuel, tolls, and driver pay for each potential repositioning lane
Service level commitments and customer detention policies
Maintenance schedules and trailer pool compliance rules
When these factors are evaluated manually, the result is often suboptimal equipment flows that fail to prevent regional shortages before they occur.
Modeling Trailer Repositioning as a Minimum-Cost Network Flow Problem
Enterprise TMS platforms represent the carrier's physical network as a time-space network or as a static graph with time-dependent costs. The empty trailer repositioning problem maps cleanly to the classic minimum-cost network flow formulation.
Network Components
Supply nodes (origins): Locations with projected trailer surplus (ending inventory greater than target safety stock)
Demand nodes (sinks): Locations with projected trailer deficit (projected demand exceeds available equipment after accounting for inbounds)
Transshipment nodes: Intermediate yards or drop yards where equipment can be staged without incurring full linehaul cost
Arcs: Feasible empty movement lanes between nodes, each carrying a cost, transit time, and driver HOS consumption value
The objective function minimizes total repositioning cost while satisfying trailer balance constraints across the planning horizon. A typical linear programming formulation appears as follows:
Minimize: Σ (cij * xij) + Σ (ok * yk)
Subject to:
Σ xij - Σ xji + si - di = bi ∀ nodes i
xij ≤ uij ∀ arcs (i,j)
Σ xij ≤ hk ∀ drivers k
xij, yk ≥ 0, integer
Where:
cij = fully burdened cost of moving one trailer from i to j (deadhead rate, fuel, tolls, driver wages)
xij = integer number of trailers to reposition from i to j
bi = net supply (+) or demand (-) at node i after accounting for loaded moves
ok = opportunity cost of assigning driver k to an empty move
hk = remaining HOS hours available for driver k within the planning window
Linear Programming and Network Solvers in TMS Architectures
Production TMS platforms implement empty trailer solvers using several complementary approaches:
1. Successive Shortest Path with Potentials
For moderate-sized networks (under 200 nodes), a successive shortest path algorithm with node potentials provides rapid integer solutions. Reduced costs are maintained using Dijkstra with potentials to guarantee optimality.
2. Linear Programming with Commercial Solvers
Larger networks integrate with solvers such as Gurobi, CPLEX, or open-source alternatives (HiGHS, SCIP). The LP is typically solved in relaxed form first, then integerized through branch-and-bound or rounding heuristics when fractional trailer counts appear.
3. Column Generation for Very Large Networks
When the number of feasible arcs explodes (inter-terminal, drop-yard, and customer combinations), column generation dynamically adds promising repositioning routes during optimization.
4. Rolling Horizon Execution
The solver executes on a rolling 3- to 7-day horizon, updated every 4-6 hours. Only the first 24-48 hours of recommendations are actioned; subsequent days are re-optimized as new order and telemetry data arrives.
Database Schema and TMS Integration Patterns
Effective dynamic repositioning requires a normalized data foundation. Core tables include:
network_nodes: terminal_id, customer_id, lat, lon, safety_stock, max_capacity
trailer_inventory: snapshot_timestamp, node_id, trailer_type, count, status (available, loaded, maintenance)
order_header & order_stop: used to forecast future trailer consumption and returns
Real-time integration with Electronic Logging Devices (ELD) and EDI feeds is essential. Strong Tower Consulting recommends event-driven architectures using Apache Kafka or Azure Service Bus to stream trailer check-in, gate activity, and load tender status into the inventory fact table. See our practice on ELD and EDI Integration for implementation details.
Recommended moves are surfaced to dispatchers through the TMS load board with clear cost justification and projected network impact. Acceptance or rejection by the dispatcher is recorded to improve future opportunity cost models through supervised learning layers.
Regulatory and Compliance Considerations
Empty repositioning movements remain subject to all FMCSA hours-of-service, ELD, and drug & alcohol testing rules. When a driver is assigned to a deadhead move, the TMS must:
Record the movement as a "deadhead" or "non-revenue" load type in the ELD
Ensure HOS compliance before tendering the move
Maintain audit-ready records of the solver decision rationale for at least six months
Integration with transportation accounting systems must properly segregate deadhead costs from revenue freight to support accurate per-mile costing and customer profitability analysis. Our Transportation Accounting Integration practice outlines the required GL mapping and cost allocation patterns.
Operational Impact and Best Practices
Carriers that deploy network flow-based repositioning engines typically observe reduced trailer shortages, lower overall deadhead percentages, and improved driver utilization. The system continuously trades off immediate cost against future network balance, preventing the "fire drill" repositioning runs that occur when yards reach zero available equipment.
Implementation success depends on three foundational practices:
Accurate daily trailer inventory and forecast data (achieved through rigorous yard management processes and real-time EDI/ELD feeds)
High-quality arc cost data that reflects fully burdened driver and equipment expense by lane
Change management that positions the solver as a decision support tool rather than an automated dictator; dispatchers must retain override authority with feedback loops back into the model
Strong Tower Consulting assists motor carriers with the full lifecycle of such initiatives, from network flow model design through solver selection, database schema development, TMS integration, and post-implementation tuning. Our TMS Implementation, Business Process Optimization, and Reporting and Analytics practices provide the necessary complementary capabilities.
Applicable Segments
This optimization approach delivers value across multiple industry verticals:
How frequently should the empty trailer solver execute?
Best practice is a rolling horizon updated every 4-6 hours during peak planning periods. This frequency captures new order intake and real-time inventory changes while avoiding solver thrash.
Can the model incorporate multi-trailer-type constraints?
Yes. The network can be modeled with separate flows for dry van, refrigerated, flatbed, and specialized equipment. Additional constraints enforce compatibility between trailer types and specific customer requirements.
What solver is appropriate for a fleet with 80 terminals?
For networks of this size, a commercial LP solver such as Gurobi or an open-source MIP solver with warm-start capabilities typically returns optimal or near-optimal integer solutions within 30-90 seconds.
How are opportunity costs for drivers calculated?
Opportunity cost is derived from historical revenue per driver-hour in each region, adjusted by current load density. The TMS maintains a moving average that the solver references when deciding whether to assign a driver to an empty move or hold them for higher-value freight.
Optimize Your Trailer Network
Strong Tower Consulting, LLC and Exspeedite LLC are separately organized sister companies under common ownership (separate EINs; liability firewall). Scott Elliott is founder and transportation systems architect of both.
Whether you are evaluating a new TMS selection, enhancing an existing platform with advanced optimization, or redesigning network operations, our team delivers authoritative guidance grounded in 18+ years of hands-on transportation systems architecture.
