A Tour-Based Urban Freight Transportation Model Based on Entropy Maximization Qian Wang, Assistant Professor Department of Civil, Structural and Environmental Engineering University at Buffalo, the State University of New York José Holguín-Veras, Professor Department of Civil and Environmental Engineering Rensselaer Polytechnic Institute SHRP2 Innovations in Freight Demand Modeling and Data Symposium Sep 15, 2010

Outline Background ▫ Motivations ▫ Objectives Methodology Case study Applications Conclusions 2

Motivations Complexity of freight activities ▫ Multiple measurement units used ▫ Multiple decision makers involved ▫ Diverse commodities shipped ▫ Trip chaining behavior  NYC: 5.5 stops/tour  Denver: 3.2 stops/tour  Passenger cars: 1 stop/tour 3 Example of a tour Base Producer Receiver 1 Receiver 2 Receiver 3Receiver 4

Motivation (Cont.) How to model and forecast urban freight movements given the limited data sources How to use GPS data without infringing on privacy ▫ Aggregation takes care of that  Smaller zones could be used, providing better detail ▫ No need to model disaggregate flows  No data available for the foreseeable future  Privacy issue will deter cooperation from carriers 4

Objectives To develop a tour-based model given: ▫ Trip production and attraction  from trip generation ▫ Travel impedances (times, cost, distance) To assess the impact of different impedance variables, such as the travel time and the handling time, on the performance of tour estimation 5

Modeling Framework 6 Tour generation Tour flow distribution model

Tour Flow Distribution Method Entropy maximization ▫ Formal procedure to find the most likely solutions given a set of constraints ▫ Provides theoretical support to gravity models It provides the flexibility to incorporate secondary data (e.g., traffic counts) to demand forecasting ▫ e.g., entropy maximization can be used to reduce the solution space for the ODS models 7

Entropy of the System Three states of the urban freight system 8 StateState Variable Micro stateIndividual tour starting and ending at a home base Meso state The number of vehicle flows (called tour flows) following a node sequence Macro stateTotal number of trips generated by a node (production) Total number of trips attracted to a node (attraction) Formulation 1: C = Total time in the commercial network; Formulation 2: C T = Total travel time in the commercial network; C H = Total handling time in the commercial network.

Entropy of the System (Cont.) Entropy: defined as the number of ways to generate the tour flow distribution solutions Entropy maximization: to find the most likely way to distribute tour flows given the constraints associated with the macro state 9

Entropy Maximization Formulations Formulation 1 10 Trip production constraints Trip attraction constraints Entropy maximization Cost constraint Nonnegativity of tour flows

Resulting Models First-order conditions (tour flow distribution models) ▫ Formulation 1: Traditional gravity trip distribution model 11

Convexity of the Formulations Second-order condition ▫ Objective function: Hessian is positive definite ▫ Constraints: linear ▫ Overall: convex program with one optimal solution Solution algorithm: primal-dual method for optimization with convex objectives (PDCO) (Saunders, 2005) 12

Case Study: Denver Metropolitan Area The Denver travel behavior inventory data ( ) (TBI) survey 13

Case Study (Cont.) Test network ▫ 919 TAZs among which 182 TAZs contain home bases of commercial vehicles ▫ 613 travel itineraries, representing a total of 65,385 tour flows per day 14

Model Estimation Procedure Step 1: Obtain input data: Os, Ds Step 2: Generate a set of candidate tours ▫ Using tour choice models ▫ Could be randomly and exhaustively generated too Step 3: Let the model find the optimal tours, i.e., the ones that match the trip generation constraints Step 4: Compare the estimations with observations 15

Performance of the Models 16 Estimated ResultsFormulation 1 MAPE6.71% Tour-time-related Lagrange multiplier ( ) Tour-travel-time-related Lagrange multiplier ( )/ Tour-handling-time-related Lagrange multiplier ( )/

Performance of the Models (Cont.) Distribution of tour time (travel + handling time) 17 Observed Estimated

Performance of the Models (Cont.) Distribution of tour travel time 18 Observed Estimated

Performance of the Models (Cont.) Distribution of tour handling time 19 Observed Estimated

Potential Applications: Could be the engine of a freight origin-destination matrix estimation technique that explicitly considers delivery tours Could be used to construct commercial vehicle tours from commodity flow estimates, without ambiguity regarding the underlying rules 20

Potential Applications (Cont.) Given the base-year tours 21 Input information: the base-year tours and the associated cost Aggregate the base-year information to get the trip productions/attractions and the total impedance Estimate the parameters (Lagrange multipliers) in the tour distribution model using the entropy maximization formulations: Estimate the future-year tour flows using the tour distribution models Calibration Application Formulation 1: Formulation 2: Predict future trip production and attraction

Conclusions The model is a general form of the gravity model It explicitly considers tour chains It is the first freight demand model able to represent tour behavior in a mathematical function It is able to replicate calibration data quite well 22

Future Work Consider more cost factors Incorporate traffic counts (ODS) Link commodity flows to vehicle flows 23

Questions? Qian Wang Department of Civil, Structural and Environmental Engineering University at Buffalo, the State University of New York 24