Eur. Transp. Res. Rev. (2011) 3:103–112DOI 10.1007/s12544-011-0051-8

ORIGINAL PAPER

Assessing the value of information for retail distributionof perishable goods

Marta Flamini · Marialisa Nigro · Dario Pacciarelli

Received: 10 January 2011 / Accepted: 5 April 2011 / Published online: 19 May 2011© The Author(s) 2011. This article is published with open access at SpringerLink.com

Abstract This paper addresses quantitative methodsfor estimating the value of information from ITS inurban freight distribution. A real-life application onthe retail distribution of perishable goods is considered.The problem is formulated as a vehicle routing prob-lem with soft time windows and time-dependent traveltimes, and solved by using information affected bydifferent degrees of detail and reliability. The practicalperformance of these solutions is then evaluated bysimulation, to assess the joint benefit of using more re-liable and detailed information with different solutionalgorithms.

Keywords Information reliability · City logistics ·ITS · Vehicle routing · Time-dependent travel times

M. FlaminiData Management S.p.A., 1, Largo Lido Duranti,00128, Rome, Italye-mail: m.flamini@consul.datamanagement.it

M. Nigro (B)Dipartimento di Scienze dell’Ingegneria Civile,Università degli Studi Roma Tre, 62, Via Vito Volterra,00146, Rome, Italye-mail: mnigro@uniroma3.it

D. PacciarelliDipartimento di Informatica e Automazione,Università degli Studi Roma Tre, 79, Via della VascaNavale, 00146, Rome, Italye-mail: pacciarelli@dia.uniroma3.it

1 Introduction

The increase of congestion in transport system requiresinnovative approaches to face the need for sustainablemobility. In this context, limiting the impact of freighttransport on road congestion is specifically important.In fact, the European freight road transport is expectedto increase by 55% by 2020 [1]. The traditional mea-sures to accommodate this growth, such as the ex-pansion of the existing transport networks, cannot bepursued, at least in urban areas. The rationalizationof the freight flows in the urban areas is thereforenecessary and this need is addressed by City Logistics[2, 3]. One of the basic concepts of city logistics isthe use of intermodal terminals. Here, goods incomingfrom different transport modes (rail, maritime, largetrucks) are stored and small vehicles are used for thedistribution of freights towards the urban area. Termi-nals are often located in the city neighborhoods, as nearas possible to the city center to reduce the distances fortruck collection and distribution [4].

Intelligent Transportation Systems (ITS) and tech-nologies can play a key role to optimize the organiza-tion of intermodal terminal and to reduce the impact offreight traffic on urban congestion. In 2008, the Euro-pean commission planned several actions aiming at theintroduction of the eFreight concept [5], consisting ofthe collection of real-time information on the locationand condition of transported goods, and of its integra-tion with other supply-chain activities and technologies,such as radio frequency identification (RFID).

In this paper we focus on the best use of ITS in-formation for the distribution of goods from an in-termodal terminal to the retailers located in an urbanarea. Specifically, we are interested in the development

104 Eur. Transp. Res. Rev. (2011) 3:103–112

of a quantitative method to estimate the value of suchinformation in the optimization process of the retaildistribution of perishable goods. The perishable goodsmarket is characterized by the short life time of prod-ucts, sometimes limited to few days, which turns outin a rapid depreciation of the product value. The dis-tribution must therefore comply with strict restrictionson the delivery times. This challenge requires, on onehand, effective optimization algorithms to plan punc-tual deliveries to the retailers at sustainable cost. Onthe other hand, there is a need for reliable and accuratedata on the road network to produce solutions that canbe implemented in practice.

Network traffic conditions deeply influence the linktravel times that constitute the main input of distri-bution problems. Travel times are affected both bysystematic variability (traffic condition in the differenttime slices) and stochastic variability (unforeseenevents, such as accidents or maintenance operations).Therefore, in order to effectively plan the deliveries,time-dependent travel times should be taken into ac-count. Tracking systems based on the RFID technologyor GPS offer a new opportunity to collect reliablereal-time information about network traffic conditions.Such information can be used both in real time, tolocate the position of a vehicle, and off line to estimatethe travel time of each element of the network with highlevel of precision and reliability. However, while thecost of implementing such measurement systems canbe easily computed, estimating the value generated byadvanced tracking systems is more difficult [6]. In fact,there is a need for scientific studies on the evaluationof the added value generated by advanced trackingsystems in distribution. This need motivates the presentwork.

The main contribution of this paper is the applicationof a new methodology to quantify the dependency ofdistribution cost from data reliability and data accuracy.The methodology is tested on a practical case studyarising in the urban freight distribution of perishablegoods. We consider an intermodal terminal located inthe suburban area of Rome (Italy) serving retailerslocated in the historical center. The center of Romeis characterized by narrow streets and high densityof commercial activities, which makes the distributionquite decoupled from the rest of the city since specificsmall vehicles have to be used in this area (smallerthan 3.5 tons). The case study is formulated as a vehiclerouting problem with soft time windows (VRPTW) forthe deliveries, in which the objective function includesthe transportation costs and the cost of late deliveries.Different solution algorithms have been implementedto solve the VRPTW, including simple greedy heuristics

and advanced tabu search algorithms. The effect of in-corporating practical experience of human dispatchersin the solution algorithm is also assessed by construct-ing a new neighborhood which takes into account thegeographical position of customers and routes. The de-gree of sensitivity of the different algorithms to processdata information has been then evaluated, thus lead-ing to a graphical representation of the dependencyof the distribution cost from the data reliability andthe algorithm adopted. Also the relation between costsand data accuracy is investigated by representing theevolution of traffic with different numbers of time slicesduring which traffic conditions are considered constant.

The paper is organized as follows. In Section 2 we re-vise some relevant related works. The research method-ology to assess the information value is described inSection 3. Section 4 deals with the formal descriptionof the vehicle routing problem. Solution algorithms aredescribed in Section 5 and the computational resultsare reported in Section 6. Some conclusions follow inSection 7.

2 Literature review

In this section we review the recent literature relatedto this paper. The approach followed in this paper isbased on (i) choice of methods and technologies fordata collection, (ii) choice of solution algorithms forsolving the vehicle routing problem described in theprevious section, (iii) computation of the added valuegenerated by data reliability in combination with thechosen solution algorithms. While an increasing num-ber of papers addresses the first two points, there is asubstantial lack of scientific research as far as the thirdpoint is concerned. Therefore, while this paper focuseson the third issue, we next review the recent literaturerelated to the first two points.

In the last years there has been an increasing inter-est in the literature on commercial vehicle tour datacollection and modeling [7]. Jarugumilli and Grasman[8] use RFID technology to enable efficient controlof inventory distribution by exchanging real-time in-formation upon arrival at each location. Wang et al.[9] use real time information from different ITS suchas RFID and GPS to optimally route and schedulevehicles in logistics and distribution services. Kim et al.[10] propose effective algorithms for data estimation,to be used once measures from the field have beencollected.

As for the literature on the vehicle routing problem,the TABUROUTE algorithm introduced by Gendrauet al. [11] is among the most well known solution

Eur. Transp. Res. Rev. (2011) 3:103–112 105

algorithms. The inclusion of time windows (VRPTW)has been addressed in a large number of papers, mostlyin the case in which travel times are time-independent.We cite, among the others: Solomon [12], Russell[13], Bramel and Simchi-Levi [14], Potvin et al. [15],Taniguchi et al. [16]. Cordeau et al. [17] considersoft time windows to take into account late and earlydelivery.

Time-independent travel times do not adequatelyrepresent all the real cases, since in practice traveltimes can be affected by strong variability both sys-tematic (traffic condition in the different time slices)and stochastic (unforeseen events, such as accidents ormaintenance operations). Limited research has beencarried out on vehicle routing problems with variabletravel times. We cite, among the others: Laporte et al.[18], Malandraki and Daskin [19], Taniguchi et al.[21, 22], Kenyon and Morton [23] and Taniguchi andShimamoto [24].

Ahn and Shin [25] are among the first researcherswho studied the vehicle routing problem with timewindows and time-dependent costs. Malandraki andDaskin [19] give a formulation of the VRPTW andtime-dependent costs, modeling the travel time fluc-tuation with a step function.

Ichoua et al. [20] propose a time-dependent modelfor a VRPTW, based on time-dependent travel speeds,computed dividing the planning horizon into three timeperiods. They extended the tabu search heuristic devel-oped by Taillard et al. [26] to solve the problem andperformed some experiments to evaluate the modelin static and dynamic environments. Fleischmann etal. [27] consider the Time-Dependent Vehicle routingproblem (TDVRP), defining the travel time functionwith a linearized step function. The authors show thatall the models, with the exception of [20], are incon-sistent since they do not represent the “no passing”(FIFO) property. Ando and Taniguchi [28] presents amodel for minimizing the total costs incorporating theuncertainty of link travel times with the early arrivaland delay penalty at customers who set up designatedtime windows.

3 Research methodology

This section describes the procedure adopted for esti-mating the value of information in our vehicle routingapplication. The basic idea behind the procedure is thatthe discrepancy between planned and implementedsolutions is only in minor part due to the inherentstochastic nature of travel times. Major differences are

due to the mismatch between the observed data, used tobuild the planned solution, and the actual travel timesoccurring in practice. In other words, the actual traveltime tij for a link (i, j) can be expressed as tij = dij + sij,where dij is a deterministic value and sij is a stochasticvariable due to perturbation events on transport de-mand and supply. The first quantity dij is the desiredvalue for solving the vehicle routing problem, such asthe expected value of tij or a value achieved with a givenprobability ψ (i.e., such that the probability Pr{tij ≤dij} = ψ). In practice, the exact value of tij is unknownand can only be estimated by collecting measures on thenetwork, which can be affected by measurement errors.Consequently, also the estimation of dij is affected bymeasurement errors. We let dest1

ij and test1ij be the esti-

mated values of dij and tij, respectively.We call discrepancy the quantity δij = test1

ij − dij. Iftest1ij is a rough estimate of tij, then the measurement

error can be much larger than the inherent stochasticityof the travel time, i.e., |δij| >> |sij|.

The use of an advanced tracking system may help tocollect more reliable information and thus to producea better estimate test2

ij of tij, i.e., an estimate such that|test2

ij − dij| << |test1ij − dij|. The value of such informa-

tion is related to the improved performance of thesystem that would have been achieved if the plannedsolution was built using the more reliable test2

ij instead oftest1ij . Since the discrepancy may vary over the different

routes to be traversed, we introduce an aggregatedvalue ε that we call the unreliability of the data set. Fora urban network with a set N of links, possible aggre-gations are the mean value of the discrepancies over allthe links, e.g. the mean value ε = 1

|N|∑

(i, j)∈N |δij|, or thesquare mean value ε = 1

|N|∑

(i, j)∈N(δij)2, or any other

aggregated representative of all data discrepancies. Inour computational experiments we use the mean value.

Our procedure computes the value of informationwith reference to a given vehicle routing algorithms A.It requires the production of several solutions with Afor varying the unreliability ε of the data set. Given thedata set and a value for the unreliability ε, we let ρ p(ε)

be the planned solution obtained with A on such dataset, ρh(ε) be the associated historical solution, obtainedby using the same routing as in ρ p(ε) and the actual datadij instead of test1

ij . Since the values tij are stochastic, alsothe performance of ρh(ε) is a stochastic variable. We letπ(ε) be the mean value of the performance achieved byρh(ε) for a given ε. Applying the same procedure forvarying ε, we get a curve π(ε) associated to the vehiclerouting procedure A being used. If using a certain typeof ITS one can decrease the information unreliabilityfrom a value ε2 to ε1 < ε2, there is then a performance

106 Eur. Transp. Res. Rev. (2011) 3:103–112

improvement π(ε2) − π(ε1), like shown by the curves ofFig. 1.

In this paper, we focus on computing the relationbetween data reliability and distribution costs. We donot address the exact computation of the probabilisticuncertainty of the information before and after theintroduction of ITS, which is very much related to thetechnology and the specific setting, and it is the subjectof more technology oriented ITS studies. However, itappears from the literature that there are many settingsin which suitable technologies, e.g. the RFID technol-ogy, make possible to reduce the unreliability ε nearlyto zero (RFID Journal October 2002 [29] and August2008 [30]).

It is worthwhile to mention that, very likely, differentvehicle routing algorithms may have different degreesof sensitivity to process data information. Therefore,when designing an intelligent transport system, it canalso be profitable to develop novel vehicle routingalgorithms that will use the more reliable information.

Figure 1 shows the cost π(ε) for two algorithmsAlgo1 and Algo2. Let us first focus on Algo1 andassume that the unreliability of the current informa-tion is ε2. Suppose that an advanced tracking systemmay reduce the unreliability down to ε1. The value ofinformation provided by the advanced tracking systemis β in Fig. 1, since this is the cost reduction achieved.Note that the value of information depends on thechosen vehicle routing algorithm. If the adoption ofthe advanced tracking system is combined with a newalgorithm Algo2, then the cost reduction becomes α +β, i.e., there is an additional benefit α due to Algo2.From Fig. 1, it follows that Algo1 is preferable to Algo2for highly unreliable data while Algo2 becomes the bestchoice for ε = ε1. In other words, it is important toassess the impact of advanced tracking systems in com-bination with different (simple and advanced) vehiclerouting algorithms. Clearly, it is worth paying the costof implementing the new tracking system and the newalgorithm Algo2 only if they generate sufficient ROI

εε2ε1

π(ε)

Algo 1

Algo 2α

β

Fig. 1 Performance for varying the unreliability

(Return On Investment), i.e., if the implementationcost is smaller than α + β.

4 Problem description

The problem addressed in this work is a vehicle routingproblem with soft time windows of [earliest,latest] de-livery times. An intermodal terminal IT must distributethe required amount of perishable goods to a givenset R of retailers by using a given set V of vehicles ofgiven capacity. We assume that an unlimited amount ofmerchandise and number of vehicles is available at IT.Each retailer r requests a certain quantity of goods dr

to be delivered within a given time window [tr, Tr].A feasible solution of the problem consists of con-

structing a route for each vehicle starting and ending inIT such that (i) the demand of each retailer is satisfied,(ii) each retailer is served by exactly one vehicle, and(iii) the capacity of each vehicle is not exceeded. In ourmodel, a vehicle arriving early at a certain retailer willwait until its earliest delivery time.

A vehicle arriving at time ar > Tr at retailer r incursa penalty cost wr for late delivery. This penalty wr isproportional to the probability pr that the delivery isrefused by the retailer:

wr = γr pr,

where γr is a given constant. We assume pr = 0 foron-time deliveries, i.e., for tr ≤ ar ≤ Tr. The probabilitythat a delivery is refused is pr = 1 for a delay ar − Tr ≥τmax and increases linearly from 0 to 1 when the arrivaltime is in the time window [Tr, Tr + τmax], as in Fig. 2.

Let ρ be the set of routes in a solution, each associ-ated to the vehicle v(ρi) used for route i. The cost ofroute i is given by three quantities: (i) the fixed costfv(ρi) associated to the usage of vehicle v(ρi), (ii) thevariable cost ci(ρi) associated to length of route ρi, and(iii) the penalty cost

∑r∈ρi

wr(ρi) for late deliveries. Theobjective function of the problem is therefore:

min|ρ|∑

i=1

[

fv(ρi) + ci(ρi) +∑

r∈ρi

wr(ρi)

]

(1)

Fig. 2 Probability of refusingdelivery

r

ar

1

0 τmaxtr Tr Tr+

Eur. Transp. Res. Rev. (2011) 3:103–112 107

5 Algorithms

In this section we describe the solution algorithms usedfor our analysis. We assess the performance of differentvehicle routing algorithms when varying the data reli-ability. Specifically, we consider a simple constructiveheuristic and two tabu search procedures.

The constructive heuristic groups retailers accord-ing to their geographical position and assigns to eachgroup the minimum number of vehicles necessary toaccommodate their total demand. Retailers belongingto the same group are ordered for increasing Tr andthen assigned in this order to vehicles. If the demandof retailer r does not fit in any of the available vehicles,a new vehicle is added and r is assigned to it. Otherwise,r is assigned to the available vehicle with the minimumremaining capacity.

When all retailers have been assigned to a vehicle, anadaptation of the 3-OPT local search algorithm [31] tothe case with time windows is used to sequence retailersserved by the same vehicle. This constructive heuristicis similar to the first steps of the procedure currentlyadopted at the terminal to plan vehicle routes.

The first tabu search procedure (hereinafter calledST or standard tabu search) implements the main fea-tures of the TABUROUTE algorithm introduced byGendrau et al. [11]. A solution S in ST is given bythe sequence of retailers served by each route. Theneighborhood of a solution S is the set of all the fea-sible solutions obtained by moving one of p randomlychosen retailers from its route in S to another routeserving at least one of the q retailers closest to it, wherep and q are two parameters of the tabu search. If amove leads to empty an existing route, the route iseliminated. An additional move consists in adding anew route to the set of routes and in assigning to itone of the p retailers. A move can lead to infeasiblesolutions that violate the capacity constraints of somevehicles. Infeasible solutions are penalized by a factordepending on the violation of the capacity constraints.

When the solution does not improve after a certainnumber of iterations, diversification strategies are usedto restart the search from new solutions.

The second tabu search procedure (hereinaftercalled AD or advanced tabu search) differs from ST forthe definition of a larger neighborhood of a solution,that is generated by considering an additional move.The new move emulates the behavior of human dis-patchers and is based on the geographical propertiesof the real application considered in this paper anddepicted in Fig. 3.

As described in Section 1, intermodal terminals aretypically located in the peripheral area of the cities.

IT

rf

rl

N(r)

r

IT

rf

rl

N(r)

r

Fig. 3 The new move

On the other hand, the retailers can be located in thecentral area of the city, as in our case study. In suchcase, each route includes a long path from IT to the firstserved retailer r f and a long path from the last retailerrl to IT. The new move allows moving a retailer r fromits current route to another, before r f or after rl, evenif r f or rl are not included in the q retailers closest to r.The solution S′ obtained after the move is included inthe neighborhood of S if the cost of S′ minus the cost ofS is below a given treshold σ .

6 Computational results

This section reports on the performance of the greedy,AD and ST algorithms on a real test case, located in asubarea of Rome (Italy). The code is implemented inC++ and runs on a PC equipped with a Intel 2 GHzprocessor and 2 GB of RAM.

6.1 Test case description

The network includes the historical center of Rome,where customers are located, and the south area untilthe Big Ring Road, where the intermodal terminalIT is located. The network is shown in Fig. 4 andconsists of 250 centroids, 425 nodes and 2,346 orientedlinks. Each node may host a customer, even if not allcustomers require a delivery in the same day. The his-torical center of Rome is characterized by many narrowstreets and by a large number of small activities, whichtranslate into specific problem characteristics such as

108 Eur. Transp. Res. Rev. (2011) 3:103–112

IT

cit

y c

en

ter

Ro

me

so

uth

1 km

Fig. 4 Rome network

the dimension and the number of customers and lowlink capacity values. The distribution of merchandisetakes place from 4:00 am to 11:00 am. In order tomodel the traffic conditions within this time window,about 280,000 vehicles are generated at the centroidsof the network considering the variable demand profileshown in Fig. 5.

For each hour, link travel times are obtained by sim-ulation using dynamic assignment model where trans-port demand can change during the simulation interval.For the dynamic simulation we use the DYNAMEQmodel: this is a dynamic traffic assignment model whichexploits variants of gradient like directions and themethod of successive averages to determine pre-trip dy-namic equilibrium path choices [32]. As a consequence,the travel times between each pair of retailers, as wellas between each retailer and the terminal IT, are time-dependent and can be represented by a vector whereeach component is associated to a certain time slice.

Table 1 Relative performance loss (percentage) between solu-tions and REF

ε GREEDY AD ST

0 271.3 2.9 33.510 449.5 47.2 73.820 456.0 53.0 88.430 481.1 59.1 90.340 512.6 59.1 90.450 559.2 60.0 111.060 618.5 70.9 111.570 647.5 63.4 110.780 675.1 64.7 116.790 697.5 72.0 118.7100 722.0 71.9 139.4

In our study, we consider these travel times values asthe actual traffic conditions in the network. To gener-ate errors on the input data, these travel times valueshave been randomly perturbed using the relation test

ij =dij(1 + x

100 ), where x is a random variable uniformlydistributed in the interval [−P, +P]. With this position,for each link (i, j) we get a discrepancy |δij| = dij|x|

100 . Weconsidered ten values for P = {10, 20, . . . , 100}, besidesthe reference case P = 0 in which input data is notaffected by error. We consider ten scenarios for thecustomer orders, each scenario consisting of one daywith 50 deliveries randomly located in the city center.For each value of P and for each scenario, ten randomperturbations of the travel times have been generated,thus obtaining a total of 1,010 instances of the vehiclerouting problem to be solved with the three algorithms.As an aggregate indicator of the unreliability we usethe unreliability ε expressed in percentage, i.e., ε =100 1

|N|∑

(i, j)∈N |δij|.

6.2 Results analysis

For the reference case ε = 0 and for the ten scenarios,Algorithm AD finds a better solution with respect toAlgorithm ST in eight out of ten cases. In the following,

Fig. 5 Demand profile

5

0

10

15

20

25

30

4.00-5.00 5.00-6.00 6.00-7.00 7.00-8.00 8.00-9.00 9.00-10.00 10.00-11.00time

dem

and

dist

ribu

tion

(%)

Eur. Transp. Res. Rev. (2011) 3:103–112 109

Fig. 6 Relative performanceloss (percentage) of solutionscosts computed by AD andST with respect to REF(seven time slices data input)

Relative performance loss with respect to REF

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50 60 70 80 90 100

ε [%]

AD

ST

[%]

the best solution obtained either by AD or ST for ε = 0is referred to as the REF solution.

Table 1 reports the average (in percentage) over allinstances of the difference between the performance ofeach of the three algorithms and the performance ofthe REF solution. In what follows, we refer to this in-dicator as the relative performance loss

[100π(ε)−REF

REF

].

For ε = 0 we report the relative performance loss overthe ten scenarios. For each ε �= 0 we report the averageover 100 instances (ten scenarios and ten perturba-tions). Clearly, the larger is the relative performanceloss, the worse is the performance of the algorithmin combination with a certain data unreliability. Thegreedy algorithm performs very poorly with respectto the two tabu search algorithms, the relative perfor-mance loss from REF ranging from 271.3 to 722.0%.With the AD and ST algorithms, the relative perfor-mance loss from REF is significantly smaller. It reachesa maximum of 139.4% with a perturbation ε = 100 inthe ST case.

A pictorial comparison between AD and ST is shownin Fig. 6. On average, AD outperforms ST for all valuesof ε, which demonstrates the effectiveness of the newneighborhood concept adopted by AD.

As for the sensitivity of the algorithms to the unreli-ability ε, Fig. 6 shows that there is a significant increaseof the distance with respect to the REF solution whenpassing from ε = 0 to ε = 10. For higher values of ε

the distances remain quite stable for AD and slightlyincrease with ε for ST. For example, from Table 1,passing from ε2 = 50 to ε1 = 40 with ST would generatea value of information equal to 0.2 REF. If in additionST is replaced with AD, the total gain increases up tomore than 0.5 REF.

This behavior highlights the lower robustness of STwith respect to AD.

The robustness of AD and ST can be explained byFig. 7. For each value of ε and for each instance, theobjective function of the solutions obtained by ADand ST with perturbed input data have been compared

Fig. 7 Average perturbationerror (percentage)

Average perturbation error

0

2

4

6

8

10

12

14

16

18

20

10 20 30 40 50 60 70 80 90 100

ε [%]

AD

ST

[%]

110 Eur. Transp. Res. Rev. (2011) 3:103–112

Fig. 8 Relative performanceloss (percentage) of solutionscosts computed by AD andST with respect to REF(three time slices data input)

Relative performance loss with respect to REF (3 time slices)

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50 60 70 80 90 100

ε [%]

AD

ST

[%]

with the objective function values obtained by the samesolutions with no perturbation on link travel times (i.e.,with ε = 0). The lowest is the difference, the highestis the robustness. We call this difference the averageperturbation error (in percentage).

It can be observed that the estimation error increasesalmost linearly with ε for both AD and ST and does notvary significantly with the algorithm but it depends onlyon ε.

In the remaining part of this section, we study thebenefit of using aggregated versus more detailed inputdata when modeling the traffic conditions in differenttime slices. The previous results are obtained using linktravel times available for each hour of the planninghorizon 4:00–11:00 am (i.e., the planning horizon isdivided into seven time slices). In order to considermore aggregated input data, the same planning horizonis divided into three time slices (from 4:00 to 7:00, from7:00 to 10:00 and from 10:00 to 11:00); the link traveltimes from 4:00 to 7:00 am (and from 7:00 to 10:00 am)

are considered constant and equal to the average valuesduring the three hours.

Figure 8 shows the relative performance loss of theobjective function values from the REF value whenusing three and seven time slices, for varying ε. TheREF value is computed by using seven time slices andε = 0. The distance from REF for the case with threetime slices ranges between 40 and 80% for AD andbetween 60 and 140% for ST. Such behavior confirmsthat AD is more resilient to perturbation with respectto ST also when the input data are more aggregated.

It is interesting to compare the performance of eachalgorithm considering three and seven time slices. Thisis shown in Fig. 9 for the AD algorithm and in Fig. 10for the ST algorithm.

As for the AD algorithm, when the input data arevery reliable (i.e., when ε = 0) there is a clear conve-nience in using seven time slices rather than three. Onthe other hand, for 10 ≤ ε ≤ 40 the difference betweenthe two cases reduces almost to zero, and it is always

Fig. 9 Relative performanceloss computed by AD withrespect to REF (three vsseven time slices data input)

Relative performance loss with respect to REF (3 vs 7 time slices)

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50 60 70 80 90 100

ε [%]

AD 7 SLICES

AD 3 SLICES

[%]

Eur. Transp. Res. Rev. (2011) 3:103–112 111

Fig. 10 Relative performanceloss computed by ST withrespect to REF (three vsseven time slices data input)

Relative performance loss with respect to REF (3 vs 7 time slices)

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50 60 70 80 90 100

ε [%]

ST 7 SLICES

ST 3 SLICES

[%]

less than 20% for higher values of ε, so that there is nobig convenience in collecting and using more detailedinput data for ε ≥ 10. When the ST algorithm is con-cerned, Fig. 10 shows that detailed input data (seventime slices) are still preferable when the perturbationε is zero and that aggregated input data (three timeslices) are slightly preferable for ε ≥ 10.

7 Conclusions

This paper addresses quantitative methods for estimat-ing the value of information from ITS in urban freightdistribution. The information adopted are link traveltimes, that can be deeply influenced by systematicand stochastic variability. Specifically, we developeda quantitative method to estimate the value of suchinformation in the optimization process of the retail dis-tribution of perishable goods. The method consists ofsolving the distribution problem by using data affectedby different degrees of reliability and accuracy. As astage of the analysis, different algorithms are evaluatedin terms of performance and robustness, to assess thebest results achievable with a given data set. In par-ticular, we define the monetary cost of unreliability asthe additional cost that has to be paid with respect tothe best solution achievable with perfect information.We tested several solution procedures, ranging fromsimple greedy algorithms to specialized tabu search al-gorithms. As for the latter case, a standard tabu searchis derived from the literature on the vehicle routingproblem. A new advanced tabu search has been devel-oped by taking into account the geographical positionof customers and routes to construct a new effectiveneighborhood.

Experimental analysis has been carried out on a realnetwork (a subarea of the city of Rome). Our resultsshow that there is a clear benefit in using detailed andhighly reliable data. When reducing the travel timeestimation error nearly to zero is not possible (e.g.,when travel time values are inherently stochastic innature) it is important to use an advanced algorithm,able to achieve good performance for a large rangeof perturbation. Our computational results also showthat when the input data perturbation is large, thereis no big convenience in using detailed informationfor the solution of the vehicle routing problem. Anaccessory result to the main objective of the paper is toshow that the advanced tabu search clearly outperformsthe standard one from both the points of view of theobjective function and the robustness.

The methodology described in this paper can beused to evaluate the marginal value of different typesof information and therefore the potential return oninvestment on the acquisition of reliable data. At thesame time, the results of this paper can be of interestalso for information providers, to evaluate the willing-ness to pay of potential customers and/or to estimatethe associated market share.

Future developments of this work will be possiblewhen practical measures on the network links will beavailable, and will address the design of the most suit-able distributions for the link travel time errors and thedefinition of the right combination of levels of inputdata aggregation, information reliability and algorithmto be used in practice. A further important researchdirection should address the problem of dynamicallyre-routing deliveries in real-time, i.e., to investigatethe benefit of adapting vehicle routes in real timeon the basis of the current traffic conditions. Severalpapers [33, 34] demonstrate that, as the uncertainty

112 Eur. Transp. Res. Rev. (2011) 3:103–112

in the travel times increases, dynamic vehicle routingstrategies becomes more and more convenient withrespect to the static strategies.

Acknowledgement This work is partially supported by theItalian Ministry of Research, Grant number RBIP06BZW8,project FIRB “Advanced tracking system in intermodal freighttransportation”.

Open Access This article is distributed under the terms ofthe Creative Commons Attribution License which permits anyuse, distribution, and reproduction in any medium, provided theoriginal author(s) and source are credited.

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