Algorithms to Quantify Impact of Congestion on Time-Dependent Real-World Urban Freight Distribution Networks

Transcription

1 s to Quantify Impact of Congestion on Time-Depenent Real-Worl Urban Freight Distribution Networs Ryan G. Conra an Miguel Anres Figliozzi Urban congestion presents consierable challenges to time-efinite transportation service proviers. Pacage, courier, an less than trucloa operations an costs are severely affecte by growing congestion levels. With congestion increasing at pea morning an afternoon perios, public policies an logistics strategies that avoi or minimize eliveries uring congeste perios have become crucial for many operators an public agencies. However, in many cases these strategies or policies can introuce unintene sie effects, such as higher labor costs, shorter woring hours, an tighter customer time winows. Research efforts to analyze an quantify the impact of congestion are hinere by the complexities of vehicle routing problems with time-epenent travel times an the lac of networwie congestion ata. Research use real-worl roa networ ata to estimate travel istance an time matrices, lan use an customer ata to localize an characterize eman patterns, congestion ata from an extensive archive of freeway an arterial street traffic sensor ata to estimate time-epenent travel times, an an efficient time-epenent vehicle routing (TDVRP) solution metho to esign routes. Novel algorithms were evelope to integrate real-worl roa networ an travel ata to TDVRP solution methos. Results show the impact of congestion on epot location, fleet size, an istance travele. Congeste urban areas present consierable challenges for less-thantrucloa (LTL) carriers, courier services, an inustries that require frequent an time-sensitive eliveries. With congestion increasing at pea morning an afternoon perios, public policies an logistics strategies that avoi or minimize eliveries uring congeste perios have become crucial for many operators an public agencies. However, in many cases, these strategies an policies can introuce unintene sie effects, such as higher labor costs, shorter woring hours, an tighter customer time winows. Although current research on vehicle routing algorithms is extensive, much less attention has been given to investigation of the impact of congestion on carrier operations. Furthermore, most algorithms for solving the time-epenent vehicle routing problem (TDVRP) foun in the existing literature o not eal with the estimation of istance an time-epenent travel time matrices. Thus, this research focuses on two primary objectives: (a) evelop efficient algorithms to apply TDVRP solution methos to actual roa networs by using Department of Civil an Environmental Engineering, Maseeh College of Engineering an Computer Science, Portlan State University, P.O. Box 751, Room 301-D, 1930 SW Fourth Avenue, Portlan, OR Corresponing author: M. A. Figliozzi, figliozzi@px.eu. Transportation Research Recor: Journal of the Transportation Research Boar, No. 168, Transportation Research Boar of the National Acaemies, Washington, D.C., 010, pp DOI: / historical traffic ata with a limite increase in computational time an memory, an (b) utilize Google Maps open-source application programming interface (API) an networ ata to prouce istance an travel time matrices. To the authors nowlege, no research effort has integrate time-epenent routing algorithms, historical traffic ata, real-worl roa networ ata, an public open-source APIs to incorporate the impact of congestion on elivery routes. LITERATURE REVIEW This section covers two main areas of research: (a) the effects of congestion an travel time variability on vehicle routes an logistics operations an (b) TDVRP solution algorithms an their application to urban areas. Direct an inirect costs of congestion on passenger travel time, shipper travel time an maret access, prouction, an labor prouctivity have been wiely stuie an reporte in the literature. The wor of Weisbro et al. provies a comprehensive review of this literature (1). Substantial progress has been mae in the evelopment of econometric techniques to stuy the joint behavior of carriers an shippers relative to congestion (, 3). Survey results suggest that the type of freight operation has a significant influence on how congestion affects carriers operations an costs. Survey ata from California inicate that congestion is perceive as a serious problem for companies specializing in LTL, refrigerate, an intermoal cargo (4). Similar conclusions are reache by reports analyzing the effects of highway limitations an traffic congestion in the Portlan, Oregon, region (5, 6). Golob an Regan ientifie a positive relationship between the level of local congestion an the purchase of routing software (7). Carriers that o not follow regular routes, such as for-hire carriers, ten to place a higher value on the use of real-time information to mitigate the effects of congestion an logistical services to plan fleet eployments (8). Other researchers attribute the scant usage of TDVRP algorithms to the lac of reliable time-epenent travel time ata, which can be particularly expensive or ifficult for small carriers to obtain (9). These authors recommen the implementation of open-access online TDVRP an ata services to increase the efficiency of routes in congeste urban areas. Another line of research investigate carrier reactions to toll measures intene to shift freight traffic to off-pea hours. Holguin-Veras et al. investigate the effects of congestion charges in New Yor City an foun that elivery times are heavily ictate by customer time winows (10). Congestion charges increase carriers operating costs while inucing little shifting of eliveries from pea to off-pea hours. This suggests an inelastic relationship between freight congestion charges an routes with time-efinite elivery times. Qua an Koster 104

2 Conra an Figliozzi 105 presente a methoology to quantify the impact of elivery constraints an urban policies by using a fractional factorial regression (11). They foun that vehicle restrictions an elivery curfews have a compouning effect on customer costs, whereas vehicle restrictions alone are costlier only when vehicle capacity is limite. There is little research into the effects of congestion on vehicle route characteristics. Figliozzi analytically moele routes (1), extening Daganzo s continuous approximations (13), an analyze how routing constraints an customer service urations affect route characteristics by using a classification base on supply-chain characteristics. This analysis showe that a ecrease in travel spee severely affects total istance travele for routes with time winow constraints, whereas capacity constraine routes are less affecte. The impact of travel time reliability on LTL elivery was also analyze by using continuous approximations an real-worl ata (14). This research conclues that travel time variability has a significant impact on carrier costs when average istance to elivery areas increases an average travel spee ecreases. Classic versions of the vehicle routing problem (VRP) such as the capacitate VRP or VRP with time winows (VRPTW) have been wiely stuie. However, time-epenent problems have receive consierably less attention. Figliozzi presente a comprehensive review of TDVRP approaches an an efficient TDVRP algorithm (15); that wor also creates benchmar problems for the TDVRP altering the classical VRPTW Solomon instances. Fleischmann et al. reviewe the aaptation of the VRP algorithms to time-epenent ata from traffic information systems in the city of Berlin (16). Eglese et al. analyze the construction of a time-epenent travel time atabase (17) by using Dstra s algorithm for time-epenent lins. Eglese et al. applie their methoology to a real-worl networ in Englan. However, these research efforts o not incorporate into their analyses the influence of time winows an recurring bottlenecs or the impact of congestion on fleet size an total istance travele. PORTLAND, OREGON, CASE STUDY Consiere a gateway to international sea an air freight transport, the city of Portlan, Oregon, has establishe itself as an important hub for international an omestic freight movements. Its favorable geography for both international ocean an omestic river freight via the Columbia River is complemente by its highway connections. I-5 is the most important freeway connecting the West Coast from Mexico to Canaa as well as southern California ports an main West Coast population centers (5). The I-5 freeway is also use by many carriers elivering in Portlan an the city s surrouning suburbs because it provies the main north south freight corrior through the city of Portlan. Recent increases in regional traffic congestion have negatively affecte freight operations. A recent report investigate the effects of congestion on Portlan-area businesses an LTL eliveries (5). That report provies insightful yet qualitative information on various strategies use by businesses to cope with congestion, aitional elivery costs, an uncertainty. The report inicates that congestion has mae some afternoon eliveries infeasible, which requires that eliveries be mae uring nonbusiness hours early in the morning. However, avoiing congesting by shifting eliveries to early morning generates aitional costs by reucing route urations. In some cases, early eliveries are not feasible near resiential areas where paring problems an noise can lea to soun or traffic orinance violations an conflicts with resients (5). The recurrent effects of traffic congestion at pea perios present aily challenges to LTL carriers in the Portlan metropolitan area, represente by a numerical analysis presente in a later section. Customer ata an epot locations are generate by using a lan use zoning map of the Portlan metropolitan area. Networ an congestion ata sources, incluing recurrent bottlenecs, are escribe, as is a methoology for applying TDVRP algorithms to real-worl networs. The methoologies an algorithms evelope in this research assume that customers emans an time winows are nown a priori, for example, the night before elivery. Congestion ata relate to nonrecurrent conitions, such as ue to accients, is not analyze an is left as a future research topic. DATA SOURCES Two main ata sources were use in this research: Google Maps API for implementation of the TDVRP algorithm an the Portlan Transportation Archive Listing (PORTAL) for obtaining historical travel time ata. Overview of Google Maps API The Google Maps API allows access to the up-to-ate street networ in the stuie region with a high level of geographical etail. The open-source application allows for consierable freeom in moifying the program an user interface (18). Figure 1 shows the process of creating customer istributions an obtaining optimize routes from the TDVRP algorithm as implemente with the API. The API consists of several interfaces: A customer selection screen where a set of customers an a single epot can be create by clicing on locations on the map. A coorinate output is provie that is then copie into a text (.txt) file. An interface that calculates the shortest paths between pairs of customers an constructs the istance an travel time origin estination matrices. Distance an travel time matrices are estimate an store as text files. Travel spee, occupancy an vehicle flow ata from traffic sensors use to incorporate the impact of congestion on travel times. A solution interface where solution sets output from the TDVRP algorithm can be loae an plotte to provie a visual verification of results. Perhaps the greatest avantage of the API is that the open-source software an high-quality networ ata can be accesse free of charge from This together with the TDVRP solution algorithm evelope to interface with the API offers very-low-cost solutions for route planning an optimization while allowing access to etaile an accurate networ ata such as roa hierarchy an restrictions (e.g., one-way streets or no-left-turn movements at intersections). The effects of congestion are inclue by moifying the travel times initially calculate by Google Maps. After the TDVRP algorithm esign the routes, the API interface can be use to obtain etaile riving irections. Simulating Congestion Effects Google Maps provies reasonable travel time estimations uring uncongeste perios. However, to increase the accuracy of travel time estimations, highway sensor ata are use. For example, segments

3 106 Transportation Research Recor 168 Select Customers Customers can be selecte by clicing once on a location on the map. The first selection is the epot. Alternatively, customer locations in ecimal latitue-longitue format can be uploae. Output Customer Coorinates Map ata Tele Atlas O-D Matrices The customer coorinate text file is uploae to the Driving Distance screen where Google Maps calculates the free-flow travel time an istance between each pair of customers. Output Travel Time O-D Matrix Output Distance O-D Matrix Map ata Tele Atlas t Calculate Results Travel time ata from PORTAL for the bottlenec locations an the free-flow spee O-D matrix are inserte into the spee function. Bottlenec coorinates are entere separately into the VRP algorithm along with the spee function. Optimize routes can be isplaye in a route plotting interface in Google Maps. Results are also provie for several performance criteria incluing number of require vehicles, total riving istance an travel Ajustable Parameters Spee Parameter Occupancy Threshol Avg. Vehicle Spacing Queuing Parameter PORTAL Traffic Data Tables p Travel Spee V n Occupancy Vehicle Flow Minimize Minimize c VRP K j C p O n p U n 1 x 0j K i, j A v n O n L n R n x c t K j C Free-flow Spees (O-D Matrices) u t Spee Function y n 1 y 0 x s u, v m 0 j Display Routes in Google Maps Interface Optimize Routes an Performance Measures FIGURE 1 Overview of TDVRP solution methoology an integration of Google Maps API.

4 Conra an Figliozzi 107 FIGURE Example with bottlenec locations an areas of effective travel spee reuction. along I-5 near traffic bottlenecs are selecte to represent areas of ecrease travel spee. The selecte segments are between freeway interchanges or on an off ramps where vehicle etector loops are locate. Detaile traffic ata are obtaine from PORTAL, Portlan s implementation of an archive ata user service, which coorinates an obtains ata from approximately 436 inuctive loop etectors along Interstate freeways in the Portlan metropolitan area. Bertini et al. give a escription of this transportation ata archive (19). Bottlenecs are moele as point locations surroune by areas of reuce travel spee. Travel in proximity to a bottlenec is expresse as a percent reuction in travel spee proportional to the spee reuction at the bottlenec location. Figure shows the bottlenec locations an areas of effective travel spee reuction. Data obtaine from PORTAL are also use to moel the impact of traffic queuing on the surrouning networ. The areas of reuce travel spee for each bottlenec location are assume as a function of the measure occupancy an vehicle inflow an outflow rates at each bottlenec location. Research has shown that traffic queues often begin to form at occupancies approximately equal to or greater than 0% (0), but accoring to spee flow ata, queues may form at occupancies as low as 13%. From these queuing concepts an assumptions, the raius of the area of travel spee reuction aroun each bottlenec where vehicle travel spee reuce is varie in proportion to the ifference in the inflow an outflow rates multiplie by average vehicle spacing when the occupancy is above a certain threshol value. Strictly, this assumes that there is conservation of vehicles (i.e., no vehicles enter or exit the roa segment in question) an ignores the presence of moving traffic queues. The travel spees use in this research are calculate from 15-min archive travel time ata average for the year 007 along the I-5 freeway corrior from the Portlan suburb of Wilsonville to Vancouver, Washington. These ata are sufficient to emonstrate the propose methoology, but consieration of seasonal or monthly variability in travel time is important for many LTL carriers an is feasible via PORTAL. In this research, it is assume that carriers account for only recurrent congestion an plan their routes the night before maing the eliveries. METHODOLOGY TDVRP Overview Figliozzi presente a escription of the TDVRP algorithm use in this experiment, along with a full TDVRP formulation (15). Because of har time winow constraints, the primary objective is the minimization of the number of vehicles or routes; the seconary objective is minimization of the travel time or istance. The TDVRP solution algorithm consists of a route construction phase an a route improvement phase, each using two separate algorithms (Figure 3). During route construction, the auxiliary routing algorithm H r etermines feasible routes with the construction algorithm H c assigning customers an sequencing the routes. Route improvement is one first with the route improvement algorithm H i, which compares similar routes an Route Construction Route Improvement Auxiliary Routing Route Construction Route Improvement Service Time Improvement H r H c H i H y PORTAL Data H yc Arrival Time H yf Google Maps API Travel Spee Data Departure Time H yb FIGURE 3 TDVRP solution metho.

5 108 Transportation Research Recor 168 consoliates customers into a set of improve routes. The service time improvement algorithm H y eliminates early time winow violations an then reuces the route uration without introucing aitional early or late time winow violations; these tass are accomplishe by using the arrival time an eparture time algorithms H yf an H yb, respectively, an customers are subsequently resequence as necessary. It is with these algorithms that the POR- TAL ata an shortest-path travel spees generate by the Google Maps API are inserte into the solution algorithm. Notation For the following travel time algorithms, the total epot woring time [e #, l # ] is partitione into a set of p time perios T p = {T 1, T,..., T p }. Each traffic bottlenec location β m β n = {β 1, β,..., β n } is assigne the following ata at each time partition T T p : O p n = [O m ] p n, table of occupancy values for each time perio T T p an bottlenec β m β n ; U p n 1 = [U m ] p n+1, table of vehicle flow inflow an outflow rates for each time perio an bottlenec location; the inflow an outflow rates at time perio T for bottlenec β m are U m an U,m+1, respectively; an vn p = [v m ] p n, table of congeste travel spees obtaine from PORTAL. All ata are collecte from PORTAL, an the point source location of each traffic bottlenec is assume to be miway between etector loops. The algorithms inclue the following ajustable parameters for each bottlenec location: R _ m R _ n = {R _ 1, R _,..., R _ m,..., R _ n}; set of initial raius values at time t = 0; L _ m L _ n = {L _ 1, L _,..., L _ m,..., L _ n}; set of average vehicle spacing values; O _ m O _ n = {O _ 1, O _,..., O _ m,..., O _ n}; set of threshol occupancy percentages that etermine the expecte onset of traffic queuing; an v _ m v _ n = {v _ 1, v _,..., v _ m,..., v _ n}; set of free-flow spees. Table 1 contains a complete listing of variable an function efinitions. Traffic Queuing The following is a summary of the H yc algorithm that assembles a table of bottlenec raii R m for each bottlenec β m an time perio T. The algorithm requires the input ata arrays O p n an U p n 1 as well as the ajustable parameters R _ n, L _ n, an O _ n. The output table R p n contains the raius value for each time perio T at each bottlenec β m in a p n array. Beginning with the conitional statement within the neste for loop for a particular β m an starting at t = 0, the algorithm can be escribe as follows: 1. First assign the variable R the base parameter value R _ m at t = 0.. Begin the iteration; if the occupancy O m at a given iteration is greater than the threshol value O _ m, a the ifferences in the outflow an inflow traffic volumes multiplie by the uration of the time partition t _ t by the average vehicle spacing L _ m to the variable R. TABLE 1 Notation Definition Variables i, j, m β i = (x i, y i ); β j = (x j, y j ); β m = (x m, y m ) a j b i e i g i t u = t Array an Vector Quantities T [t, t ] T p = {T 1, T,..., T p }, R m R n = { R 1, R,..., R n } L m Ln = { L 1, L,..., L n } O m O n = { O 1, O,..., O n } v m v n = { v 1, v,..., v n ] U m, U,m+1 Un+1 p = [U m ] p n+1 O p n = [O m ] p n v p n = [v m ] p n Function f(x µ, x v, y µ, y v ) Inices for set of consecutive customers (i, j) an bottlenecs (m) Geographic coorinates of customer i, customer j an bottlenec m, respectively Arrival time at customer j Departure time from customer i Lower time winow for customer i Service time at customer i Iterate riving istance variable Driving istance between customers i an j calculate by the Google Maps API Free-flow travel time between customers i an j calculate by the Google Maps API Free-flow spee use in TDVRP algorithm Set of time perios as fraction of epot woring time Set of initial raius values at each bottlenec location at time t = 0 Set of average vehicle spacing values for each bottlenec location Set of threshol occupancy percentages that etermine the expecte onset of traffic queuing Bottlenec spee parameters Table of vehicle flow inflow an outflow rates for each time perio an bottlenec Table of occupancy values for each time perio an bottlenec Spee at bottlenec B m for the th time perio entere as a p n array Eucliean istance between two sets of x an y coorinates

6 Conra an Figliozzi 109 _ 3. If the occupancy Om is less _than Om an the raius variable R is greater than the base parameter Rm, then subtract the quantity from Step from R. _ 4. Tae the maximum of the set [R, Rm]; this an the secon conition of Step _ 3 prevent R from being assigne a negative value an ensure that Rm is a lower boun for the variable R when the preicte traffic queue is ispersing. _ 5. Otherwise, retain R = Rm. 6. Construct a column vector Rp of R values obtaine from each iteration. 7. Repeat Steps 1 through 6 n times an construct the output matrix Rnp from the column vectors Rp obtaine from each iteration. The Hyr algorithm as or subtracts expecte lengths of traffic queues to the raius of the effective area of each bottlenec that is epenent on whether the measure _ occupancy is above or below each threshol value containe in On. The table of values in Rpn is reference by the Hyf an Hyb algorithms escribe in etail in the following section. The objective is to extrapolate travel time trens from the ata that are available an apply them to the surrouning roa networ. = D (1) where D = Eucliean istance between customers i an j, = shortest-path riving istance from customer i to customer j calculate by the API, an = iterate istance from i to j along the actual riving route (a erivation of this function is given in the appenix). With the law of cosines (see Figure 4), the istance from a point on the Eucliian connecting line to each bottlenec at a given time iteration in the forwar iterative calculation can be shown to be ( D + D jm Dim ) rm = D + D jm The following is a summary of the arrival time an eparture time algorithms Hyf an Hyb aapte from Figliozzi (15) that estimate travel times between pairs of customers βi an βj by using the travel time ata. The Hyf algorithm calculates the expecte arrival time at a customer βj when eparting from a previous customer βi by using a forwar-iterative process. Similarly, the Hyb algorithm uses a bacwar iterative process an simultaneously calculates the require eparture time from customer βi to reach customer βj. The impact of bottlenecs as vehicles are moving through ifferent perios is a function of the estimate istance between the vehicle an the bottlenec at the beginning of each time perio. A linear approximation of the vehicle location is use to reuce computational complexity because shortest-path an Eucliean istances are highly correlate. High levels of correlation between Eucliian an shortestpath istances are usually foun in urban areas (1). The istance trav- ( D + Dim D jm ) rm = D + Dim rm 1 (33) The travel spee function sm is applie at each time iteration T an calculates a spee value for each bottlenec. This function calculates congeste travel spees sm as reuctions in the API-erive spee u proportional to the spee _ reuction measure at the traffic bottlenecs such that sm /u = vm /vm if the virtual location on the Eucliean connecting line is within the raius R_m. Here vm is the time-varying spee obtaine from PORTAL, an vm is an ajustable parameter that may represent the freeway free-flow spee. In other wors, the reuction in travel spee ue to congestion in the surrouning networ is assume to be proportional to the reuction observe from the PORTAL : Actual route D : Eucliean connecting line 1 D D D D jm D Djm D Dim rm D Dim Djm rm ( xm, ym ) Djm FIGURE 4 () where Dim an Djm are Eucliean istances between customer i an bottlenec βm an customer j an bottlenec βm, respectively. Similarly, for the bacwar iterative process of the eparture time algorithm, the istance from the nearest bottlenec is Arrival an Departure Time s (xi, yi ) ele along the Eucliean connecting line is calculate as a percentage of the actual route traverse such that Illustration of the metho to approximate bottlenec influence. ( xj, yj ) Dim

7 110 Transportation Research Recor 168 freeway ata at the bottlenec (etector station) with the slowest travel spee. This function can be expresse as s m uv m rm R = vm u r > R where r m is the istance from a point along the Eucliean connecting line to a bottlenec β m. The following is a summary of the H yf algorithm pseuocoe: 1. First etermine if the arrival time a i is less than the lower time winow e i at customer i If so, then the vehicle waits an the expecte eparture time is e i plus the service time g i. If not, then the eparture time is simply the arrival time plus the service time. Determine for the iscrete time perio T with bouns [t, t _ ] that the expecte eparture time b i lies in. This is the initial value for the iterator in the while loop. 3. Determine the Eucliean istance of each traffic bottlenec to the location β i = (x i, y i ) of customer i; the spee function is calculate for each value m an a row vector S n of spees is assemble. The initial travel spee of the vehicle in the subsequent forwar-iterative process is calculate as the minimum value of S n, that is, the travel spee is only as fast as that impose by the bottlenec with the worst travel spee (only among the subset of bottlenecs whose area of influence affects the path between customers at a given time). 4. Terminate the while loop when the vehicle has reache its estination. In each perio, spees are recalculate an istances accumulate until the vehicle has reache its estination. Output: the expecte arrival time a j at customer j when eparting from customer i at time b i. The H yb algorithm wors in a similar fashion: given a customer j at location v j with an expecte arrival time a j obtaine from the H yf algorithm, etermine the require eparture time b i from customer i at location β i to mae the trip between β i an β j without allowing for late time winow violations. Calibration m m m Travel times can be calibrate by ajusting R _ n, L _ n, O _ n, v _ n parameters as well as the time-epenent travel spees provie by PORTAL ( 4) (v p n). Directional an time-of-ay effects can be incorporate. Memory requirements are reuce because the algorithms wor with one travel time an istance matrix. Simple linear functions an intuitive parameters are use to aapt free-flow travel times to congeste conitions. EXPERIMENTAL SETTING To test the moel with real-worl constraints, two elivery perios are moele an analyze: (a) an early morning elivery perio that avois most of the morning pea hour traffic congestion but with tighter time winows, an (b) an extene morning elivery time that increases the feasible woring time but with increase travel uring the morning pea. Figure 5 provies a qualitative comparison of the simulate elivery times. A total of 50 customer locations are use (Figure 6) with constraints assigne accoring to the zoning criteria. All customers normally serve after 9:00 a.m. are assume to be able to shift elivery times before this hour. Time winows of 15 min are ranomly assigne to all customer types. Aitionally, eliveries to all customers in mixeuse an resiential areas are prohibite before 7:00 a.m. to moel require compliance with local noise orinances. In the early-morning elivery option, this reuces the effective epot woring time to just h for these customers. The extene morning elivery option provies a 4-h woring time for these customers but inclues the effects of the morning pea-hour congestion to a greater egree. The calibration of the moel was teste by varying the travel spee parameters v _ n to alter the simulate travel spee erive from the PORTAL travel time ata an containe in the travel spee table v p n. EXPERIMENTAL RESULTS Results comparing the number of vehicles an total istance travele uring the morning an extene morning elivery perios are presente in this section. In aition, to incorporate the impact of travel time reliability, time-varying travel spees from PORTAL are ecrease by a coefficient δ. This ajustment maintains the overall tren in travel spee variation throughout the elivery perio but allows for ajustments to the travel time to more accurately reflect real-worl ifferences between average travel spees an the actual istribution of travel spees. A value δ =1 utilizes average timevarying travel spee PORTAL ata an assumes that no har timewinow violations tae place if realize travel times are at least the average travel spee. However, if the carriers woul lie to Early Morning Delivery Extene Early Morning Delivery 15 min. time winows Constraine 15 min. time Customers in winows (Resiential areas) 03:00 05:00 07:00 09:00 03:00 07:00 09:00 11:00 Congestion intensifies FIGURE 5 Moele elivery perios, constraine customers, an time winow constraints.

8 Conra an Figliozzi 111 Central Central Suburban Customers with service time constraints FIGURE 6 Customer service area an epot locations. account for travel time unreliability, a value of δ < 1 can be use in the calculations as follows: s m uv m δ rm R = vm u r > R m m m A value of δ < 1 guarantees a higher value of customer service (14). The sensitivity to travel time unreliability an buffer times was teste by setting the parameter δ={0.4, 0.6, 0.8, 1}. Impact of Congestion on Number of Vehicles For the number of require vehicles (Figure 7), the central epot showe less sensitivity to changes in travel time reliability than i the suburban epot. As expecte (14), reuce travel spee appears to have a greater impact on fleet size when the epot has a suburban location. The number of vehicles require is consistently less for the extene early-morning elivery perio, an a larger fleet is still require when the epot has a suburban location. Impact of Congestion on Total Distance Travele Figure 8 compares total vehicle miles travele (VMT). Similar to the require number of vehicles, total VMT is significantly higher for () 5 tours originating at the suburban epot location. Constraine service times for customers in the early-morning elivery perio also appear to affect total VMT to a slightly greater extent than oes travel spee. CONCLUSIONS This research propose a new methoology for integrating real-worl roa networs an travel ata to time-epenent vehicle routing methos. The use of traffic sensor ata an Google Maps API provies a unique approach to interface routing algorithms, travel time, an congestion ata. Intuitive algorithms an parameters are use to incorporate the effects of congestion on time-epenent travel time matrices. The propose methoology is a significant improvement for representing the impact of congestion in congeste urban areas leveraging on existing open-source ata an applications. The results show the ramatic effects of congestion on carrier fleet sizes an istance travele. The results also suggest that congestion has a significant impact on fleet size, particularly for epots locate in suburban areas outsie the customer service area. APPENDIX A The following is the erivation of the bottlenec istance function r for the forwar-iterative calculation in the arrival time algorithm. An ientical argument with the istance iterate in the bacwar

9 Number of Vehicles % Morning Ext. Morning 60% 80% 100% Travel Time Reliability (δ) (a) Number of Vehicles % Morning Ext. Morning 60% 80% 100% Travel Time Reliability (δ) (b) FIGURE 7 Effects of congestion on fleet size: (a) central epot an (b) suburban epot. Total Distance Travele (miles) Central Suburban % 60% 80% 100% Travel Time Reliability (δ) (a) Total Distance Travele (miles) Central 400 Suburban % 60% 80% 100% Travel Time Reliability (δ) (b) FIGURE 8 Effects of congestion on total VMT: (a) extene morning elivery perio an (b) early morning elivery perio.

10 Conra an Figliozzi 113 irection from a customer j to i obtains the bottlenec istance function for the eparture time algorithm in a trivial manner. Let θ im be the angle opposite D im, the Eucliean istance from customer i to bottlenec B m. With the law of cosines, D im = D + D jm D D jm cos(θ im ), D + Djm Dim cos ( θ im )= ( A-1) DD θ im is also the angle opposite to r. Equating r an Equation A-1, an with the law of cosines again, r m D D = D D jm + ACKNOWLEDGMENTS The authors than the Oregon Transportation, Research an Eucation Consortium, the Port of Portlan, an Portlan State University Research Aministration for sponsoring this research. 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