2002 Taniguchi Thompson

E. Taniguchi, Department of Civil Engineering, Kyoto University, Yoshidahonmachi,Sakyo-ku, Kyoto 606-8501, Japan. R. G. Thompson, Department of Civil andEnvironmental Engineering, University of Melbourne, Victoria 3010, Australia.

have their own specific objectives and tend to behave in a differentmanner. City logistics models need to recognize these factors.

Quantification of the consequences of city logistics initiatives isnecessary for their evaluation and planning. Predicting the impactsof city logistics initiatives for evaluation purposes requires modelingto be undertaken. Models should describe the behavior of the keystakeholders involved in urban freight transport. They should alsoincorporate the activities of freight carriers, including transportingand loading and unloading goods at depots or customers. Modelsmust also describe the traffic flow on urban roads for freight vehiclesas well as passenger cars. Models are also required to quantify thechanges in costs of logistics activities, traffic congestion, emissionsof hazardous gases, and noise levels after implementing city logisticsinitiatives.

MODELING FRAMEWORK

City logistics is based on the systems approach, of which modelingis a key component (4). Models are used to estimate the effects ofvarious changes in the urban distribution system without actuallychanging the system. There are three general types of network mod-els that are typically used for predicting the effects of city logisticsinitiatives: (a) supply models, (b) demand models, and (c) impactmodels (6). Supply models are used to predict the level of service ofthe freight system based on network characteristics and estimateddemand. Demand models predict the demand for urban goods move-ment on specific transportation links based on industry and residentcharacteristics within an urban area as well as the level of service onthe links. Impact models predict the financial, energy, social, envi-ronmental, and economic impacts of city logistics initiatives basedon the predicted demand and level of service.

The modeling framework adopted in this paper is composed oftwo submodels: (a) a probabilistic model for vehicle (pickupdeliv-ery truck) routing and scheduling problem with time windows(VRPTW-P) for each company and (b) a dynamic traffic simulationmodel for the fleet of pickupdelivery trucks and passenger cars onthe road network within the city.

The optimal assignment of vehicles to customers, the departuretime, and the visiting order of customers for each freight carrier aredetermined by the VRPTW-P model and become inputs to the dy-namic traffic-simulation model. The dynamic traffic-simulationmodel is based on a macroscopic dynamic-simulation BOX model(7 ). This model estimates the distribution of travel times on eachlink in 1-h intervals. The VRPTW-P model is then re-solved usingthe updated distribution of travel times on each link obtained fromthe BOX model. Thus, the distribution of travel times for each linkis represented by a normal distribution, in 1-h time intervals. Themodel, therefore, incorporates time-dependent travel times.

There are many commercial software packages for vehicle routingand scheduling. However, they generally use one value of forecasted

Urban freight systems are experiencing many problems due to higher lev-els of service and lower costs being demanded by shippers, with carriershaving to operate in increasingly congested road conditions. Trucks oper-ating in urban areas produce many negative impacts for society in termsof emissions, crashes, noise, and vibration. City logistics aims to globallyoptimize urban freight systems by considering the costs and benefits ofschemes to the public as well as the private sector. The concepts of citylogistics are introduced, and an outline is presented of some models thathave recently been developed to predict the consequences of intelligenttransportation systems. In particular, a stochastic vehicle routing andscheduling procedure that incorporates the variation of travel times isdescribed. Results indicate that this approach can lead to significantreduction in operating costs by carriers as well as shorter routes withfewer trucks and increased reliability for customers. This procedure alsoreduces emissions and fuel consumption.

There are many challenging problems concerning urban freighttransport. Shippers and freight carriers are required to provide higherlevels of service with lower costs to meet various needs of customers.They have made efforts to rationalize their freight transportation sys-tems, but this has often led to an increase in pickupdelivery trucktraffic in urban areas. This increase in the number of freight vehiclesusing urban roads has become a major source of traffic congestion,with many associated negative environmental impacts, such as airpollution and noise. In addition, current global environmental agree-ments urge freight carriers to reduce CO2 emissions produced fromtheir vehicles as well as from passenger cars.

Some researchers [e.g., Ruske (1), Kohler (2), Taniguchi and vander Heijden (3), and Taniguchi et al. (4)] have proposed the idea ofcity logistics to solve these difficult problems. The definition of citylogistics can be stated as the process for totally optimizing the logis-tics and transport activities by private companies with the support ofadvanced information systems in urban areas considering the trafficenvironment, its congestion, safety and energy savings within theframework of a market economy (5). Although some of the citylogistics initiatives listed below have only been proposed, others havealready been implemented in several cities:

Advanced information systems, Cooperative freight transport systems, Public logistics terminals, Load factor controls, and Underground freight transport systems.

There are four key stakeholders involved in urban freight trans-portation: (a) shippers, (b) freight carriers, (c) residents, and (d) admin-istrators. All of these key stakeholders in urban freight transportation

Transportation Research Record 1790 45Paper No. 02-2649

Modeling City Logistics

Eiichi Taniguchi and Russell G. Thompson

travel time for a link of road network. The authors developed anew model that incorporates the variation of travel times using sto-chastic programming techniques. The model uses historical data oftravel times.

STOCHASTIC VEHICLE ROUTING AND SCHEDULING

The distribution of goods in urban areas using road-based vehicleshas led to many environmental and social problems, such as air pol-lution, crashes, and noise. There is, therefore, a need to establish effec-tive procedures for minimizing the environmental and social costs oftransporting goods within cities.

Distribution Trends

Driven freight transportation systems (DFTS) characterize manycontemporary logistics services in manufacturing and retail sectors.Intelligent transportation systems (ITS) is a fundamental componentof just-in-time, quick-response, and efficient-consumer-responsesystems (8). However, narrow customer-specified time windows canlead to substantial increases in the travel time and number of trucksused to deliver goods (4). Such customer demands are leading tomore distance being traveled by trucks, resulting in increased emis-sions, noise, and energy consumption. Therefore, new proceduresneed to be developed that support DFTS but reduce the social andenvironmental costs of such delivery systems.

Intelligent Transportation Systems

Many cities have already developed extensive monitoring systemscapable of collecting vast amounts of data relating to the perfor-mance of urban traffic networks. Numerous ITS have already beendeveloped to automatically collect vehicle travel times (9). Tech-nology incorporating vehicle license-plate recognition using image-processing techniques has been implemented to collect and predictvehicle travel times in real time (10).

Several other methods can be used to automatically collect traveltime information for trucks, including specialized equipment withinvehicles such as global positioning systems (GPS) or electronic tags.GPS allow the dynamic location of a vehicle to be determined usingsatellite technology. Electronic tags installed on vehicles can bedetected by induction loops or other electronic scanning equipmentas trucks pass detectors. Travel times can be determined by compar-ing multiple readings of the same vehicle at different locations in thenetwork. Many cities now have some form of automatic travel-timedata-collection systems for performance monitoring and congestionmanagement. Private companies can also use such technology tomonitor travel times as part of their fleet management systems.

Stochastic Programming

Stochastic programming allows historical travel-time patterns that arerepresented by probability distributions to be used in vehicle routingand scheduling optimization procedures. Here, the objective functionexplicitly incorporates expected penalty costs that are estimatedusing stochastic travel times and the penalties incurred for arrivals atcustomers outside the designated time windows (Equation 1 andFigure 1).

46 Paper No. 02-2649 Transportation Research Record 1790

VRPTW-P Model Formulation

The VRPTW-P model is defined where a depot and a number of cus-tomers are specified for each freight carrier. A fleet of identical vehi-cles collects goods from customers and delivers them to the depot ordelivers goods to customers from the depot. A designated time win-dow specifies the desired time period the customer is to be visited.For example, in the case of collecting goods, vehicles depart fromthe depot and visit a subset of customers for picking up goods insequence and return to the depot to unload them. A vehicle is allowedto make multiple trips per day. Each customer must be assigned toexactly one route of a vehicle, and all the goods from each customermust be loaded on the vehicle at the same time. The total weight ofthe goods in a route must not exceed the capacity of the vehicle. Thisproblem is used to determine the optimal assignment of vehicles tocustomers, the departure time, and the order of visiting customers fora freight carrier. The VRPTW-P model explicitly incorporates thedistribution of travel times for identifying the optimal routes anddeparture times of vehicles.

The VRPTW-P model minimizes the total cost of distributinggoods with truck-capacity and designated-time constraints. The totalcost is composed of three components: (a) fixed cost of vehicles; (b) vehicle operating cost, that is, proportional to time traveled andspent waiting at customers; and (c) delay penalty for missing thedesignated pickup or delivery time at customers.

Let

C(t0, X) = total cost (yen);t0 = departure time vector for all vehicles at

the depot, t0 = {tl,0 l = 1, m};X = assignment and order of visiting cus-

tomers for all vehicles, X = {xl l = 1, m};xl = assignment and order of visiting cus-

tomers for vehicle l, xl = {n(i) i = 1, Nl};

Penalty (yen/min.)

Probability of arrival time

Penalty of early arrival and delay (yen/min.)

Arrival time (min.)

Arrival time (min.)

Arrival time(min.)

Cd ,n(i )Ce,n(i )

ten(i )tsn(i )1

1

FIGURE 1 Penalty for early arrival and delay atcustomers for the probabilistic model.

n(i) = node number of ith customer visited by avehicle;

d( j) = number of depots (= 0);Nl = total number of customers visited by

vehicle l;n0 = total number of d( j) in xl ;m = maximum number of vehicles available;cf,l = fixed cost for vehicle l (yen/vehicle);

l (xl) = 1 if vehicle l is used, 0 otherwise;Ct,l (tl,0, xl) = operating cost for vehicle l (yen);Cp,l (tl,0, xl) = penalty cost for vehicle l (yen);

ct,l = operating cost per minute for vehicle l(yen/minute);

tl,n(i) = departure time of vehicle l at customern(i);

T_

(tl,n(i), n(i), n(i + 1)) = average travel time of vehicle l betweencustomer n(i) and n(i + 1) at time tl, n(i);

tc,n(i) = loading/unloading time at customer n(i);pl,n(i) (tl, 0, t, xl) = probability that a vehicle departing the

depot at time tl, 0 arrives at customer n(i)at time t;

cd,n(i) (t) = delay penalty cost per minute at customern(i) (yen/minute);

ce,n(i) (t) = early arrival penalty cost per minute atcustomer n(i) (yen/minute);

N = total number of customers;D [n(i)] = demand of customer n(i) in kilograms;

tl,0 = last arrival time of vehicle l at the depot;ts = starting of possible operation time of

trucks;te = end of possible operation time of trucks,

Wl (xl) = load of vehicle l (kg); andWc,l = capacity of vehicle l (kg).

Then the model can be formulated as follows:

Minimize

where

subject to

D n i Wl ln i l

( )[ ] = ( )( ) x

x

( )6

N Nll

m

=

=

1

5( )

n0 2 4 ( )

E C t p t t c t c t dtp l l l l n i l l d n i e n ii

Nl

, , , , , ,, , , ( )0 0

00

3x x( )[ ] = ( ) ( ) + ( )[ ]( ) ( ) ( )=

E C t c T t n i n i tt l l l t l l n i c n ii

Nl

, , , , ,, , , ( )0 1

0

1 2x( )[ ] = ( ) +( )[ ] +{ }( ) +( )=

C c E C t

E C t

f l l l t l l ll

m

l

m

p l l ll

m

t0 011

01

1

, ,

, ( )

, , ,

, ,

X x x

x

( ) = ( ) + ( )[ ]

+ ( )[ ]

==

=

Taniguchi and Thompson Paper No. 02-2649 47

where

The problem specified by Equations 1 through 10 is to determinethe variable X, that is, the assignment of vehicles and the visitingorder of customers, and the variable t0, the departure time of vehi-cles from the depot. Note that n(0) and n(Nl + 1) represent the depotin Equations 2 and 3.

The distribution of travel times is required in Equation 1 for deter-mining the expected value of operating costs and penalty costs. Thisis the major difference between the probabilistic model (VRPTW-P)and the standard or forecast model (VRPTW-F), with the forecastmodel using only one value to represent the travel times, whereastravel times in the probabilistic model are represented by a statisticaldistribution. The dynamic traffic simulation calculates the distribu-tion of travel times, which can be approximated by the normal dis-tribution for every hour. Then the updated normal distribution is usedas input to the probabilistic model.

Figure 1 shows the penalty for vehicle delay and early arrivals atcustomers. The time period (t en(i) t sn(i)) of the penalty functiondefines the width of the soft time window in which vehicles arerequested to arrive at customers. If a vehicle arrives at a customerearlier than t sn(i), it must wait until the start of the designated timewindow and a cost is incurred during waiting. If a vehicle is delayed,it must pay a penalty proportional to the amount of time it wasdelayed. This type of penalty is typically observed in goods distri-bution to shops and supermarkets in urban areas. Multiplying thepenalty function and the probability of arrival time as shown in Fig-ure 1 can identify the penalty of early arrival and delay at customersfor the probabilistic model. The forecast model assumes the partic-ular time of a truck arrival. Therefore, the penalty for early arrivaland delay can be estimated by multiplying the penalty function bythe amount of time the truck arrives early or late.

The VRPTW-P is a nondeterministic polynomial (NP)-hardcombinatorial optimization problem. It requires heuristic methodsto efficiently obtain good solutions. Recently, several researchershave applied heuristic algorithms such as genetic algorithms (GAs)[e.g., Thangiah et al. (11)], simulated annealing [e.g., Kokubugataet al. (12)], and tabu search [e.g., Potvin et al. (13)] to obtain approx-imate solutions for the VRPTW. Gendreau et al. reviewed the appli-cation of such modern heuristic approaches to VRP and describedthe potential of such methods for tackling complex, difficult com-binatorial optimization problems (14). The model described in thispaper uses a GA to solve the VRPTW-P. GA was selected becauseit is a heuristic procedure that can simultaneously determine thedeparture time and the assignment of vehicles as well as the visitingorder of customers. GA generally starts with an initial population ofindividuals (solutions) and from these a next generation (set of solu-tions) is produced. Parents of subsequent generations are selectedbased on their performance or fitness. Using the characteristics of theparents, a number of operations are performed (crossover and muta-tion) to produce successive generations and to avoid local optimalsolutions. Generations continue to be produced until a satisfactorysolution is found.

= + ( ) +( )[ ] +{ }( ) +( )=

t t T t n i n i tl l l n i c n ii

Nl

, , , ,, , ( )0 0 1

0

1 10

t tl e, ( )0 9

t ts l , ( )0 8

W Wl l c lx( ) , ( )7

This model adopts the delay penalty that depends on the delaytimes at customers. However, if a truck of a freight carrier oftenarrives late at customers, it will have difficulty in renewing the con-tract the next time. The model represents such circumstances in amathematical way. Therefore, it is not easy to quantify the delaypenalty. If the delay penalty is increased, freight costs will obviouslyincrease. The early-arrival penalty can be simply time costs of wait-ing at nearby customers.

DYNAMIC TRAFFIC SIMULATION MODEL

The dynamic traffic simulation (modified BOX) model is based ona model that was originally developed by Fujii et al. (7 ). This modelis essentially a macroscopic model, but because the origin and desti-nation of each vehicle are defined, it is actually a hybrid macroscopic/microscopic model. Vehicles are assumed to choose the shortest pathwhen they arrive at a node using an estimated average travel time.The modified BOX model consists of two components: flow simula-tion and route-choice simulation. A sequence of boxes is used to rep-resent each link. Groups of vehicles flowing out of a box and into thenext box during the scanning interval represent the flow on links.There are two assumptions for modeling links: (a) the maximum flowduring a scanning interval is the same for all sections on links, and(b) no inflow and outflow are allowed in the middle of links. A con-sequence of the first assumption is that only the lowest section of alink can be a bottleneck, where a congestion queue starts. Two statesof flow, congested flow and free flow, are represented. The time fora vehicle to proceed through a congested queue Tc is given by

where Fc is number of vehicles in a congestion queue and Ce is theeffluent traffic volume.

The effluent traffic volume is the traffic volume that can flow outof the lowest section of a link into the lower link. The time requiredto go through the running area without any queue Tf is estimated by

where

Lf = length of flowing area without any queue,Vf = free running speed,K = traffic density,

K0 = critical traffic density, andQmax = maximum traffic volume.The modified BOX model explicitly describes the flow of

pickupdelivery trucks that depart from a depot and return to thesame depot. Pickupdelivery trucks are converted to passenger-carunits and the first-in, first-out rule is assumed on all links. The modelwas further modified to identify the arrival of specific vehicles atassigned nodes (customers).

The simulation model described above estimates travel times oneach link and allows link costs to be determined. Drivers are assumedto compose a cognitive map for each link based on its estimated linkcost. Drivers then choose routes based on their minimum travel cost

TL KQ K K

QVf

f

f= > =

max

max ( )if 0 13

TLV

K K QVf

f

f f= =if 0 12max ( )

T FCc

c

e

= ( )11


from the current node to the destination using their cognitive map. Itis assumed that all drivers have some experience in driving withinthe defined network. The function for estimating the link cost is

where

Ck = estimated cost on link k,Tkt = travel time on link k at time t, andk = disturbance term.

In this study, the disturbance term k is assumed to be normallydistributed, with the zero mean and variance 2 represented by

VRPTW-P APPLICATIONS

Test Conditions

The model described in the previous section was applied to a testnetwork with 25 nodes and 40 links, as shown in Figure 2. This roadnetwork is composed of the same type of roads, with free runningspeed of 40 km/h. Any node within the network can generate andattract passenger-car traffic. These nodes are referred to as centroidsand are also candidate nodes to be visited by pickupdelivery trucks.Ten freight carriers are assumed to operate a maximum of 12 pickupdelivery trucks in this network. Each freight carrier has one depotthat is randomly located on the network. Three different types oftrucks, having capacities of 2, 4, and 10 tons, respectively, can beused. However, only up to four trucks of each type can be operatedby each carrier. The passenger-car equivalence rates, operatingcosts, and fixed costs for each type of pickupdelivery truck arebased on results from recent studies of truck operations in Japan.The number of customers for each carrier was generated randomlybetween 14 and 22. The actual nodes to be visited for each carrierwere also determined randomly from all nodes in the network. Thefreight demand at each customer was determined based on the dis-tribution of freight demand at Kobe City.

k N~ , ( )0 152( )

C Tk kt k= + ( )14

1

6

11

16

21

2

@2.67km * 4 = 10.7km

@2.

67km

* 4

= 1

0.7k

m 7

12

17

22

3

8

13

18

23

4

9

14

19

24

5

10

15

20

25

FIGURE 2 Test road network.

Three types of time windows were permitted in this study: 1-h time windows for morning (9:0012:00), afternoon (13:0017:00),and no time window. The type and starting time of each cus-tomers time window were based on a recent survey in the Kobeand Osaka areas. The dynamic traffic simulation provides the dis-tribution of travel times on each link for the scanning interval. Inthis study, the scanning interval is 1 h. When the optimal routesand schedules were initially calculated, the average travel times oneach link were assumed to be equal to the travel times using freerunning speeds.

The dynamic traffic simulation requires information on passenger-car behavior and on optimal routes and schedules of pickupdeliverytrucks produced by the VRPTW-P model. This includes the depar-ture time and visiting order of customers. Passenger cars in this studyinclude actual passenger cars and trucks other than those that are con-sidered in the optimal routing and scheduling model. Passenger carorigindestination (O-D) tables for every hour were estimated usingtraffic generation rates at each centroid and the probability of O-Dchoice. The number of passenger cars for each hour was generatedusing a temporal demand pattern based on the traffic census conductedin Kobe City.

The model described here uses an iterative procedure for repre-senting day-to-day variation. Therefore, the travel time provided bythe dynamic simulation fluctuates between days. Figure 3 shows thecalculation procedure. Here, the generation of total passenger carschanged 4,375 vehicles/day 10% at all nodes (175 vehicles/dayat each node). After 10 days of operation, the iterative procedurestopped. The fluctuation of travel time at each link was within 5%.At the end of 10 days of operation, optimal routes and scheduleswere determined for freight carriers. Then they encountered threedifferent traffic conditions, Cases A, B, and C. The total generationof passenger cars per day for Case A was 6,500 vehicles/day; forCase B, 5,450 vehicles/day; and for Case C, 4,375 vehicles/day at allnodes. The generation at Case C is the same as in the previous 10 daysof operation. This generation was uniformly located at all nodes.Case A was more congested than Case B, which was more congestedthan Case C. The average speeds of Cases A, B, and C were 30, 35,and 38 km/h, respectively.


Results

Table 1 shows the change in total costs for 10 freight carriers for thethree traffic conditions. The table indicates that the probabilisticmodel can reduce the total costs compared with the forecast modelin all cases. The reduction of total costs from the forecast modelincreases in Cases A and B, with higher levels of congestion thanCase C. This means that freight carriers can obtain more benefits byusing the probabilistic model when traffic congestion becomesworse. The value of the stochastic solution (VSS) is defined as thepercentage of the total cost reduction by using the probabilisticmodel from the forecast model. The VSS in the three cases is 11%to 17%, which is a considerable amount of benefit by incorporatingthe uncertainty of travel times.

Table 1 also indicates that the delay penalty decreased by 24% to35% with the probabilistic model, which means that this model pro-vides better service to customers by reducing the risk of delay. How-ever, the early arrival penalty increased by 8% to 11%. The fixed costin three cases increased by about 5%, and the operation cost remainedat the same level as for the forecasted model. The small increase in thefixed cost is due to the slight increase in the number of trucks used bythe 10 freight carriers as shown in Table 2. The table shows that thenumber of 2-ton trucks was reduced by one and that two additional4-ton trucks were used in the optimal routes and schedules of theVRPTW-P model. As the authors assumed that each freight carrierhas 12 pickupdelivery trucks, the increase in the number of trucks iswithin the limitation of owned pickupdelivery trucks.

Here is an examination of why the probabilistic model candecrease total costs. Figures 4 and 5 show an example of an optimaldiagram of operating trucks given by probabilistic and forecastedmodels at the end of 10 days of operation in Figure 3. In Figures 4and 5, the horizontal lines, which reach both ends of the graph, indi-cate that the depot and other horizontal lines show the time windowsof customers. These figures demonstrate that trucks tend to arrive atcustomers earlier within the time window for the probabilistic modelthan for the forecasted model. In this case in Figures 4 and 5, thetotal delay time by the probabilistic model was 99 min and by theforecasted model was 907 min, which is 10 times as large as the timegiven by the probabilistic model. The optimal operation of the prob-abilistic model in this case used two trucks, whereas the forecastedmodel used one truck. In this way, the probabilistic model providesthe routing and scheduling planning to avoid delay at customers.

variation of car generation 4375 veh./day10%

Case B

5450 veh./day(car generation)

Case A6500 veh./day

(car generation)

VRP model

What day?1st - 10th day

Accumulationof

travel times

VRP model

BOX model

visiting order

Evaluation of freight costs and the environment

Case C4375 veh./day

(car generation)

BOX model BOX model BOX model

11th day

Model Costs Case A Case B Case Cfixed cost 238,043 238,043 238,043

Forecasted operation 214,207 197,634 188,051early arrival 20,608 22,496 24,356modeldelay 789,125 507,169 363,604total cost 1,261,983 965,342 814,054fixed cost 250,671 250,671 250,671change 5.3 5.3 5.3operation 212,495 195,822 187,991

Probabilistic change -0.8 -0.9 0.0early arrival 22,764 24,970 26,287modelchange 10.5 11.0 7.9delay 601,797 331,945 256,786change -23.7 -34.5 -29.4total cost 1,087,742 803,423 721,748change -13.8 -16.8 -11.3

unit: yen/dayFIGURE 3 Flowchart of the calculation procedure.

TABLE 1 Change in Total Costs of 10 Freight Carriers


to lead to solutions in which trucks arrive at customers earlier toavoid delay penalties.

Table 4 shows the CO2 emissions estimated based on the solutionsobtained by both the forecasted and probabilistic models, which werecalculated based on the average running speed of trucks. The CO2emissions of trucks decreased by about 6% using the probabilisticmodel compared with the forecasted model, whereas the CO2 emis-sions produced by passenger cars remained almost at the same levelfor both models. The reduction of CO2 emissions by trucks wasmainly due to 10-ton trucks. As shown in Table 3, the travel time of10-ton trucks decreased using the VRPTW-P model, which con-tributed to a reduction in total CO2 emissions from trucks, becausethe unit emission rate of 10-ton trucks is larger than for other smalltrucks. This is the reason why a reduction of CO2 emissions by truckswas achieved in spite of the increase of total travel time of trucks.

As shown in Table 4, the total CO2 emissions by passenger carsand trucks decreased by 1% to 3% using the probabilistic modelcompared with the forecasted model. Therefore, incorporating theuncertainty of travel times using the probabilistic model not onlyallows freight carriers to reduce their total costs but also improvesthe environment in terms of reducing CO2 emissions.

A dynamic vehicle routing and scheduling model with real-timetravel-time information has also been recently developed (15). Pre-liminary results indicate that this model can lead to a significant reduc-tion in operating costs, an increased level of service for customers, anda decrease in the running time for trucks.

Model Type of vehicle Number of vehicles2 ton truck 14 ton truck 310 ton truck 14

total 182 ton truck 04 ton truck 510 ton truck 14

total 19

Forecastedmodel

Probabilisticmodel

TABLE 2 Change in the Number of Trucks (10 Freight Carriers, Cases A, B, and C)

FIGURE 4 Example of an optimal trajectory diagram of operatingtrucks (forecasted model, 10-ton truck).

FIGURE 5 Example of an optimal trajectory diagram of operatingtrucks: (a) probabilistic model, the first 10-ton truck, and (b) probabilistic model, the second 10-ton truck.

The table below shows the total time to spare after arriving at cus-tomers until the end of their time windows. The total time to spareusing the VRPTW-P model is 20.5% longer than that using VRPTW-F model. The longer time to spare within the time window using theprobabilistic model allows drivers to avoid delays at customers incase of increasing travel times due to unexpected traffic congestion.This leads to the reduction of delay penalty as well as total costs. Thereason why the probabilistic model leads to longer time to spare isthat the delay penalty shown in Figure 1 is set much larger than theearly-arrival penalty. The specific value of the delay penalty for 2-,4-, and 10-ton trucks was five times as large as the early arrivalpenalty of a 4-ton truck. Therefore, trucks need to arrive earlier toavoid the high delay penalty. On the other hand, when the forecastedmodel is used, a single value of travel time is used instead of thetravel time distribution. No penalty is imposed for trucks unless theyarrive after the end of the time window. This can lead to optimalroutes in which trucks arrive very close to the end of time windows.

Total time to spare until the end of the time window (10 freightcarriers) is as follows:

Total time to spare (min)

Forecasted model 19,469Probabilistic model 23,452Difference, % 20.5

Table 3 shows the total travel time. The total travel time using theprobabilistic model is slightly larger than that using the forecastedmodel. The actual running time for both passenger cars and trucksdoes not increase much, but the waiting time of trucks increases by12% to 15%. This is due to the tendency of the probabilistic model


recently, collection of such data has been very limited. However,today sophisticated ITS allows us to obtain these data at low costs. Forpractical use, a conventional assignment software package can takeplace in the dynamic traffic simulation in the modeling procedure.Doing so would make it possible to apply the model to a large-scalenetwork of an entire urban area.

Public sectors should play an important role in installing equip-ment for measuring variable travel times on roads and in providinghistorical data sets to the logistics industry.

Some shippers and freight carriers are very interested in theauthors models, and the authors are undertaking a project to assessthe benefits of applying the models in practical cases with real traveltime data in the Osaka area of Japan. Once the benefits of using themodels are recognized in practical situations, shippers and freightcarriers will use them.

REFERENCES

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2. Kohler, U. An Innovating Concept for City-Logistics. 4th World Congresson Intelligent Transport Systems (CD-ROM), Berlin, 1997.

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7. Fujii, S., Y. Iida, and T. Uchida. Dynamic Simulation to EvaluateVehicle Navigation. Proc., Vehicle Navigation & Information SystemsConference, IEEE, 1994, pp. 239244.

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Publication of this paper sponsored by Committee on Urban Freight Transportation.

Model Type of vehicle Case A Case B Case Cpassenger car 66,497 49,001 36,1342 ton truck 65 40 39

Running 4 ton truck 499 447 417time

Runningtime

10 ton truck 3,398 3,111 2,964subtotal of trucks 3,962 3,598 3,419

Waiting truck 957 1,049 1,139time

Waitingtime

71,416 53,648 40,693passenger car 68,198 49,082 36,111change (%) 2.6 0.2 -0.12 ton truck 0 0 04 ton truck 932 813 761

10 ton truck 3,125 2,856 2,716subtotal of trucks 4,057 3,670 3,477

change (%) 2.4 2.0 1.7truck 1,093 1,208 1,271

change (%) 14.2 15.2 11.673,348 53,960 40,859

2.7 0.6 0.4

Forecastedmodel

Probabilisticmodel

unit: minute/day

total

totalchange (%)

Model Type of vehicle Case A Case B Case Cpassenger car 1686 1313 988

Forecasted 2 ton truck 2 1 14 ton truck 19 18 17model

10 ton truck 789 745 721subtotal of trucks 809 764 739

total 2495 2077 1727passenger car 1709 1314 987change (%) 1.4 0.1 0.02 ton truck 0 0 0

Probabilistic 4 ton truck 34 32 3110 ton truck 723 683 662model

subtotal of trucks 756 715 693change (%) -6.5 -6.4 -6.3

total 2466 2029 1680change (%) -1.2 -2.3 -2.7

unit: kg-C/day

TABLE 3 Total Travel Time

TABLE 4 CO2 Emissions

CONCLUSIONS

ITS provides many opportunities for reducing the social, environ-mental, and financial costs of goods distribution in urban areas. Inparticular, automatic vehicle-identification systems, systems mon-itoring vehicle location, provide us with a very good data set ofvariable travel times. Vehicle routing and scheduling proceduresincorporating these systems have good potential for being effectivecity logistics initiatives.

This paper described a probabilistic vehicle routing and schedulingmodel based on ITS. A reduction in the number of trucks, vehicle-kilometers of travel, and operating costs can be achieved by using theprobabilistic vehicle routing and scheduling model. This would resultin substantial social, environmental, and financial benefits. Thus, theprobabilistic model is an effective city logistics initiative.

For putting this type of modeling to practical use, users need to col-lect historical data of travel times on each link of a network. Until

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2002 Taniguchi Thompson