A Multimodal Passenger-and-Package Sharing Network for ...

Research ArticleA Multimodal Passenger-and-Package Sharing Network forUrban Logistics

Yuxiong Ji Yujing Zheng Jizhou Zhao Yu Shen and Yuchuan Du

Key Laboratory of Road and Traffic Engineering of the Ministry of Education Tongji University Shanghai 201804 China

Correspondence should be addressed to Yu Shen yshentongjieducn

Received 6 November 2019 Revised 15 January 2020 Accepted 8 February 2020 Published 18 March 2020

Academic Editor Giuseppe Musolino

Copyright copy 2020 Yuxiong Ji et al -is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

-is paper envisions a multimodal passenger-and-package sharing (PPS) network for urban logistics integrating metro taxi andtruck A hub-and-spoke structure is designed including hubs located at metro stations and service stores connected to the hubsPackages are transported by metro on backbone links between the hubs and are carried by taxis or trucks between service storesand hubs depending on the unit costs of these twomodes and capacity constraint of the taxi Amixed integer linear programmingmodel for hub location problemsmdashfusing the multiassignment p-hub median problem without capacity constraints and thecapacitated multiassignment p-hub covering problemmdashis formulated to optimize the multimodal PPS network -e model isimplemented based on the real-world data in Shanghai (China) under a series of scenarios to evaluate the network performancefrom two perspectives the number of hubs and the proportion of taxi drivers who are willing to carry packages -e scenariosshow that with increased number of hubs the spatial distribution of hubs disperses from the city center to peripheral areas andmore areas can be serviced by taxis -ere is however a trade-off between the operation cost saved by taxis and the establishmentcost of an extra hub-e analysis also presents that if the proportion of taxis willing to carry packages associates with the incentivepayments to taxi drivers an optimal value of incentives exists by balancing the operation costs of taxis and trucks

1 Introduction

-e demand for urban parcel delivery booms with the preva-lence of e-commerce in the recent years Take China as anexample Over 40 billion packages were delivered in urban areasin 2017 with an increase of 28 comparing with the previousyear [1] -e booming demand for urban parcel deliveriespotentially leads to heavy urban freight traffic that inevitablybrings negative impacts on traffic congestion and air pollutionTo mitigate the negative effects and to improve urban mobilitythe European Commission recommends a passenger-and-package sharing (PPS) system integrating passenger and freighttransportation [2] and some typical services was overviewed andintroduced by Sampaio et al [3] In general three sharingoptions are proposed share of space (eg multiuse lanes andnight deliveries) share of public transport vehicles and networksand share of urban delivery facilities such as delivery bays andgoods lockers [4ndash7] -is study focuses on the PPS networkdesign with passengers and packages sharing the same publictransport vehicles and networks

Current studies on the PPS system mainly focus onvehicle routing for package pickup and delivery consideringvarious scenarios like taxi sharing or self-owned vehiclerouting between public transit stations and customers Forexample Li et al [8] formulate a share-a-ride problem tooptimize taxi routes and schedules to better match thesupply of taxis and the demand from passengers and parceldeliveries -e model is evaluated in Tokyo city by Nguyenet al [9] and extended by Li et al [10] by integrating sto-chastic travel times and delivery locations Masson et al [11]propose a public transit-based PPS system that firstly usesbuses to deliver the packages from a consolidationdistri-bution center to a set of bus stops and then dispatches a fleetof freighters to deliver packages to customers Taking intoaccount time windows schedules and stochastic demandsGhilas et al [12 13] use the public transit as a part of freightjourney and optimize the pickup-and-delivery routes ofprivate vehicles between given transfers and demand nodesFatnassi et al [14] assess the potential of integrating personalrapid transit and freight rapid transit vehicles into one

HindawiJournal of Advanced TransportationVolume 2020 Article ID 6039032 16 pageshttpsdoiorg10115520206039032

network with the objective of minimizing the movements ofempty vehicles and the waiting times of passengers andpackages Yildiz and Savelsbergh [15] explore the service andcapacity planning problem in store-to-door meal deliverywhere the delivery service is provided by individualrsquos willingto participate in such activity

-e contribution of this studymdashdifferent from currentstudies on vehicle routing in a PPS systemmdashis to design themultimodal PPS network with the hub-and-spoke structure-e idea of the hub-and-spoke network design for multi-modal logistics networks is widely supported by pastscholars [16] By integrating multiple modes into one lo-gistics network the new system is able to achieve economiesof scale more effectively thus improving the transport ef-ficiency [17 18] Current literatures mainly focus on theintercity multimodal logistics network Qu et al [19] designa logistics network integrating ocean and coastal routesinland waterways railways roadways and airways withnonlinear transfer costs between different modes Takinginto account demand uncertainties and network disruptionsFotuhi and Huynh [20] identify the rail links to retrofitexisting intermodal hubs to expand and locations of newhubs in the rail-road network Similarly Kim and Ryerson[21] identify a set of unaffected hubs during network dis-ruption in the US ocean-inland freight network

A conceptual design of the multimodal PPS network forurban parcel delivery is envisioned and drawn in Figure 1integrating metro carriages taxis and trucks -e fusion ofmetro taxi and truck absorbs the advantages of the threemodes metro trains follow predetermined routes andschedules with high reliability punctuality and large car-rying capacities taxis and trucks are flexible and are able toprovide door-to-door services -e carrying capacity of taxisis constrained by the willingness of drivers to help carryingpackages -e capacity of trucks is unlimited since thefreighters are fully controlled by the couriers However thedelivery cost of trucks is higher than the cost of the sharedtaxis

To explore the optimal design of a multimodal PPSnetwork we formulate the network design task into hublocation problems (HLPs) -e rest of the paper is organizedas follows Section 2 reviews current HLPs and statesthe novelty of the proposed multimodal PPS network InSection 3 we propose a variant of the HLP model anddevelop a mixed integer linear programming model with amodified genetic algorithm to optimize the hub-and-spokenetwork Section 4 presents an example of Shanghai for thecase study and provides quantitative assessment of thenetwork from the perspectives of the number of hubs andthe proportion of taxi drivers who are willing to carrypackages Finally we conclude the study and offer somediscussions

2 Literature Review Hub Location Problems

Hub location problems are firstly proposed by OrsquoKelly in1980s [22ndash24] Typical HLPs can be classified based on theirobjectives the p-hub median problems locate p hubs tominimize the total routing cost [25ndash31] the p-hub center

problems locate p hubs so that the maximum cost betweenany OD pair can be minimized [25 32] and the p-hubcovering problems aim to maximize the total flow betweenall OD pairs covered by p hub facilities [33] In these studiesthe number of hubs to be established ie p is prespecifiedInstead of predetermining the number of hubs some worksassume a setup and operation cost for each hub with theobjective of minimizing the sum of hub cost and routing cost[29 34] or maximizing the system profit [35] Compre-hensive reviews can be found in Alumur and Kara [36]Campbell and OrsquoKelly [37] and Farahani et al [38]

-e network topology of HLPs depends on the structureof backbone links and spoke links Typically the hubs arecompletely connected However in some special cases in-complete interhub network structures eg ring [39] star[40] tree [41 42] and line [43] are adopted In terms of thedesign of spoke links for flow assignment a demand nodecan be connected to one or multiple hubs ie single ormultiple assignment structures Aykin [44] and Martins deSa et al [43] extend the topology of spoke links by con-sidering that the flows between some OD pairs can beshipped directly without being routed through hubs Besidesdirect links Lin and Chen [45] integrate stopovers andfeeders to the network Klincewicz [46] introduce a spokenetwork in which a demand node is allowed to be linked to ahub through other demand nodes In addition to thebackbone-and-spoke bilevel networks some researchesconsider the trilevel network connecting hierarchical hubsand demand nodes [40 47]

-e capacity of links is another essential feature of theHLPs Capacity constraints on flows are usually applied onhubs [25 48ndash52] links [53 54] or both [55] as exogenousconstraints Some studies also treat hub capacities as deci-sion variables to select the optimal hub capacity from a listset of predefined capacity levels each of which is associatedwith a fixed setup cost [56ndash58] Consider that the capacitylimits make the model more realistic though it increases thecomputation time in most cases

-e hub location-routing problem introduced byNagy and Salhi [59] combines the HLPs with the vehiclerouting problems (VRPs) where the vehicle routes areoptimized with respect to hub locations and flow as-signments simultaneously -e combination of HLPs andVRPs both of which are NP-hard problems leads to agreat growth in the solution cost -us the hub location-routing problems are normally formulated with a hier-archical structure in which the upper and lower levelsdeal with the HLPs and VRPs respectively [59ndash62] In thisstudy the vehicle route planning is not considered forsimplification

-is study applies a complete interhub structure Ademand node is allowed to be connected to multiple hubsto improve the flexibility and capacity of the network asmetro stations are completely connected by metro lines andtransfer stations -e spoke links are served by taxis andtrucks -e features of the two modesmdasheg the costs todeliver a package and the capacity constraintsmdashvarylargely -e study also takes into account the exogenousconstraints on spoke links served by taxi due to the driversrsquo

2 Journal of Advanced Transportation

willingness to help carrying packages -e spoke linksserved by truck and the backbone links served by metro areuncapacitated -e fusion of these modes enriches theformulation of HLPs

3 Methodology

31 Model Settings and Assumptions Figure 1 illustrates allpotential routes of an origin-destination (OD) pair -eservice stores spread out in the city for first-mile packagecollection and last-mile delivery -e hub facilities are lo-cated at metro stations for package storage and transfer fullyconnected by the metro network Between service stores andhubs packages are transported by taxi with limited carryingcapacities and by truck without capacity limits according tothe costs of these twomodes In the hub-and-spoke networkthe backbone links and the spoke links are served by metroand taxitruck respectively

-e envisioned multimodal PPS network also includesthe following characteristics Standardized delivery box-esmdashfitting into the trunks of taxi and truckmdashand containersdesigned for metro carriages are used for parcel transfer-e boxes and containers are (un) packed and reassembledat stores and hubs -e requests for package delivery to taxiscan be automatically matched by a central operation plat-form guiding the taxi drivers if they need to transportpackages besides passengers-e platform is also responsibleto rent trucks from cooperative on-demand logistic com-panies to deliver the packages that cannot be covered by taxisand to arrange the transportation of package in the metronetwork

-e following assumptions are made for modeling

(i) -e service stores are the OD nodes of the model

(ii) Packages have to be routed via at least one hub

(iii) Packages of an OD pair can be routed throughmultiple hubs

(iv) On spoke links the package flows served by taxi areconstrained by taxi flows the proportion of driverswho are willing to carry packages and the trunkcapacity of each taxi -e package flows served bytruck are unlimited

(v) -e capacities on hub facilities and backbone linksserved by metros are unlimited

Finally we focus on the low-cost urban courier servicewithout the constraints of the same-day delivery-erefore the system is evaluated in the dimension of costrather than time

32 Model Formulation Table 1 summarizes the inputsparameters and variables used in this study -e packageflows in this model are treated as multicommodity flows[63] Each commodity i represents the packages origi-nating from node i For commodity i denote zik and uik asthe flows routed from the origin service store i to hub k bytaxi and truck respectively yikl as the flows routed be-tween hubs k and l and xilj and vilj as the flows routedfrom hub l to destination service store j by taxi and truckrespectively

-e multimodal PPS network design problem is for-mulated as the mixed integer linear programming (MILP)problem expressed as follows

min TC 1113944iisinΩ

1113944kisinΘ

cik times zik + 1113944jisinΩ

1113944lisinΘ

clj times 1113944iisinΩ

xilj + 1113944iisinΩ

1113944kisinΘ

tik

times uik + 1113944jisinΩ

1113944lisinΘ

tlj times 1113944iisinΩ

vilj + 1113944kisinΘ

1113944lisinΘk

mkl times 1113944iisinΩ

yikl

+ 1113944kisinΘ

gk times hk

(1)

st

1113944kisinΘ

hk p (2)

1113944kisinΘ

zik + uik( 1113857 1113944jisinΩ

Wij i isin Ω

(3)

1113944lisinΘ

xilj + vilj1113872 1113873 Wij (i j) isin Ω2 (4)

zik le θ times Fik times rik (i k) isin Ω times Θ (5)

1113944iisinΩ

xilj le θ times Flj times rlj (l j) isin Θ timesΩ (6)

1113944lisinΘ

yikl + 1113944jisinΩ

xikj + vikj1113872 1113873 1113944lisinΘ

yilk + zik + uik( 1113857 (i k) isin Ω times Θ

(7)

zik + uik + xikj + vikj + yikl + yilk leQ times hk (i j k l) isin Ω2 times Θ2

(8)

hk isin 0 1 k isin Θ (9)

zik uik xilj vilj yikl ge 0 (i j k l) isin Ω2 times Θ2 (10)

Metro line

Origin

Destination

Service storesHub facilitiesSpoke links by taxi

Spoke links by truckBackbone links by metro

Figure 1 A conceptual multimodal passenger-and-packagesharing network

Journal of Advanced Transportation 3

Objective function (1) is set to minimize the total cost(TC) consisting of 6 terms which indicate

(i) -e cost to transport packages

(1) From origin stores to hubs by taxi(2) From hubs to destination stores by taxi(3) From origin stores to hubs by truck(4) From hubs to destination stores by truck(5) Between hubs by metro

(vii) -e cost to establish and to operate the hubsrespectively

Constraint (2) guarantees that there are exactly p hubfacilities to be established Constraint (3) and constraint (4)represent that for commodity i and the total package floworiginated from node i and destined to node j is in accordancewith the demand Constraints (5) and (6) ensure that packageflows transported by taxi between demand nodes and hubs areconstrained by taxi flows theWTCP and the capacity of thetaxi trunk Constraint (7) is the flow conservation equationsfor each commodity i at each hub k of which the left and rightsides are outgoing and incoming flows respectively Con-straint (8) indicates that the package flows related to hub k aregreater than zero only if hub k is established whereQ is a largenumber Constraints (9) and (10) specify the binary and non-negative types of decision variables

-e proposed model generalizes and is an extension oftwo classic types of HLPs If no taxi drivers are willing to carrypackages (ie rij 0) or if the payments for incentive cij are setto be relatively high the package flows by taxi become zero-e spoke links are serviced by truck only In this case themodel becomes a typical multiassignment p-hub medianproblem without capacity constraints If the costs to transportpackages by truck tij are set to be relatively high the modeltends to minimize the amount of trucks and to maximize thepackage flows transported by taxi with capacitated spokelinks In this case the model becomes similar to a capacitatedmultiassignment p-hub covering problem

33 Modified Genetic Algorithm Method -e developedMILP model to solve the HLPs is NP-hard due to the in-terrelationship between locating hub facilities and designingnetwork topology Past studies focusing on exact algorithmseg branch-and-bound [64] branch-and-cut [65] Lagrang-ian relaxation [66] and Benders decomposition [67] mainlyhandle the HLPs with limited scale To solve the HLPs with alarger scale heuristic algorithmsmdasheg the general variableneighborhood search approach [68] the memetic algorithmmapping two local search heuristics developed by Maric et al[69] and the genetic algorithm (GA) adopted by Lin et al [55]for capacitated p-hub median problemsmdashare able to providethe near-optimal solutions with less computation time

In this study we propose a modified GAmethod to solvethe large-scale HLP problems -e HLP model consists ofbinary variables indicating hub locations and non-negativecontinuous variables indicating package flows -e modifiedGA considers the set of binary variables as an individual Foreach individual the fitness function is the objective functionof themodel mentioned above where binary variables are setfixed -e detailed algorithm is presented in Appendix withthe parameters empirically set as in Table 2

To investigate the validity and efficiency of the modifiedGA we conduct a series of computational experimentscomparing the computation times and optimal solutionsgenerated by the GAwith those solved by exact algorithms inCPLEX (with default parameters) [70] listed in Table 3 Weuse (N H p) to denote the problem scale where N is thenumber of OD nodes H is the number of candidate hubsand p is the number of hubs to establish Table 3 shows thatwhen N is greater than 110 andor H is greater than 80CPLEX fails to provide a feasible solution in some caseswithin max time limit (ie 24 hours)

-e results show that the computation time of the exactalgorithm increases rapidly with the number of stores andhubs In terms of the quality of solutions if optimal solutionscan be efficiently provided by the exact algorithms the GAachieves the same or similar results If suboptimal solutions

Table 1 Summary of notations

Input parametersΩ Set of nodes representing service storesΘ Set of potential hub locations ΘsubΩWij Package demand from node i to jFij Taxi flow from node i to jrij Proportion of taxi drivers who are willing to carry packages from node i to j namely ldquoWTCPrdquoθ Average number of packages that could be contained in a taxi trunkgk Cost for establishing and operating hub kcij Incentive payment per package for taxi drivers from node i to jmkl Transport cost per package from hub k to l by metrotij Transport cost per package from node i to j by truckp Number of hubs to be established

Variableshk Binary variable indicating whether a hub is established at node k 1 if so 0 otherwisezik Package flow routed from node i to hub k by taxiuik Package flow routed from node i to hub k by tuckyikl Package flow emanating from node i routed from hub k to hub l by metroxilj Package flow emanating from node i routed from hub l to node j by taxivilj Package flow emanating from node i routed from hub l to node j by truck


with gaps can be provided by the exact algorithms the GAcan even achieve better A feasible solution can still beprovided by the GA when the exact algorithm fails toprovide a feasible solution in reasonable time

4 Case Study An Example of Shanghai

41 Data and Study Area -e study area is encircled by theouter-ring expressway of Shanghai China covering 680square km with great population densities and high eco-nomic activities We tessellate the study area into 171identical square zones with the length of 2 km In each zoneone service store is designated to service the area -ere are106 zones containing at least one metro station which areconsidered as the candidate locations to establish hub fa-cilities In addition the zones with main land use of agri-culture industry or nature parks are excluded from theanalysis due to scarce demand for delivery service in theseareas-us 127 zones are selected for the optimization of themultimodal PPS network with 94 candidate hub locations-e spatial distribution of zones and candidate hubs ispresented in Figure 2

630 million packages were delivered in Shanghai in 2015with the spatial distribution presented in Figure 3 -edistribution is heterogeneous and in general the demandconcentrates in the central areas In the top ten zones withthe highest demands 311 of the total packages are sent outfrom these areas and 172 of the packages are delivered intothe areas

Based on the automatic vehicle location data of about13000 taxismdashaccounting for one fourths of the total taxisoperated in Shanghaimdashin April 2015 we extract the originand destination of the taxi trips and scale up the number ofthe trips to synthesize the entire taxi service in Shanghai -eresults show that most taxi trips are originated from ordestined to metro stations where the zones with metrostations generate 901 of taxi trips Figure 4(a) presents thespatial distribution of the origins of taxi trips whileFigure 4(b) shows the distribution of the destinations of taxitrips -e two figures suggest that it is reasonable to utilizemetro stations as transfer locations between metros and taxis

We empirically calculate the cost to establish andoperate a hub as 8k CNY per day based on the average costto lease a shop in metro stations (according to the datafrom 58com Inc a Chinarsquos Craigslist equivalent) the areaof hubs for package storage and the equipment and laborcosts in Shanghai according to the Shanghai StatisticYearbook in 2016-e cost to carry the packages by truck is

estimated according to the pricing plan of renting a medium-sized truck from Lalamove an on-demand logistics companyproviding intracity delivery and courier services in Shanghai(for each truck trip 65 CNY for the first 5 km and 4 CNYkmfor more than 5 km (source Lalamove)) -e unit cost fortransporting a package bymetro is set as 5 of the regular fare(for each customer 3 CNY for the first 6 km and 1 CNY per10 km for more than 6 km at most 15 CNY (source ShanghaiShentong Metro)) Each taxi and truck is able to carry 10 and50 packages respectively -e average distances between thezones are calculated as the Euclidean distances between thecentroids of each zone

42 Scenario Analysis Among a number of factors affectingthe system performance we designed three scenarios toevaluate the proposed multimodal PPS network from thefollowing perspectives

(i) Number of hubs(ii) Proportion of taxi drivers who are willing to carry

packages named as ldquoWTCPrdquo

(1) WTCP independent from the incentives(2) WTCP dependent on the incentives

Each scenario contains several subscenarios Table 4summarizes the attributes of each scenario and sub-scenario in details Among the subscenarios A6 B3 and C3are the same while B1 and C1 are the same

Scenario A consists of 7 subscenarios In the scenario theimpacts of different numbers of hubs p (ie 5 6 8 10 12 15and 20) are tested -eWTCP is fixed 50 taxi drivers arewilling to carry packages To compute the delivery cost bytaxi on each spoke link we set that a taxi driver is able toreceive an extra 5 of the regular trip fare (for each taxi trip14 CNY for the first 3 km 25 CNYkm for 3ndash15 km and 38CNY for more than 10 km (source Shanghai MunicipalTransportation Commission)) for every additional packageto deliverWith the capacity of 10 packages a taxi driver mayget at most 50 more than the regular fare

Scenario B consists of 5 subscenarios Different WTCP(ie 0 25 50 75 and 100) are tested with theincentive fixed at 5 of the trip fare -e number of hubs isfixed to 15 -e subscenario B1 represents a metro-truckonly network without taxi -e formulation becomes atypical multiassignment p-hub median problem withoutcapacity constraints

Scenario C consists of 5 subscenarios where C1 is thesame as B1 Different from scenario B the WTCP dependson the incentive We assume that with an extra 0 255 75 and 10 of regular taxi fare for each package 025 50 75 and 100 of taxi drivers are willing to carrypackages -e number of hubs is also fixed to 15

421 Scenario A Number of Hubs Figure 5(a) illustrates thetrends of total cost and transport cost with increased numberof hubs in which the difference of two series of valuesrepresents the cost to establish and to operate the hubsMorehubs lead to more packages transported by taxi which

Table 2 -e parameters of GA

Parameter ValuePopulation size K 50Desired average tournament size Ft 54Crossover fraction Pc 07Mutation fraction Pm 01Stall generation limit Gs 50Function tolerance τ 001Max time limit Tmax 24 (hours)


1 2 3 4

6 7 8 9 10 11 12

13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33 34 35

36 37 38 39 40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59 60 61

62 63 64 65 66 67 68 69 70 71 72 73

74 75 76 77 78 79 80 81 82 83 84 85 86

87 88 89 90 91 92 93 94 95 96 97

98 99 100 101 102 103 104 105 106 107 108

109 110 111 112 113 114 115

116 117 118 119 120 121 122 123

124 125 126 127

2 km

Outer ring road

Metro line

Demand node

Candidate hub

N

5

Figure 2 -e study area of Shanghai China (source authorsrsquo revision based on OpenStreetMap)

gt242418120600

2 km N

(a)

gt242418120600

2 km N

(b)

Figure 3 Spatial distribution of demand for package delivery (source authorsrsquo revision based on the Shanghai Municipal Postal Ad-ministration) (a) Package demand distribution outgoing and (b) package demand distribution incoming

Table 3 Comparison of results and computation times of the algorithms

Scale of the problemExact algorithm in CPLEX Modified GA

Computation time (min) Best solution Gap () Computation time (min) Best solution(40 28 5) 86 83139 00 267 83139(40 28 15) 154 159712 00 466 159712(70 30 8) 2015 358149 00 1839 358656(70 40 14) 14400lowast 378673 31 8924 374123(100 30 15) 14400lowast 818480 56 10561 782291(100 75 15) 14400lowast 700527 148 14400lowast 670920(110 30 15) 14400lowast 901690 205 14400lowast 858458(110 80 20) 14400lowast nfsp 90 14400lowast 781913(127 94 15) 14400lowast nfsp 233 14400lowast 973549(127 94 20) 14400lowast nfsp 134 14400lowast 977518lowast-e upper time limit ie 24 hours nfsp no feasible solution provided


Table 4 Design of the scenarios

Scenario Number of hubs WTCP IncentivesAA1 5 50 50 of trip fareA2 6 50 50 of trip fareA3 8 50 50 of trip fareA4 10 50 50 of trip fareA5 12 50 50 of trip fareA6 15 50 50 of trip fareA7 20 50 50 of trip fareBB1 15 0 Not availableB2 15 25 50 of trip fareB3 15 50 50 of trip fareB4 15 75 50 of trip fareB5 15 100 50 of trip fareCC1 15 0 Not availableC2 15 25 25 of trip fareC3 15 50 50 of trip fareC4 15 75 75 of trip fareC5 15 100 100 of trip fare

Number of hubs4 6 8 10 12 14 16 18 20 22

800k

850k

900k

950k

1000k

1050k

1100k

Hub cost

Total costTransport cost

(a)

Number of hubs4 6 8 10 12 14 16 18 20 22

30

40

50

60

70

80

(b)

Figure 5 System cost (a) and proportion of packages transported by taxi on spoke links (b) by number of hubs

gt404030201000

2 km N

(a)

gt404030201000

2 km N

(b)

Figure 4 Spatial distribution of taxi trips (source authorsrsquo revision based on the data provided by Shanghai Qiangsheng Taxi) (a) Taxi flowdistribution outgoing and (b) taxi flow distribution incoming


1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

5 hubs

6 hubs

8 hubs

10 hubs

(a)

Figure 6 Continued


reduces the transport costs on spoke links as shown inFigure 5(b) Nonetheless the marginal savings of transportcost declines with more hubs established With 5 additionalhubs established the increase of the hub cost is 40k CNYFrom 5 hubs to10 hubs 182 of the packages are shiftedfrom the truck to taxi while the transport cost reduces by895k CNY From 15 hubs to 20 hubs the packagesrsquo modalshift from the truck to taxi is 79 with only 342k CNY oftransportation cost saved According to the figures the totalcost reaches minimum with 15 hubs Beyond 15 hubs thecost to set up an extra hub becomes greater than the re-duction of the transportation cost

Figure 6 presents the proportions of packages trans-ported by taxi and the spatial distribution of hubs by

subscenario With 5 hubs the system mostly assigns thehubs into the central area with greater demand As a resultthe periphery zones close to the outer-ring expressway areunderserved by taxis Among all 127 zones there is no zonein which more than 50 of the packages can be served bytaxi -e rest of the packages are transported by truck with ahigher cost With 6 8 10 12 15 and 20 hubs the systemcovers more periphery zones and the number of zones whereover 50 of demand can be served by taxis increases to 2 1131 68 110 and 127 respectively

-e optimal locations of hubs in each multimodal PPSnetwork are demonstrated in figures A link connecting to aservice store (blue dot) and a hub (red dot) represents thepackage transported between a service store and a hub by

1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

12 hubs

15 hubs

20 hubs

(a) (b)

(b)

Figure 6 Proportion of package demand transported by taxi in each zone (a) and the spatial distribution of hubs (b)


taxi -e color of a link is the same as its origin node -ewidth of the link represents the package flow through thelink In the figures there are several hub facilities clusteredtogether in the central area One plausible reason is that thepackage demand and taxi flow are both higher in the centralarea -e establishment of hubs in these zones is able toservice more demand with limited resources If more hubfacilities are allowed some hubs spread out near the outer-ring expressway to expand the coverage of demand

Take the scenario with 15 hubs as an example -edetailed routing procedures for packages from an originservice store to all destination stores are illustrated inFigure 7 -e routing process consists of three phases In thefirst phase most of the packages are transported by the taxito the close hubs Due to the constrained carrying capacitybetween the service store and hubs the rest are transported

to hub by trucks In phase 2 the packages are transported bymetro to the hubs connecting to their destination storesFinally the packages are routed from the hubs to the re-spective destination stores in phase 3 On spoke linksoriginated from the hubs in the central area the packages aremostly transported by taxis while on the spoke linksoriginated from the hubs in other areas most packages aretransported by trucks due to the insufficiency of taxis

422 Scenario B WTCP Independent from IncentivesUnder this scenario the payments for incentive are inde-pendent from the WTCP If there are no taxi driverswilling to carry packages the PPS network becomes a metro-truck system which generates relatively high transport costson spoke links As shown in Figures 8(a) and 9(b) if WTCP

Phase 1 Phase 2 Phase 3

Service stores

Hub facilities

Spoke links by taxi from service stores

Spoke links by taxi from hubs

Spoke links by trucks

Backbone links by metro

Figure 7 Package routing procedures

WTCP0 25 50 75 100

1400k

1300k

1200k

1100k

1000k

900k

800k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)

Figure 8 Total cost (a) and proportion of packages transported by taxi on spoke links (b) with different WTCP (independent frompayments for incentive)


increases thanks to lower delivery costs comparing withtrucks the total cost decreases and more packages arecarried by taxis on spoke links

With more taxis willing to carry packages the optimalhub locations become more dispersed in the city Figure 9illustrates the specific hub locations of the five subscenariosunder scenario B with the WTCP and the average hubdistance listed in the caption If no taxi drivers are willing tocarry packages the hub locations are optimized withoutconsidering the distribution of taxi flows If 25 of taxis arewilling to carry packages the optimal network tends tocluster hubs in the central area of the city where the packagedemands and taxi supplies are both high -e layout allowsmore service stores in the central area linking to hubs Withthe increase of WTCP the central area can be serviced byfewer hubs and some hubs are relocated to peripheral areasto cover more package demands

With more taxis involved more trucks are expected to besaved in the logistics system We divide the study area intothree partsmdashcentral middle and outer partsmdashaccording tothe locations of Shanghai inner- middle- and outer-ringexpressways (see Figure 10(a)) With WTCP increasingfrom 0 to 100 8932 7643 and 5970 of truck flowis saved in the central middle and outer parts respectively(see Figure 10(b)) -e central part benefits the most fromthe PPS network followed by the middle and outer part-is

result implies that the PPS network could mitigate thenegative effects of urban logistics on traffic congestion andair pollution in the urban areas

423 Scenario C WTCP Independent from IncentivesUnder this scenario the WTCP depends on incentivepaymentmdashthe unit cost of taxi delivery Figures 11(a) and11(b) present the trends of total cost and proportion ofpackage flows delivered by taxis on spoke links respectivelyAlthough the increased WTCP allows more packages toshift from the truck to taxi the increase of incentive raisesthe total costs of the systemWith greater incentives the PPSnetwork prefers trucks to transport packages on most spokelinks leading to the reduction of taxi delivery -e resultsshow that under the linear assumption of incentive-WTCPrelationship the optimal payment for incentive is around25 of regular taxi fare per package with 25 of WTCPIn this case despite of the fact that the proportion taxi usageis not the highest it generates the minimum total cost due tolower payments for incentive

5 Conclusion and Discussion

-is study envisions a multimodal PPS network integratingmetro taxi and truck with a hub-and-spoke network Onspoke links the PPS network balances the usage of taxis and

(b)(a) (c)

(d) (e)

Figure 9 Optimal hub locations of scenario B (a) 0 945 km ie hub location of the metro-truck network without taxis (b) 25 716 km(c) 50 813 km (d) 75 885 km and (e) 100 892 km


trucks for package transport according to the unit costs ofthese twomodes and capacity constraints of taxis-e designof the multimodal PPS network is formulated into a HLPwith the mixed integer linear programming framework -edeveloped model is an extension to the two classic types ofHLPs the multiassignment p-hub median problem withoutcapacity constraints if the spoke links are serviced by truckonly and a capacitated multiassignment p-hub coveringproblem if the model tends to minimize the amount oftrucks and to maximize the package flows transported bytaxi with capacitated spoke links A modified GA is devel-oped taking into account the constraints of carrying capacityby taxi

To demonstrate the potentiality of the multimodal PPSnetwork for urban logistics the network is adopted based on

the real-world data of Shanghai A series of scenarios aredesigned to assess the performance of the system from twoperspectives the number of hubs and the proportion of taxidrivers who are willing to carry packages -e scenariosshow that with increased number of hubs the spatial dis-tribution of hubs disperses from the city center to peripheralareas and more areas can be serviced by taxis More hubslead to more packages transported by taxi which reduces thecosts on spoke links but the marginal savings of transportcost declines as well -ere is nevertheless a trade-off be-tween the operation cost saving by taxis and the estab-lishment cost of an extra hub -e analysis also presents thatwith given number of hubs if the WTCP is independentfrom the incentive payments withmore taxis willing to carrypackages the total cost of the system keeps decreasing

WTCP0 25 50 75 100

800k

900k

1000k

1100k

1200k

1300k

1400k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)

Figure 11 Total cost (a) and proportion of packages transported by taxi on spoke links (b) with different WTCP (dependent on paymentfor incentive)

2km

ExpresswayCentral part

Middle partOuter part

(a)

WTCP0 25 50 75 100

0

1k

2k

3k

4k

5k

6k

7k

8k

Central partMiddle partOuter part

(b)

Figure 10 Truck flow of different parts of Shanghai (a) Study area divided into three parts and (b) truck flow (in- and out-flow) of each part


However if the proportion of taxis willing to carry packagesincreases with the incentive payments to taxi drivers anoptimal value of incentives exists by balancing the operationcosts of taxis and trucks

For future works some hypothetical assumptions madein this study can be further released For instance thecurrent network requires the packages to be routed via atleast one hub while a network that allows direct connectionsbetween service stores could extend the network coverage Inaddition the influence of various partitioning methods ofthe study area on the resulting network can be furtherevaluated It is also recommended to consider the willing-ness of taxi drivers to participate in PPS activities as a de-cision variable in network optimization It can be an effectivemeans to adjust the carrying capacities since more taxis maybe willing to participate in the PPS activities with greaterincentives Finally the PPS network may lead to the reba-lancing of taxis which may result in different optimizednetwork patterns

Appendix

Steps and Pseudocodes of the Modified GA

-e modified GA iterates from Step 3 to 6 and stops if theconvergence criterion is satisfied

Step 1 Coding a hub location arrangement is repre-sented by an individual consisting of a binary string oflength Np I(k) = 1 if node k is selected to locate a hubfacility Otherwise I(k) = 0Step 2 Initialization a population of individuals israndomly generated with a size of K For each indi-vidual p genes are selected from in total n geneswithout replacement and assigned as 1 -e other genes

equal 0 Each individual has exactly p number of ldquo1rdquorepresenting p nodes to locate hub facilitiesStep 3 Fitness evaluation the fitness function is set asthe objective function of the model developed inSection 32 Giving selected hub locations the sub-problem becomes a linear programming problem in-volving continuous variables x y z u and v that canbe solved efficiently to evaluate the fitness of eachindividualStep 4 Selection the fine-grained tournament selec-tion strategy (FGTS) is adopted to select K individualsfrom the population [71] Denote Ft as the desiredaverage tournament size -e strategy performsweighted sampling of |Ft| + 1 with replacement fromthe population k1 times and performs weightedsampling of |Ft| with replacement k2 times -e weightof an individual equals its fitness value For eachsample the one with the lowest fitness value is se-lected -e values of k1 and k2 are determined by thefollowing equations

k1 + k2 K

k1 times Ft

11138681113868111386811138681113868111386811138681113868 + 11113872 1113873 + k2 times Ft

11138681113868111386811138681113868111386811138681113868 K times Ft

(A1)

Step 5 Crossover two offsprings from a pair of parentsare produced -e basic crossover operator randomlyexchanges the codes of each gene-e number of ldquo1rdquo inthe resulting offspring may not equal p To address thisproblem we simultaneously exchange the codes for twogenes to ensure that each offspring has p ldquo1rdquo valuesAlgorithm 1 describes the crossoverStep 6 Mutation the gene code of an individual israndomly shifted from 0 to 1 or from 1 to 0 To ensurethat there are p number of ldquo1rdquo in an individual after themutation operation we change the codes of two genes

I1⟵ First parent I2⟵ Second parentNp⟵Number of potential hub locationsi⟵ 0 j⟵Np+ 1while ilt jfor k⟵ (i+ 1) to (jminus 1)if I1(k) 1 and I2(k) 0

i⟵ k breakend ifi⟵Np

end forfor k⟵ (jminus 1) to (i+ 1)if I1(k) 0 and I2(k) 1

j⟵ k breakend ifj⟵ 0

end forif ilt jExchange (I1(i) I2(i)) and (I1(j) I2(j)) with probability Pc

end ifend while

ALGORITHM 1 Crossover operation


that have different codes simultaneously Algorithm 2describes the mutationConvergence criterion the algorithm stops when (1)the average relative change in the fitness function valueover stall generation limit Gs is less than functiontolerance τ or (2) the computation time exceeds timelimit Tmax

Data Availability

-edata used to support the results of this study are availablefrom the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is research was supported by the National Natural ScienceFoundation of China (71671124) and Shanghai Science andTechnology Committee (17DZ1204404)

References

[1] National Bureau of Statistics of China China StatisticalYearbook 2018 China Statistics Press Beijing Beijing China2018

[2] European Commission Green Paper towards a New Culturefor Urban Mobility European Commission Brussels Bel-gium 2007

[3] A Sampaio M Savelsbergh L Veelenturf andT van Woensel ldquoCrowd-based city logisticsrdquo in SustainableTransportation and Smart Logistics pp 381ndash400 ElsevierAmsterdam Netherlands 2019

[4] A van Binsbergen and J Visser ldquoNew urban goods distri-bution systemsrdquo in Proceedings of the Conference on UrbanTransport Systems Miami FL USA March 1999

[5] C Shaefer and N Dalkmann ldquoA new and innovative ap-proach for bus systems in rural areasrdquo in Proceedings of theEuropean Transport Conference Strasbourg France October2003

[6] A Trentini and N Mahlene ldquoToward a shared urbantransport system ensuring passengers amp goods cohabitationrdquoTeMA Journal of Land Use Mobility and Environment vol 3no 2 2010

[7] A Trentini and N Malhene ldquoFlowmanagement of passengersand goods coexisting in the urban environment conceptualand operational points of viewrdquo ProcediamdashSocial and Be-havioral Sciences vol 39 pp 807ndash817 2012

[8] B Li D Krushinsky H A Reijers et al ldquo-e share-a-rideproblem people and parcels sharing taxisrdquo European Journalof Operational Research vol 238 no 1 pp 31ndash40 2014

[9] N-Q Nguyen N-V-D Nghiem P-T Do K-T LEM-S Nguyen and N Mukai ldquoPeople and parcels sharing ataxi for Tokyo cityrdquo in Proceedings of the Sixth InternationalSymposium on Information and Communication Tech-nologymdashSoICT 2015 pp 90ndash97 Hue Vietnam December2015

[10] B Li D Krushinsky T Van Woensel and H A Reijers ldquo-eshare-a-ride problem with stochastic travel times and sto-chastic delivery locationsrdquo Transportation Research Part CEmerging Technologies vol 67 pp 95ndash108 2016

[11] R Masson A Trentini F Lehuede et al ldquoOptimization of acity logistics transportation systemwithmixed passengers andgoodsrdquo EURO Journal on Transportation and Logistics vol 6no 1 pp 81ndash109 2017

[12] V Ghilas E Demir and T V Woensel ldquo-e pickup anddelivery problem with time windows and scheduled linesrdquoINFOR Information Systems amp Operational Research vol 54no 2 pp 1ndash21 2016

[13] V Ghilas E Demir and T V Woensel ldquoA scenario-basedplanning for the pickup and delivery problem with timewindows scheduled lines and stochastic demandsrdquo Trans-portation Research Part B Methodological vol 91 pp 34ndash512016

[14] E Fatnassi J Chaouachi and W Klibi ldquoPlanning and op-erating a shared goods and passengers on-demand rapidtransit system for sustainable city-logisticsrdquo TransportationResearch Part B Methodological vol 81 pp 440ndash460 2015

[15] B Yildiz and M Savelsbergh ldquoService and capacity planningin crowd-sourced deliveryrdquo Transportation Research Part CEmerging Technologies vol 100 pp 177ndash199 2019

[16] M SteadieSeifi N P Dellaert W Nuijten T Van Woenseland R Raoufi ldquoMultimodal freight transportation planning aliterature reviewrdquo European Journal of Operational Researchvol 233 no 1 pp 1ndash15 2014

[17] P Arnold D Peeters and I -omas ldquoModelling a railroadintermodal transportation systemrdquo Transportation ResearchPart E Logistics and Transportation Review vol 40 no 3pp 255ndash270 2004

[18] B Groothedde C Ruijgrok and L Tavasszy ldquoTowards col-laborative intermodal hub networks a case study in the fastmoving consumer goods marketrdquo Transportation ResearchPart E vol 41 no 6 pp 567ndash583 2005

I⟵An individualNp⟵Number of potential hub locationsO⟵ Set of the locations of genes in I with the code of oneZ⟵ Set of the locations of genes in I with the code of zerono⟵Number of ones in Inz⟵Number of zeros in In⟵min (no nz)for k⟵ 1 to nChange the codes of the genes (I(O(k)) I(Z(k))) with probability Pm

end if

ALGORITHM 2 Mutation operation


[19] Y Qu T Bektas and J Bennell ldquoSustainability SI multimodemulticommodity network design model for intermodalfreight transportation with transfer and emission costsrdquoNetworks and Spatial Economics vol 16 no 1 pp 303ndash3292016

[20] F Fotuhi and N Huynh ldquoReliable intermodal freight networkexpansion with demand uncertainties and network disrup-tionsrdquo Networks and Spatial Economics vol 17 no 2pp 405ndash433 2017

[21] H Kim and M S Ryerson ldquo-e q-Ad hoc hub locationproblem for multi-modal networksrdquo Networks and SpatialEconomics vol 17 no 3 pp 1015ndash1041 2017

[22] M E Orsquokelly ldquo-e location of interacting hub facilitiesrdquoTransportation Science vol 20 no 2 pp 92ndash106 1986

[23] M E OrsquoKelly ldquoActivity levels at hub facilities in interactingnetworksrdquoGeographical Analysis vol 18 no 4 pp 343ndash356 1986

[24] M E Orsquokelly ldquoA quadratic integer program for the location ofinteracting hub facilitiesrdquo European Journal of OperationalResearch vol 32 no 3 pp 393ndash404 1987

[25] J F Campbell ldquoInteger programming formulations of dis-crete hub location problemsrdquo European Journal of Opera-tional Research vol 72 no 2 pp 387ndash405 1994

[26] J F Campbell ldquoHub location and the p-hub median prob-lemrdquo Operations Research vol 44 no 6 pp 923ndash935 1996

[27] J F Campbell ldquoHub location for time definite trans-portationrdquo Computers amp Operations Research vol 36 no 12pp 3107ndash3116 2009

[28] J Ebery ldquoSolving large single allocation p-hub problems withtwo or three hubsrdquo European Journal of Operational Researchvol 128 no 2 pp 447ndash458 2001

[29] N Ghaffarinasab and B Y Kara ldquoBenders decompositionalgorithms for two variants of the single allocation hub lo-cation problemrdquo Networks and Spatial Economics vol 19no 1 pp 83ndash108 2019

[30] M Vidovic S Zecevic M Kilibarda et al ldquo-e p-hub modelwith hub-catchment areas existing hubs and simulation acase study of Serbian intermodal terminalsrdquo Networks andSpatial Economics vol 11 no 2 pp 295ndash314 2011

[31] X Sun W Dai Y Zhang et al ldquoFinding-hub median lo-cations an empirical study on problems and solution tech-niquesrdquo Journal of Advanced Transportation vol 2017 ArticleID 9387302 23 pages 2017

[32] B Y Kara and B C Tansel ldquoOn the single-assignment p-hubcenter problemrdquo European Journal of Operational Researchvol 125 no 3 pp 648ndash655 2000

[33] B Qu and K Weng ldquoPath relinking approach for multipleallocation hub maximal covering problemrdquo Computers ampMathematics with Applications vol 57 no 11-12 pp 1890ndash1894 2009

[34] H Karimi and M Bashiri ldquoHub covering location problemswith different coverage typesrdquo Scientia Iranica vol 18 no 6pp 1571ndash1578 2011

[35] S Gelareh and D Pisinger ldquoFleet deployment network designand hub location of liner shipping companiesrdquo Trans-portation Research Part E Logistics and Transportation Re-view vol 47 no 6 pp 947ndash964 2011

[36] S Alumur and B Y Kara ldquoNetwork hub location problemsthe state of the artrdquo European Journal of Operational Researchvol 190 no 1 pp 1ndash21 2008

[37] J F Campbell and M E OrsquoKelly ldquoTwenty-five years of hublocation researchrdquo Transportation Science vol 46 no 2pp 153ndash169 2012

[38] R Z Farahani M Hekmatfar A B Arabani et al ldquoHublocation problems a review of models classification solution

techniques and applicationsrdquo Computers amp Industrial En-gineering vol 64 no 4 pp 1096ndash1109 2013

[39] C-H Lee H-B Ro and D-W Tcha ldquoTopological design of atwo-level network with ring-star configurationrdquo Computers ampOperations Research vol 20 no 6 pp 625ndash637 1993

[40] M Labbe and H Yaman ldquoSolving the hub location problem ina star-star networkrdquo Networks vol 51 no 1 pp 19ndash33 2008

[41] I Contreras E Fernandez and A Marın ldquoTight bounds froma path based formulation for the tree of hub location prob-lemrdquo Computers amp Operations Research vol 36 no 12pp 3117ndash3127 2009

[42] I Contreras E Fernandez and A Marın ldquo-e tree of hubslocation problemrdquo European Journal of Operational Researchvol 202 no 2 pp 390ndash400 2010

[43] E Martins de Sa I Contreras J-F Cordeau et al ldquo-e hubline location problemrdquo Transportation Science vol 49 no 3pp 500ndash518 2015

[44] T Aykin ldquoLagrangian relaxation based approaches tocapacitated hub-and-spoke network design problemrdquo Euro-pean Journal of Operational Research vol 79 no 3pp 501ndash523 1994

[45] C-C Lin and S-H Chen ldquoAn integral constrained gener-alized hub-and-spoke network design problemrdquo Trans-portation Research Part E Logistics and TransportationReview vol 44 no 6 pp 986ndash1003 2008

[46] J G Klincewicz ldquoHub location in backbonetributary net-work design a reviewrdquo Location Science vol 6 no 1ndash4pp 307ndash335 1998

[47] H Yaman ldquo-e hierarchical hub median problem with singleassignmentrdquo Transportation Research Part B Methodologicalvol 43 no 6 pp 643ndash658 2009

[48] N Bolandabb ldquoPreprocessing and cutting for multiple allo-cation hub location problemsrdquo European Journal of Opera-tional Research vol 155 no 3 pp 638ndash653 2004

[49] V Rodriguez M Alvarez and L Barcos ldquoHub location undercapacity constraintsrdquo Transportation Research Part E Logis-tics and Transportation Review vol 43 no 5 pp 495ndash5052007

[50] D Chauhan A Unnikrishnan and M Figliozzi ldquoMaximumcoverage capacitated facility location problem with rangeconstrained dronesrdquo Transportation Research Part CEmerging Technologies vol 99 pp 1ndash18 2019

[51] J Puerto A B Ramos A M Rodrıguez-Chıa andM C Sanchez-Gil ldquoOrdered median hub location problemswith capacity constraintsrdquo Transportation Research Part CEmerging Technologies vol 70 pp 142ndash156 2016

[52] I Correia S Nickel and F Saldanha-da-Gama ldquoMulti-product capacitated single-allocation hub location problemsformulations and inequalitiesrdquo Networks and Spatial Eco-nomics vol 14 no 1 pp 1ndash25 2014

[53] D Bryan ldquoExtensions to the hub location problem formu-lations and numerical examplesrdquo Geographical Analysisvol 30 no 4 pp 315ndash330 1998

[54] H Yaman and G Carello ldquoSolving the hub location problemwith modular link capacitiesrdquo Computers amp Operations Re-search vol 32 no 12 pp 3227ndash3245 2005

[55] C-C Lin J-Y Lin and Y-C Chen ldquo-e capacitated p-hubmedian problem with integral constraints an application to aChinese air cargo networkrdquo Applied Mathematical Modellingvol 36 no 6 pp 2777ndash2787 2012

[56] I Correia S Nickel and F Saldanha-da-Gama ldquoSingle-as-signment hub location problems with multiple capacitylevelsrdquo Transportation Research Part B Methodologicalvol 44 no 8-9 pp 1047ndash1066 2010


[57] S Elhedhli and H Wu ldquoA Lagrangean heuristic for hub-and-spoke system design with capacity selection and congestionrdquoINFORMS Journal on Computing vol 22 no 2 pp 282ndash2962010

[58] I Contreras J-F Cordeau and G Laporte ldquoExact solution oflarge-scale hub location problems with multiple capacitylevelsrdquo Transportation Science vol 46 no 4 pp 439ndash4592012

[59] G Nagy and S Salhi ldquo-e many-to-many location-routingproblemrdquo Top vol 6 no 2 pp 261ndash275 1998

[60] M Wasner and G Zapfel ldquoAn integrated multi-depot hub-location vehicle routing model for network planning of parcelservicerdquo International Journal of Production Economicsvol 90 no 3 pp 403ndash419 2004

[61] J U Sun ldquoAn integrated hub location andmulti-depot vehiclerouting problemrdquo Applied Mechanics and Materials vol 409-410 pp 1188ndash1192 2013

[62] G Musolino C Rindone A Polimeni and A VitettaldquoPlanning urban distribution center location with variablerestocking demand scenarios general methodology andtesting in a medium-size townrdquo Transport Policy vol 80pp 157ndash166 2019

[63] A T Ernst and M Krishnamoorthy ldquoExact and heuristicalgorithms for the uncapacitated multiple allocation p-hubmedian problemrdquo European Journal of Operational Researchvol 104 no 1 pp 100ndash112 1998

[64] L Canovas S Garcıa and A Marın ldquoSolving the uncapa-citated multiple allocation hub location problem by means ofa dual-ascent techniquerdquo European Journal of OperationalResearch vol 179 no 3 pp 990ndash1007 2007

[65] S Garcıa M Landete and A Marın ldquoNew formulation and abranch-and-cut algorithm for the multiple allocation p-hubmedian problemrdquo European Journal of Operational Researchvol 220 no 1 pp 48ndash57 2012

[66] H Pirkul and D A Schilling ldquoAn efficient procedure fordesigning single allocation hub and spoke systemsrdquo Man-agement Science vol 44 no 12 pp S235ndashS242 1998

[67] R S de Camargo G de Miranda Jr and H P L LunaldquoBenders decomposition for hub location problems witheconomies of scalerdquo Transportation Science vol 43 no 1pp 86ndash97 2009

[68] A Ilic D Urosevic J Brimberg and N Mladenovic ldquoAgeneral variable neighborhood search for solving the unca-pacitated single allocation p-hub median problemrdquo EuropeanJournal of Operational Research vol 206 no 2 pp 289ndash3002010

[69] M Maric Z Stanimirovic and P Stanojevic ldquoAn efficientmemetic algorithm for the uncapacitated single allocation hublocation problemrdquo Soft Computing vol 17 no 3 pp 445ndash4662013

[70] CPLEX ldquoIBM ILOG V128 userrsquos manual for CPLEXrdquo 2017[71] V Filipovic ldquoFine-grained tournament selection operator in

genetic algorithmsrdquo Computing and Informatics vol 22no 2 pp 143ndash161 2012


network with the objective of minimizing the movements ofempty vehicles and the waiting times of passengers andpackages Yildiz and Savelsbergh [15] explore the service andcapacity planning problem in store-to-door meal deliverywhere the delivery service is provided by individualrsquos willingto participate in such activity

-e contribution of this studymdashdifferent from currentstudies on vehicle routing in a PPS systemmdashis to design themultimodal PPS network with the hub-and-spoke structure-e idea of the hub-and-spoke network design for multi-modal logistics networks is widely supported by pastscholars [16] By integrating multiple modes into one lo-gistics network the new system is able to achieve economiesof scale more effectively thus improving the transport ef-ficiency [17 18] Current literatures mainly focus on theintercity multimodal logistics network Qu et al [19] designa logistics network integrating ocean and coastal routesinland waterways railways roadways and airways withnonlinear transfer costs between different modes Takinginto account demand uncertainties and network disruptionsFotuhi and Huynh [20] identify the rail links to retrofitexisting intermodal hubs to expand and locations of newhubs in the rail-road network Similarly Kim and Ryerson[21] identify a set of unaffected hubs during network dis-ruption in the US ocean-inland freight network

A conceptual design of the multimodal PPS network forurban parcel delivery is envisioned and drawn in Figure 1integrating metro carriages taxis and trucks -e fusion ofmetro taxi and truck absorbs the advantages of the threemodes metro trains follow predetermined routes andschedules with high reliability punctuality and large car-rying capacities taxis and trucks are flexible and are able toprovide door-to-door services -e carrying capacity of taxisis constrained by the willingness of drivers to help carryingpackages -e capacity of trucks is unlimited since thefreighters are fully controlled by the couriers However thedelivery cost of trucks is higher than the cost of the sharedtaxis

To explore the optimal design of a multimodal PPSnetwork we formulate the network design task into hublocation problems (HLPs) -e rest of the paper is organizedas follows Section 2 reviews current HLPs and statesthe novelty of the proposed multimodal PPS network InSection 3 we propose a variant of the HLP model anddevelop a mixed integer linear programming model with amodified genetic algorithm to optimize the hub-and-spokenetwork Section 4 presents an example of Shanghai for thecase study and provides quantitative assessment of thenetwork from the perspectives of the number of hubs andthe proportion of taxi drivers who are willing to carrypackages Finally we conclude the study and offer somediscussions

2 Literature Review Hub Location Problems

Hub location problems are firstly proposed by OrsquoKelly in1980s [22ndash24] Typical HLPs can be classified based on theirobjectives the p-hub median problems locate p hubs tominimize the total routing cost [25ndash31] the p-hub center

problems locate p hubs so that the maximum cost betweenany OD pair can be minimized [25 32] and the p-hubcovering problems aim to maximize the total flow betweenall OD pairs covered by p hub facilities [33] In these studiesthe number of hubs to be established ie p is prespecifiedInstead of predetermining the number of hubs some worksassume a setup and operation cost for each hub with theobjective of minimizing the sum of hub cost and routing cost[29 34] or maximizing the system profit [35] Compre-hensive reviews can be found in Alumur and Kara [36]Campbell and OrsquoKelly [37] and Farahani et al [38]

-e network topology of HLPs depends on the structureof backbone links and spoke links Typically the hubs arecompletely connected However in some special cases in-complete interhub network structures eg ring [39] star[40] tree [41 42] and line [43] are adopted In terms of thedesign of spoke links for flow assignment a demand nodecan be connected to one or multiple hubs ie single ormultiple assignment structures Aykin [44] and Martins deSa et al [43] extend the topology of spoke links by con-sidering that the flows between some OD pairs can beshipped directly without being routed through hubs Besidesdirect links Lin and Chen [45] integrate stopovers andfeeders to the network Klincewicz [46] introduce a spokenetwork in which a demand node is allowed to be linked to ahub through other demand nodes In addition to thebackbone-and-spoke bilevel networks some researchesconsider the trilevel network connecting hierarchical hubsand demand nodes [40 47]

-e capacity of links is another essential feature of theHLPs Capacity constraints on flows are usually applied onhubs [25 48ndash52] links [53 54] or both [55] as exogenousconstraints Some studies also treat hub capacities as deci-sion variables to select the optimal hub capacity from a listset of predefined capacity levels each of which is associatedwith a fixed setup cost [56ndash58] Consider that the capacitylimits make the model more realistic though it increases thecomputation time in most cases

-e hub location-routing problem introduced byNagy and Salhi [59] combines the HLPs with the vehiclerouting problems (VRPs) where the vehicle routes areoptimized with respect to hub locations and flow as-signments simultaneously -e combination of HLPs andVRPs both of which are NP-hard problems leads to agreat growth in the solution cost -us the hub location-routing problems are normally formulated with a hier-archical structure in which the upper and lower levelsdeal with the HLPs and VRPs respectively [59ndash62] In thisstudy the vehicle route planning is not considered forsimplification

-is study applies a complete interhub structure Ademand node is allowed to be connected to multiple hubsto improve the flexibility and capacity of the network asmetro stations are completely connected by metro lines andtransfer stations -e spoke links are served by taxis andtrucks -e features of the two modesmdasheg the costs todeliver a package and the capacity constraintsmdashvarylargely -e study also takes into account the exogenousconstraints on spoke links served by taxi due to the driversrsquo



3 Methodology













1113944kisinΘ


1113944lisinΘ



1113944kisinΘ

tik


1113944lisinΘ



1113944lisinΘk


yikl

+ 1113944kisinΘ

gk times hk

(1)

st

1113944kisinΘ

hk p (2)

1113944kisinΘ

zik + uik( 1113857 1113944jisinΩ

Wij i isin Ω

(3)

1113944lisinΘ



1113944iisinΩ


1113944lisinΘ


xikj + vikj1113872 1113873 1113944lisinΘ


(7)


(8)



Metro line

Origin

Destination






































1 2 3 4

6 7 8 9 10 11 12

13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33 34 35

36 37 38 39 40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59 60 61

62 63 64 65 66 67 68 69 70 71 72 73

74 75 76 77 78 79 80 81 82 83 84 85 86

87 88 89 90 91 92 93 94 95 96 97

98 99 100 101 102 103 104 105 106 107 108

109 110 111 112 113 114 115

116 117 118 119 120 121 122 123

124 125 126 127

2 km

Outer ring road

Metro line

Demand node

Candidate hub

N

5


gt242418120600

2 km N

(a)

gt242418120600

2 km N

(b)








Number of hubs4 6 8 10 12 14 16 18 20 22

800k

850k

900k

950k

1000k

1050k

1100k

Hub cost


(a)

Number of hubs4 6 8 10 12 14 16 18 20 22

30

40

50

60

70

80

(b)


gt404030201000

2 km N

(a)

gt404030201000

2 km N

(b)



1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

5 hubs

6 hubs

8 hubs

10 hubs

(a)

Figure 6 Continued






1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

12 hubs

15 hubs

20 hubs

(a) (b)

(b)








Service stores

Hub facilities






WTCP0 25 50 75 100

1400k

1300k

1200k

1100k

1000k

900k

800k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)










(b)(a) (c)

(d) (e)






WTCP0 25 50 75 100

800k

900k

1000k

1100k

1200k

1300k

1400k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)


2km



(a)

WTCP0 25 50 75 100

0

1k

2k

3k

4k

5k

6k

7k

8k


(b)





Appendix





k1 + k2 K

k1 times Ft

11138681113868111386811138681113868111386811138681113868 + 11113872 1113873 + k2 times Ft

11138681113868111386811138681113868111386811138681113868 K times Ft

(A1)







end ifend while




Data Availability




Acknowledgments


References




















end if




























































3 Methodology













1113944kisinΘ


1113944lisinΘ



1113944kisinΘ

tik


1113944lisinΘ



1113944lisinΘk


yikl

+ 1113944kisinΘ

gk times hk

(1)

st

1113944kisinΘ

hk p (2)

1113944kisinΘ

zik + uik( 1113857 1113944jisinΩ

Wij i isin Ω

(3)

1113944lisinΘ



1113944iisinΩ


1113944lisinΘ


xikj + vikj1113872 1113873 1113944lisinΘ


(7)


(8)



Metro line

Origin

Destination






































1 2 3 4

6 7 8 9 10 11 12

13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33 34 35

36 37 38 39 40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59 60 61

62 63 64 65 66 67 68 69 70 71 72 73

74 75 76 77 78 79 80 81 82 83 84 85 86

87 88 89 90 91 92 93 94 95 96 97

98 99 100 101 102 103 104 105 106 107 108

109 110 111 112 113 114 115

116 117 118 119 120 121 122 123

124 125 126 127

2 km

Outer ring road

Metro line

Demand node

Candidate hub

N

5


gt242418120600

2 km N

(a)

gt242418120600

2 km N

(b)








Number of hubs4 6 8 10 12 14 16 18 20 22

800k

850k

900k

950k

1000k

1050k

1100k

Hub cost


(a)

Number of hubs4 6 8 10 12 14 16 18 20 22

30

40

50

60

70

80

(b)


gt404030201000

2 km N

(a)

gt404030201000

2 km N

(b)



1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

5 hubs

6 hubs

8 hubs

10 hubs

(a)

Figure 6 Continued






1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

12 hubs

15 hubs

20 hubs

(a) (b)

(b)








Service stores

Hub facilities






WTCP0 25 50 75 100

1400k

1300k

1200k

1100k

1000k

900k

800k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)










(b)(a) (c)

(d) (e)






WTCP0 25 50 75 100

800k

900k

1000k

1100k

1200k

1300k

1400k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)


2km



(a)

WTCP0 25 50 75 100

0

1k

2k

3k

4k

5k

6k

7k

8k


(b)





Appendix





k1 + k2 K

k1 times Ft

11138681113868111386811138681113868111386811138681113868 + 11113872 1113873 + k2 times Ft

11138681113868111386811138681113868111386811138681113868 K times Ft

(A1)







end ifend while




Data Availability




Acknowledgments


References




















end if




























































































1 2 3 4

6 7 8 9 10 11 12

13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33 34 35

36 37 38 39 40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59 60 61

62 63 64 65 66 67 68 69 70 71 72 73

74 75 76 77 78 79 80 81 82 83 84 85 86

87 88 89 90 91 92 93 94 95 96 97

98 99 100 101 102 103 104 105 106 107 108

109 110 111 112 113 114 115

116 117 118 119 120 121 122 123

124 125 126 127

2 km

Outer ring road

Metro line

Demand node

Candidate hub

N

5


gt242418120600

2 km N

(a)

gt242418120600

2 km N

(b)








Number of hubs4 6 8 10 12 14 16 18 20 22

800k

850k

900k

950k

1000k

1050k

1100k

Hub cost


(a)

Number of hubs4 6 8 10 12 14 16 18 20 22

30

40

50

60

70

80

(b)


gt404030201000

2 km N

(a)

gt404030201000

2 km N

(b)



1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

5 hubs

6 hubs

8 hubs

10 hubs

(a)

Figure 6 Continued






1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

12 hubs

15 hubs

20 hubs

(a) (b)

(b)








Service stores

Hub facilities






WTCP0 25 50 75 100

1400k

1300k

1200k

1100k

1000k

900k

800k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)










(b)(a) (c)

(d) (e)






WTCP0 25 50 75 100

800k

900k

1000k

1100k

1200k

1300k

1400k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)


2km



(a)

WTCP0 25 50 75 100

0

1k

2k

3k

4k

5k

6k

7k

8k


(b)





Appendix





k1 + k2 K

k1 times Ft

11138681113868111386811138681113868111386811138681113868 + 11113872 1113873 + k2 times Ft

11138681113868111386811138681113868111386811138681113868 K times Ft

(A1)







end ifend while




Data Availability




Acknowledgments


References




















end if














































































1 2 3 4

6 7 8 9 10 11 12

13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33 34 35

36 37 38 39 40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59 60 61

62 63 64 65 66 67 68 69 70 71 72 73

74 75 76 77 78 79 80 81 82 83 84 85 86

87 88 89 90 91 92 93 94 95 96 97

98 99 100 101 102 103 104 105 106 107 108

109 110 111 112 113 114 115

116 117 118 119 120 121 122 123

124 125 126 127

2 km

Outer ring road

Metro line

Demand node

Candidate hub

N

5


gt242418120600

2 km N

(a)

gt242418120600

2 km N

(b)








Number of hubs4 6 8 10 12 14 16 18 20 22

800k

850k

900k

950k

1000k

1050k

1100k

Hub cost


(a)

Number of hubs4 6 8 10 12 14 16 18 20 22

30

40

50

60

70

80

(b)


gt404030201000

2 km N

(a)

gt404030201000

2 km N

(b)



1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

5 hubs

6 hubs

8 hubs

10 hubs

(a)

Figure 6 Continued






1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

12 hubs

15 hubs

20 hubs

(a) (b)

(b)








Service stores

Hub facilities






WTCP0 25 50 75 100

1400k

1300k

1200k

1100k

1000k

900k

800k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)










(b)(a) (c)

(d) (e)






WTCP0 25 50 75 100

800k

900k

1000k

1100k

1200k

1300k

1400k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)


2km



(a)

WTCP0 25 50 75 100

0

1k

2k

3k

4k

5k

6k

7k

8k


(b)





Appendix





k1 + k2 K

k1 times Ft

11138681113868111386811138681113868111386811138681113868 + 11113872 1113873 + k2 times Ft

11138681113868111386811138681113868111386811138681113868 K times Ft

(A1)







end ifend while




Data Availability




Acknowledgments


References




















end if



























































1 2 3 4

6 7 8 9 10 11 12

13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33 34 35

36 37 38 39 40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59 60 61

62 63 64 65 66 67 68 69 70 71 72 73

74 75 76 77 78 79 80 81 82 83 84 85 86

87 88 89 90 91 92 93 94 95 96 97

98 99 100 101 102 103 104 105 106 107 108

109 110 111 112 113 114 115

116 117 118 119 120 121 122 123

124 125 126 127

2 km

Outer ring road

Metro line

Demand node

Candidate hub

N

5


gt242418120600

2 km N

(a)

gt242418120600

2 km N

(b)








Number of hubs4 6 8 10 12 14 16 18 20 22

800k

850k

900k

950k

1000k

1050k

1100k

Hub cost


(a)

Number of hubs4 6 8 10 12 14 16 18 20 22

30

40

50

60

70

80

(b)


gt404030201000

2 km N

(a)

gt404030201000

2 km N

(b)



1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

5 hubs

6 hubs

8 hubs

10 hubs

(a)

Figure 6 Continued






1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

12 hubs

15 hubs

20 hubs

(a) (b)

(b)








Service stores

Hub facilities






WTCP0 25 50 75 100

1400k

1300k

1200k

1100k

1000k

900k

800k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)










(b)(a) (c)

(d) (e)






WTCP0 25 50 75 100

800k

900k

1000k

1100k

1200k

1300k

1400k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)


2km



(a)

WTCP0 25 50 75 100

0

1k

2k

3k

4k

5k

6k

7k

8k


(b)





Appendix





k1 + k2 K

k1 times Ft

11138681113868111386811138681113868111386811138681113868 + 11113872 1113873 + k2 times Ft

11138681113868111386811138681113868111386811138681113868 K times Ft

(A1)







end ifend while




Data Availability




Acknowledgments


References




















end if





























































Number of hubs4 6 8 10 12 14 16 18 20 22

800k

850k

900k

950k

1000k

1050k

1100k

Hub cost


(a)

Number of hubs4 6 8 10 12 14 16 18 20 22

30

40

50

60

70

80

(b)


gt404030201000

2 km N

(a)

gt404030201000

2 km N

(b)



1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

5 hubs

6 hubs

8 hubs

10 hubs

(a)

Figure 6 Continued






1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

12 hubs

15 hubs

20 hubs

(a) (b)

(b)








Service stores

Hub facilities






WTCP0 25 50 75 100

1400k

1300k

1200k

1100k

1000k

900k

800k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)










(b)(a) (c)

(d) (e)






WTCP0 25 50 75 100

800k

900k

1000k

1100k

1200k

1300k

1400k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)


2km



(a)

WTCP0 25 50 75 100

0

1k

2k

3k

4k

5k

6k

7k

8k


(b)





Appendix





k1 + k2 K

k1 times Ft

11138681113868111386811138681113868111386811138681113868 + 11113872 1113873 + k2 times Ft

11138681113868111386811138681113868111386811138681113868 K times Ft

(A1)







end ifend while




Data Availability




Acknowledgments


References




















end if



























































1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

5 hubs

6 hubs

8 hubs

10 hubs

(a)

Figure 6 Continued






1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

12 hubs

15 hubs

20 hubs

(a) (b)

(b)








Service stores

Hub facilities






WTCP0 25 50 75 100

1400k

1300k

1200k

1100k

1000k

900k

800k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)










(b)(a) (c)

(d) (e)






WTCP0 25 50 75 100

800k

900k

1000k

1100k

1200k

1300k

1400k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)


2km



(a)

WTCP0 25 50 75 100

0

1k

2k

3k

4k

5k

6k

7k

8k


(b)





Appendix





k1 + k2 K

k1 times Ft

11138681113868111386811138681113868111386811138681113868 + 11113872 1113873 + k2 times Ft

11138681113868111386811138681113868111386811138681113868 K times Ft

(A1)







end ifend while




Data Availability




Acknowledgments


References




















end if































































1007550250

2 km N

1007550250

2 km N

1007550250

2 km N

12 hubs

15 hubs

20 hubs

(a) (b)

(b)








Service stores

Hub facilities






WTCP0 25 50 75 100

1400k

1300k

1200k

1100k

1000k

900k

800k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)










(b)(a) (c)

(d) (e)






WTCP0 25 50 75 100

800k

900k

1000k

1100k

1200k

1300k

1400k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)


2km



(a)

WTCP0 25 50 75 100

0

1k

2k

3k

4k

5k

6k

7k

8k


(b)





Appendix





k1 + k2 K

k1 times Ft

11138681113868111386811138681113868111386811138681113868 + 11113872 1113873 + k2 times Ft

11138681113868111386811138681113868111386811138681113868 K times Ft

(A1)







end ifend while




Data Availability




Acknowledgments


References




















end if
































































Service stores

Hub facilities






WTCP0 25 50 75 100

1400k

1300k

1200k

1100k

1000k

900k

800k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)










(b)(a) (c)

(d) (e)






WTCP0 25 50 75 100

800k

900k

1000k

1100k

1200k

1300k

1400k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)


2km



(a)

WTCP0 25 50 75 100

0

1k

2k

3k

4k

5k

6k

7k

8k


(b)





Appendix





k1 + k2 K

k1 times Ft

11138681113868111386811138681113868111386811138681113868 + 11113872 1113873 + k2 times Ft

11138681113868111386811138681113868111386811138681113868 K times Ft

(A1)







end ifend while




Data Availability




Acknowledgments


References




















end if


































































(b)(a) (c)

(d) (e)






WTCP0 25 50 75 100

800k

900k

1000k

1100k

1200k

1300k

1400k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)


2km



(a)

WTCP0 25 50 75 100

0

1k

2k

3k

4k

5k

6k

7k

8k


(b)





Appendix





k1 + k2 K

k1 times Ft

11138681113868111386811138681113868111386811138681113868 + 11113872 1113873 + k2 times Ft

11138681113868111386811138681113868111386811138681113868 K times Ft

(A1)







end ifend while




Data Availability




Acknowledgments


References




















end if






























































WTCP0 25 50 75 100

800k

900k

1000k

1100k

1200k

1300k

1400k

(a)

WTCP0 25 50 75 100

0

10

20

30

40

50

60

70

80

(b)


2km



(a)

WTCP0 25 50 75 100

0

1k

2k

3k

4k

5k

6k

7k

8k


(b)





Appendix





k1 + k2 K

k1 times Ft

11138681113868111386811138681113868111386811138681113868 + 11113872 1113873 + k2 times Ft

11138681113868111386811138681113868111386811138681113868 K times Ft

(A1)







end ifend while




Data Availability




Acknowledgments


References




















end if





























































Appendix





k1 + k2 K

k1 times Ft

11138681113868111386811138681113868111386811138681113868 + 11113872 1113873 + k2 times Ft

11138681113868111386811138681113868111386811138681113868 K times Ft

(A1)







end ifend while




Data Availability




Acknowledgments


References




















end if




























































Data Availability




Acknowledgments


References




















end if



































































































































Date post:	10-Apr-2022
Category:	Documents
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