Optimization Models for Long-haul Freight Transportation Teodor Gabriel Crainic Dept. Management and Technology Université du Québec à Montréal and Centre for Research on Transportation Université de Montréal/H.E.C./Poly 2000

Transportation Systems Physical (Conceptual) Infrastructure and Services Production, Consumption of Goods and Services SUPPLYDEMAND Movements of people, goods, vehicles = Traffic Costs/profits, delays, energy, emissions, … Economic and legal environment

Transportation Systems Physical (Conceptual) Infrastructure and Services Production, Consumption of Products and Services SUPPLYDEMAND Movements of people, goods, vehicles = Traffic Costs/profits, delays, energy, emissions, … Economic and legal environment

Transportation Systems Physical (Conceptual) Infrastructure and Services Production, Consumption of Products and Services Modes and Services Stations and Terminals Vehicles and Convoys Routes and Frequencies Costs and Tariffs Economic Criteria Service Quality Criteria Mode Choice Multimodal Multicommodity Flows Performance measures

Transportation Systems Passengers vs. Freight User/Shipper vs. Carrier Urban vs. Interurban/Regional Uni- vs. Multi/Inter-modal Integration ? Intelligent Transportation Systems - ITS

Passenger Transportation Customized (door-to-door) services: private cars, walking, other modes vs. Consolidation transportation: transit Urban Multimodal Short planning horizons (hours) dependent upon time-of-day, day-of-week, week-of-year, … authorities plan, users decide

Freight Transportation Producers who own or operate the transportation fleet (and infrastructure) vs. For hire carriers Long-haul (intercity) transportation vs. Local vehicle routing and distribution Multimodal transportation system of a region vs. Carrier network and services Consolidation transportation vs. Customized (door-to-door) services

A B C a b c d e f Main route Feeder route Pick up and delivery route

Freight Transportation Many more actors/deciders/issues Variable planning horizons Products Terminals

Planning Levels Strategic Long-term Designs the system structure Tactic Medium-term Designs the service structure Operational Time-dependent Makes happen: dynamic management and control of resources, routes, schedules,...

Strategic System Analysis and Planning International, national, regional planning All (most) products All (most) transportation modes (infrastructure networks and services) Scenario analysis (what if ?) Infrastructure modifications Evolution of demand Technology changes Variations in policy and economic environment …

Methodological Approaches Spatial price equilibrium Route/mode choice/loading Network optimization Sequential shipper-carrier System-wide representation

System-wide Modelling Zones: origins and destination of freight Modes: transportation means/services Nodes and modal links Intermodal transfers Products: commodity groups Demand: origin-destination matrices by product (and mode choice) Output:product flows and costs on links (modes), transfers, and paths

Model Nonlinear (convex) multimode multicommodity network flow formulation

Technological Transfer Computer-based decision support systems Custom-made vs. tool box Example: STAN, Strategic Transportation Analysis, software for multimodal, multiproduct transportation systems

Consolidation Transportation Long distance freight carriers One vehicle/convoy serves many customers Railways Less-than-truckload motor carriers Intermodal container transportation Express package services Control agencies,...

Consolidation Transportation Accounts for a huge proportion of the freight moved both in volume and value Vital component of transportation and economic systems Less studied (compare to VRP, location, pure design) Fewer, more remote players Messier problems and formulations

A B C a b c d e f Main route Feeder route Pick up and delivery route

Consolidation Transportation Characteristics Regular services Consolidation terminals Frequencies and Schedules Operation efficiency = profits Service quality = customer satisfaction

Physical Network terminal Aterminal Cterminal Dterminal Eterminal F SERVICE: - origin terminal - destination terminal - mode - frequency Mode 1 Mode 2 terminal B

terminal Aterminal Bterminal Cterminal Dterminal Eterminal F ITINERARY: Path of services used to move freight from its origin to its final destination (B, F) (A, E) (B, F) Physical and Service Networks

terminal Aterminal Cterminal Dterminal Eterminal F Trade-offs: Operating costs minimisation vs. service quality maximization (B, F) (A, E) Freight consolidation BEST SERVICE AT MINIMUM COST (A, E) terminal B (B, F) and Itineraries

Cost vs. Service Trade-offs Number of markets satisfying the service targets (%) Firm 42% $ $ 73% $ 87% M (in 1000$) transportation and handling costs

Carrier Tactical Planning Goal: optimal allocation and utilisation of resources to achieve the economic and customer service objectives of the company Means: tactical plan (load, transportation, … plan) Evaluation tool of strategic alternatives

Carrier Tactical Planning Interrelated decisions Service selection: routes, frequencies, schedules Traffic distribution: itineraries, flow distribution Terminal policies Empty balancing Interactions and trade-offs Among operations Between cost and service quality (time) measures

Tactical planning issues for freight carriers generally addressed through Service Network Design formulations and methods

Service Network Design Its planning => Network view Planning horizon Strategic/Tactical Tactical/Operational Generally several interacting resources Usually several interacting objectives Certainly many decisions Static or dynamic (deterministic) formulations

Service Network Design: Model Classes Location Frequency Schedules/Dispatching (Dynamic)

Location Design Strategic long term design of infrastructure considering impact on services and traffic Location of terminals Location-routing Not many models specific for long-haul consolidation freight transportation Deterministic service network design models used to simulate scenarios

Location Design A few discrete location models Production-distribution Hub-network design Multicommodity location-allocation with balancing requirements

Multicommodity Plant Location The basic formulation Locate facilities to optimize the distribution of several commodities from plants to customers Capacities Product production at plants Customer demands by product

Multicommodity Plant Location

Production-distribution Network ABC PlantsWarehouse Terminals Customers

Production-distribution Locate depots to optimize the distribution of several independent products from plants to customers Capacities Product production at plants Total storage at depots/warehouses Customer demands by product

Production-distribution Network ABC PlantsWarehouse Terminals Customers

Production-distribution

Hub-location Locate terminals to consolidate regional flows into high-volume efficient inter-regional movements Trade-offs Consolidation time and costs (+ longer distances) More efficient transportation Long distance: full loads on large vehicles Short distance: small vehicles Increased flexibility in crew and fleet management

Production-distribution Network ABC PlantsWarehouse Terminals Customers

A B C a b c d e f Main route Feeder route Pick up and delivery route

Hub-location Integer (0,1) location/design variables at hubs Transportation flow variables Location and transportation costs Capacities Particular operations and service requirements

A Container Land Distribution and Transportation System Loaded container Empty container Empty vehicle

Location with Balancing Locate depots to optimize the distribution and transportation of empty containers Movements Customer to depot: return movement Depot to customer: allocation following request Between depots: to counter supply-demand imbalances and reposition for future periods

Network Structure (flows of empty containers) customers depots demand supply k j

Network Structure (flows of empty containers) customers depots demand supply k j

Location With Balancing Formulation

Location with Balancing Formulation

Frequency Service Network Design Objectives Strategic planning and scenario analysis Study of interactions and trade-offs among subsystems, decisions, objectives Typical issues What type of service? How often over the planning horizon? Terminal workloads Traffic itineraries (includes empties)

Two Major Approaches Service levels as Decisions Service levels as Output

Service Frequencies: Decisions Integer frequencies Continuous flows Nonlinear Mixed Integer formulations: frequency-related measures (costs, delays-congestion, etc.) Physical network: given infrastructure Service network: decision structure Traffic itineraries: on service network

F4 A1F1 A2F2 A3F3 A3 C X1 A4 C X2 A4 S C X3 A2 C A4 C X4 A2 T ITINERARIES FOR A TRAFFIC-CLASS (O-D-C) PHYSICAL NETWORK (NODES, LINKS) A4 SERVICE LEG SERVICE NETWORK (ROUTES, STOPS, MODES, FREQUENIES)

Model Elements Physical network Nodes: rail yards and stations, LTL breakbulk and end-of-line terminals, ports, … Links: tracks, roads, … Capacities and operational rules Service Route, type, costs,... Frequency

Model Elements Demand Market = origin, destination, commodity Empty vehicles = product(s) Volume Costs, service and operational rules Set of feasible itineraries Itinerary flows

Model Minimize Fixed cost of offering service Costs of moving the freight through the service network Penalties on unsatisfied service objectives or operational rules and characteristics (e.g., capacities) Subject to Demand satisfaction Service and operation constraints

Service Frequencies as Decision Variables Minimize Subject to and integer Specific service and operation constraints

Service Cost Determined by system characteristics and (potentially) all other services Cost of operations in terminals and en-route Cost of time (average delay) spent in terminals and en-route

Itinerary Cost Determined by system characteristics and (potentially) all services and itinerary flows for all markets Cost of operations in terminals and en-route Cost of time (delay) spent in terminals and en-route

Itinerary Cost Capacity considerations on service segments Compliance with service targets

Delays - A Few Examples Rail yard operations: car classification and blocking, train formation, … Consolidation of freight in vehicles Waiting at terminal gates before admission Train delays due to meetings and overtakes on the lines of the network. Departure/connection delays in terminals: the waiting time for the designated service to be available

Delays Representation: Congestion functions Models: Engineering procedures + queuing models

Service Levels: Outputs To operate or not (0,1) variables Continuous flows MIP (linear) formulations Frequencies from flows with lower bounds (minimum service levels)

A B C Main route Feeder route

Model Elements Network Nodes: LTL breakbulk and end-of-line terminals, … Links: services Service Breakbulk-to-breakbulk End-of-line breakbulk terminals Operational rules and costs Minimum service levels

Model Elements Demand Market = end-of-line end-of-line Volume: number of vehicles Costs and routing rules Empty vehicles Truckload movements (eventually)

Model Minimize Cost of running direct services at determined levels: Max{Minimum service level, Flow} Cost of moving the empties Cost of handling vehicles in breackbulks and end-of-lines Subject to Satisfy demand Routing policies (e.g., 1 route per market) Balance equipment

Model Service levels Minimize Total System Cost

Model Constraints Routing policies Demand satisfaction

Model Constraints Trailer balancing Variable specification

Dynamic Service Network Design Objectives Planning of schedules If or when services depart Traffic itineraries Space-time graphs

Space-time Diagram Holding arc Empty repositioning Loaded movement End of horizon Terminals Time Current PeriodFuture Periods

Dynamic Service Network Design To operate or not a given service at a given moment (0,1) variables Continuous flows (usually) Capacity constraints/considerations Special operational constraints (often) MIP formulations: the previous formulations in a time-dependent framework Deterministic (for now)

Most service network design and related issues yield Fixed Cost, Capacitated, Multicommodity Network Design Formulations

LINEAR PATH-BASED FORMULATION

SERVICE NET.DES. SOLUTION METHODS Network design formulations are difficult (even in simple cases) Problem instances are very large (time dependencies) Mainly heuristics and metaheuristics A few MIP (+ heuristics) methods Some models integrated in decision support systems

SOLUTION METHODS Work in progress on network design Metaheuristics Model analysis and polyhedral characterization Branch-and-bound (and cut, and price, …) Hybrids Parallel optimization

CONCLUSIONS Transportation offers many challenges and opportunities: planning, operations management, control (dynamic, real-time) Operations Research and Mathematical Programming models and methods offer good analysis framework and solution approaches Need to develop efficient implementations and user-friendly decision support systems

Many challenges yet Models (more realistic, more real-time) Math. analysis of formulations Computing efficiency Integration with Telecommunications Electronic commerce

Operational Planning and Management Crew scheduling Terminal and Line-haul operations Empty vehicle distribution and repositioning Dynamic allocation and dispatching of resources

Issues Time-dependent elements (e.g., demand) and decisions Stochastic variations in demands, supplies, travel times, … Network interactions still strong Impact of real-time information and ITS Decision support systems