Urban Freight Tour Models: State of the Art and Practice Jos - PowerPoint PPT Presentation

1 Urban Freight Tour Models: State of the Art and Practice José Holguín-Veras, Ellen Thorson, Qian Wang, Ning Xu, Carlos González-Calderón, Iván Sánchez-Díaz, John Mitchell Center for Infrastructure, Transportation, and the Environment (CITE)

Outline 2  Introduction, Basic Concepts  Urban Freight Tours: Empirical Evidence  Urban Freight Tour Models  Simulation Based Models  Hybrid Models  Analytical Models  Analytical Tour Models  Conclusions

3 Introduction and Basic Concepts

Basic Concepts 4  A supplier sending shipments from its home base (HB) to six receivers R3 R2 R1 S-2 R4 R5 S-1 Notation: S-3 Loaded vehicle-trip Empty vehicle-trip R6 Commodity flow Consumer (receiver) HB  The goal is to capture both the underlying economics of production and consumption, and realistic delivery tours

5 Empirical Evidence on Urban Freight Tours

Characterization of Urban Freight Tours (UFT) 6  Number of stops per tour depends on: Country, city, type of truck, the number of trip chains, type of carrier, service time, and commodity transported 9 Average number of stops/tour 8 New York City Amsterdam 7 6 5 Denver 4 Alphen Apeldoorn 3 2 1 Schiedam 0 10,000 100,000 1,000,000 10,000,000 Population

Characterization of Urban Freight Tours (UFT) 7  Denver, Colorado (Holguín-Veras and Patil,2005): Combination Stops/Tour Single Truck Truck Average 6.5 7.0 1 tour/day 7.2 7.7 2 tours/day 4.5 3.7 3 tours/day 2.8 3.3  Port Authority of NY and NJ (HV et al., 2006):  By type of company:  Common carriers: 15.7 stops/tour  Private carriers: 7.1 stops/tour  By origin of tour:  New Jersey: 13.7 stops/tour  New York: 6.0 stops/tour

Characterization of Urban Freight Tours (UFT) 8  NYC and NJ (Holguin-Veras et al. 2012):  Average: 8.0 stops/tour 12.6%: 1 stop/tour  54.9%: < 6 stops/tour 8.7% do > 20 stops  Parcel deliveries: 50-100 stops/tour

9 Urban Freight Tour Models

Urban Freight Tour Models 10  The UFT models could be subdivided into:  Simulation models  Hybrid models  Analytical models

11 Simulation Models

Simulation Models 12  Simulation models attempt to create the needed isomorphic relation between model and reality by imitating observed behaviors in a computer program  Examples include:  Tavasszy et al. (1998) (SMILE)  Boerkamps and van Binsbergen (1999) (GoodTrip)  Ambrosini et al., (2004) (FRETURB)  Liedtke (2006) and Liedtke (2009) (INTERLOG)

13 Hybrid Models

Hybrid Models 14  Hybrid models incorporate features of both simulation and analytical models (e.g., using a gravity model to estimate commodity flows, and a simulation model to estimate the UFTs)  Examples include:  van Duin et al. (2007)  Wisetjindawat et al. (2007)  Donnelly (2007)

15 Analytical Models

Analytical Models 16  Analytical models attend to achieve isomorphism using formal mathematic representations based on behavioral, economic, or statistical axioms  Two main branches:  Spatial Price equilibrium models (disaggregate)  Entropy Maximization models (aggregate)  Examples include:  Holguín-Veras (2000), Thorson (2005)  Xu (2008), Xu and Holguín-Veras (2008)  Holguín-Veras et al. (2012)  Wang and Holguín-Veras (2009), Sanchez and Holguín-Veras (2012)

17 Entropy Maximization Tour Flow Model

Entropy Maximization Tour Flow Models 18  Based on entropy maximization theory (Wilson, 1969; Wilson, 1970; Wilson, 1970)  Computes most likely solution given constraints  Key concepts:  Tour sequence: An ordered listing of nodes visited  Tour flow: The flow of vehicle-trips that follow a sequence  The problem is decomposed in two processes:  A tour choice generation process  A tour flow model

Entropy Maximization Tour Flow Model 19  Tour choice: To estimate sensible node sequences  Tour flow: To estimate the number of trips traveling along a particular node sequence Tour choice generation Tour flows 2014/4/15

Entropy Maximization Tour Flow Model 20  Definition of states in the system: State State Variable Individual commercial vehicle journey starting and ending at a home base Micro state (tour flow) by following a tour ; The number of commercial vehicle journeys (tour flows) following Meso state a tour sequence. Macro state Total number of trips produced 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.

21 Static version of EM Tour Flow Model

 The equivalent model of formulation 2: Entropy Maximization Tour Flow Model 22 M    MIN Z ( t ln t t ) m m m  1 m Subject to: M   Trip production  ( ) a t O i im m i constraints  1 m M   Total travel time  c t C ( ) T m T m 1 constraint  1 m M    c t C Total handling time ( ) H m H m 2  1 constraint m  t 0 m

Entropy Maximization Tour Flow Model 23  First-order conditions (tour distribution models) N N          * * * * * Formulation 1: t exp( a c ) exp( a ) exp( c ) m i im m i im m   i 1 i 1 N       * * * * t exp( a ) exp( c c ) Formulation 2: m i im 1 Tm 2 Hm  1 i  Traditional gravity trip distribution model   * * t A O B D exp( c ) ij i i j j ij Formulation 1 and the traditional GM model have exactly the same number of parameters

Entropy Maximization Tour Flow Model 24  The optimal tour flows are found under the objective of maximizing the entropy for the system  The tour flows are a function of tour impedance and Lagrange multipliers associated with the trip productions and attractions along that tour  Successfully tested with Denver, Colorado, data:  The MAPE of the estimated tour flows is less than 6.7% given the observed tours are used  Much better than the traditional GM

Case Study: Denver Metropolitan Area 25  Test network  919 TAZs among which 182 TAZs contain home bases of commercial vehicles  613 tours, representing a total of 65,385 tour flows / day  Calibration done with 17,000 tours (from heuristics)  Estimation procedure  Sorting input data: aggregate the observed tour flows to obtain trip productions and total impedance  Estimation: estimate the tour flows distributed on these tours using the entropy maximization formulations  Assessing performance: compare the estimated tour flows with the observed tour flows

 Estimated vs. observed tour flows Performance of the Models

27 Time-Dependent Freight Tour Synthesis Model

TD-FTS Model 28  Bi-objective Program: PROGRAM TD-ODS 1 Possible combinations   K M     of flow d d d Minimize z ( x ) x ln( x ) x m m m   d 1 m 1 2   A K K ' M Function to replicate  1       k kd d Minimize e ( x ) v x   a am m   2 TD traffic counts     a 1 k 1 d 1 m 1 Subject to: Trip Production K M      d Constraint g x O i N im m i   d 1 m 1 I can drop Trip K M       d x D j N jm m j Attraction Constraint   d 1 m 1 K M   Impedance Constraint  d c x C m m   d 1 m 1     x d 0 , m M , d K m

TD-FTS Model 29  Multi-attribute Value formulation: PROGRAM TD-FTS3       Utility function from DM       U e ( x ), z ( x ) v e ( x ) v z ( x ) Minimize 1 1 2 2 Subject to: Trip Production K M         d y ( ) x D j N , y Y j , y jm m , y j Constraint per Industry   d 1 m 1 K M Y   (  d c x C Impedance Constraint ) m m , y    d 1 m 1 y 1      x d 0 , m M , d K , y Y m , y

Application to the Denver Region 30 Daily Flows Time Intervals Flows Estimates Modeling Overall* Estimates Early Morning Morning After Noon Evening Approach RMSE MAPE RMSE MAPE RMSE MAPE RMSE MAPE RMSE MAPE RMSE MAPE Tour Flows S/TD-EM 39.8 31.2% 58.5 274.7% 45.6 42.3% 55.5 46.4% 39.5 106.1% 50.3 117.0% S/TD-FTS-A 17.2 16.6% 14.5 231.0% 14.7 29.2% 14.8 31.0% 9.5 68.7% 13.6 76.1% S/TD FTS-B 8.0 0.8% 9.5 46.3% 9.1 3.8% 6.4 4.9% 5.9 12.3% 9.1 22.9% OD Flows DCGM 116.0 79.5% 39.6 364.8% 42.0 94.5% 47.2 78.2% 25.8 148.1% 60.4 170.4% S/TD-EM 32.1 21.0% 58.3 257.0% 44.1 36.9% 56.9 42.7% 41.6 100.4% 50.7 109.0% S/TD-FTS-A 13.8 11.3% 12.6 153.4% 12.9 23.6% 14.6 25.8% 12.6 61.4% 13.2 66.1% S/TD FTS-B 5.7 5.2% 7.5 42.9% 8.9 9.0% 9.3 6.3% 10.5 21.6% 9.1 19.8%  TD-FTS MAPE’s : 0.8%-76.1%  Static Entropy Maximization (S-EM): MAPE’s 31.2%- 117%  Gravity Model (DCGM): MAPE 79.5%  Temporal aspect better captured using TD-FTS