Research Article How to Choose Last Mile Delivery Modes...

Research ArticleHow to Choose lsquolsquoLast Milersquorsquo Delivery Modes for E-Fulfillment

Xuping Wang12 Linmin Zhan1 Junhu Ruan13 and Jun Zhang1

1 Institute of Systems Engineering Dalian University of Technology Dalian 116024 China2 School of Business Dalian University of Technology Panjin 124221 China3 School of Electrical and Electronic Engineering Faculty of Engineering Computer andMathematical Sciences University of AdelaideAdelaide SA 5005 Australia

Correspondence should be addressed to Junhu Ruan junhuruanadelaideeduau

Received 11 February 2014 Revised 1 May 2014 Accepted 15 May 2014 Published 11 June 2014

Academic Editor Kwok-WoWong

Copyright copy 2014 Xuping Wang et al This 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

ldquoLast milerdquo delivery has become one of the bottlenecks of e-logistics This paper aims to explore the competitiveness of three ldquoLastmilerdquo delivery modesmdashattended home delivery (AHD) reception box (RB) and collection-and-delivery points (CDPs) in differentscenarios especially in high population density scenarioThe advantages and disadvantages of eachmode are introduced firstTheneachmodersquos operation efficiency is solvedwith different kinds of vehicle routing problem (VRP)models and genetic algorithm (GA)Finally the cost of each mode is calculated on the basis of cost structures and operation efficiencies The results show that differentmodes are suitable for different scenarios (i) AHD and independent reception box work better in a scenario with sparse populationor small order quantity (ii) shared reception box and CDPs are more appropriate in the scenario with high population density andlarge order quantity and the better one depends on the cost of labors and facilities (iii) RB is desirable in some circumstances asdelivering fresh vegetables and fruits to the ones living in high-grade communities

1 Introduction

E-commerce develops rapidly in recent years [1] Accordingto the data fromChina Internet Network InformationCenterChina has the second biggest online shopping market asits online sales broke through 12 trillion in 2012 [2] E-commerce can hardly do without the support of e-logisticsThe ldquolast milerdquo delivery which accounts for 30 of totale-logistics cost [3] has become one of the bottlenecks ofe-commerce Nowadays attended home delivery (AHD)reception box (RB) and collection-and-delivery points(CDPs) are the three existing ldquolast milerdquo delivery modesin China This paper mainly explores the competitivenessof three delivery modes in different scenarios especially inhigh-density areas in viewofChinarsquos high population densityHigh population density leads to high residential density[4 5] Population density has an important effect on deliveryefficiency [6]

Currently AHDmdashcouriers send goods to customersrsquodoorsteps receive customersrsquo signatures and leave for thenext onemdashis the most widespread ldquolast milerdquo delivery mode

AHD provides the opportunities with customers face to facebut its low operation efficiency is likely tomake it undesirableto handle massive orders Most researchers focused on thebalance between cost and customer satisfaction Narrowdelivery time slots are more popular with customers but theygreatly reduce routing efficiency and lead to a huge cost [7]Hill et al made explicit tradeoff between the benefits of shortdelivery time guarantees and the cost of late deliveries [8]The concept of optimal position of the delivery window intoa cost-based delivery performance model was introducedin [9] Further Campbell and Savelsbergh concentrated onusing time slot incentives to cut down delivery cost andimprove profits [10] In AHD couriers always have to waste alot of time waiting for customers so RB and CDPs are therein the environment

There are three kinds of reception boxes (1) independentreception box is installed at the garage or home yard of thecustomer (2) delivery box is equipped with a docking mech-anism and will be retrieved after goods inside are taken away(3) shared reception box is installed near customers for theirshared usage Couriers put goods in the boxes and customers

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 417129 11 pageshttpdxdoiorg1011552014417129

2 Mathematical Problems in Engineering

pick up goods at any time using messaged passwords In thisway couriers are released from time limitation while theirdelivery efficiencies are improved Moreover RB could beused as a refrigerated cabinet to store organic vegetables andfruits However the investment of reception boxes is largePunakivi et al compared AHD and RB from the perspectiveof cost and payback period They found that up to 60 costreductions are achievable by using RB and the operationalcost of delivery box is on the same level as the reception boxwhen delivery boxes are not picked up until the next deliverytime [11] Further Punakivi and Tanskanen found that costcan be saved as high as 55ndash60 by using shared receptionbox compared to the concept offering attended receptionwithtwo-hour timewindows However thismode is only suited tocustomers living in blocks of flats [12]

Collection-and-delivery points refer to conveniencestores plot properties and other institutions which belongto or cooperate with express companies as the place wherecustomers come to pick up goods Couriers just scan andput goods in certain places in CDPs Operation efficiency isimproved dramatically because a CDP could serve severaldelivery points at the same time When CDPs are located atareas that already generate consumer trips their satisfactionwill seldom or never be affected seriously because littleadditional travel by consumers will be required to collecta package [13] Lee and Whang suggested CDPs are one ofthe five best ways to solve ldquolast milerdquo delivery problem [14]Different distribution of the third institutions has importantinfluences on delivery cost and environment [15] Customermileage could be reduced by eighty percent by using CDPsfor failed first-time home shopping deliveries [16] BesidesCDPs is beneficial to the cooperating parties because about25 CDPs users would make a purchase when collecting orreturning their parcels [13]

Different delivery modes have different characteristicsand delivery efficiencies The choice of the most appropriateldquolast milerdquo delivery mode in different scenarios has no quan-titative guidance This paper reveals the variations of threedelivery modesrsquo cost and operation efficiencies in differentscenarios

The rest of the paper is organized as follows In Section 2the method is proposed to calculate the total cost of differentdelivery modes Each modersquos operation efficiency is solvedwith VPRmodels and genetic algorithmThen on the basis ofoperation efficiencies and cost structures analyzed the totalcost of each mode is calculated In Section 3 the specificexperiment is conducted and the competitiveness of eachmode is analyzed At last the conclusions are drawn andfurther research directions are raised

2 Method

This section proposes a method to calculate the total cost ofdifferent ldquolast milerdquo delivery modes First some assumptionsare made to define this problem Second VRP models arebuilt to achieve operation efficiencies according to eachmodersquos characteristics and genetic algorithm is adoptedto solve the VRP problems Last the cost structures are

proposed to calculate the total cost of each delivery modetogether with operation efficiencies

21 Assumptions Some assumptions are made according tothe status quo of ldquolast milerdquo operation in China as follows

(1) Packages will not be sent twice Couriers will get intouch with the receivers before they start to deliverthe customersrsquo goods Actually first-delivery failure israre in China

(2) Reception box employed in this paper is communalreception box with drawers of different sizes It usesluggage locker technology and PIN codes to controlthe delivery It is assumed all the goods could beloaded into the boxes In rural and suburban areasmost people live in single detached family Indepen-dent reception box and delivery box are desirable inthis case because an important advantage of RB is thatcustomers could get goods nearby However in high-density area most families live in blocks of flats thuscommunal reception box is preferable [12]

(3) The collection-and-delivery points employed in thispaper are convenience stores supermarkets subwaystations and some other institutions which cooper-ate with express companies In reality CDPs couldbe built in two ways setting up CDPs by expresscompanies themselves and collaborating with thirdparties [15]The former one requiresmore investmentand bears more risk Thus it is rational for expresscompanies to cooperate with other organizations inthe early stage

(4) CDPs and reception boxes are set up abiding strictlyby the principles listed below (i) CDPs should belocated within a five-minute driving distance by carfrom customer address [15] (ii) each community(a delivery point stands for a community in thispaper)mdasha group of peoplewho live in the same areamdashhas one reception box at least to guarantee customersatisfaction from the view of fair [17] (iii) CDPsshould be accessible to the major road network andparking should be permitted and easy

22 Delivery Efficiency Different ldquolast milerdquo delivery modeshave different delivery efficiencies Measuring the operationefficiency of each mode is fundamental for calculating itstotal cost Operation efficiency could be measured by averagedelivery time per order 119905119895 with 119895 distinguishing differentmodes The larger the 119905119895 is the lower the operation efficiencyis

According to delivery process no matter which modeit is total delivery time per day consists of three partsas formula (1) shows time spent on the road 119905

road119895 time

spent starting or stopping the vehicle 119905119904119895 and time spentserving customers 119905service119895 respectively 119905service119895 indicates timespent walking to customersrsquo doorstep waiting for consigneesrsquosignatures scanning bar codes unpacking and inspectinggoods in AHD time spent walking to the places putting

Mathematical Problems in Engineering 3

goods into appropriate drawers and scanning bar codes inRB time spent unloading and scanning bar codes in CDPs

Therefore total time spent per day could be

119905sum119895 = 119905

road119895 + 119905

119904119895 + 119905

service119895 (1)

The calculation of 119905119904119895 and 119905service119895 is simpler than 119905road119895 thusthe calculation of 119905119904119895 and 119905service119895 is introduced first 119905119904119895 is theaverage time of parking multiplied by parking times 119905service119895 isaverage service time per order multiplied by the number oforders The formulae of 119905service119895 in three modes are exactly thesame as 119905119904119895

The process of calculating the value of 119905road119895 is muchmore complex In AHD it is a typical VRPTW (vehiclerouting problemwith time window) problem in view of a fewcustomersrsquo requirements of delivery time windows [18ndash21] inRB it is a VRP problem [22ndash24] and in CDPs it is a VRPproblem on the basis of cluster analysis [25ndash28] Details andbasis of modeling are introduced below

Here is the VRPTWmodel of AHD Notations to be usedin the VRPTWmodel are defined as follows

119877 The set of routes

119898 The set of delivery points

119889119894119895The distance between delivery point 119894 and deliverypoint 119895

119902119894 Daily demand of delivery point 119894

119902 Total daily demand of this region

1199020 119902119899+1 The demand of depot 1199020 = 119902119899+1 = 0

119876V The capacity of a vehicle

120582 The time spent on serving a customer

120590 The time spent on starting and stopping a vehicle

V Average velocity

119879 The daily working time

119909119894119895119902 Arc(119894 119895) appears in route 119903

119910119894119903 Delivery point 119894 is served by route 119903

119904119894 The starting time of serving delivery point 119894

[119886119894 119887119894] The delivery time window of delivery point 119894

The formula could be as followsObjective function

min 119905road

=

119877

sum119903=1

119898+1

sum119894=0

119898+1

sum119895=0

119909119894119895119903 (119889119894119895

V) (2)

subject to119898

sum119894=1

119902119894 = 119902 (3)

119877

sum119903=1

119910119894119903 = 1 119894 = 1 2 3 119898 (4)

119898

sum119894=0

119909119894119895119903 = 119910119895119903 119895 = 1 2 119898 + 1 119903 = 1 2 119877 (5)

119898+1

sum119895=1

119909119894119895119903 = 119910119894119903 119894 = 0 1 2 119898 119903 = 1 2 119877 (6)

119898+1

sum119895=1

1199090119895119903 = 1 119903 = 1 2 119877 (7)

119898

sum119894=0

119909119894(119898+1)119903 = 1 119903 = 1 2 119877 (8)

119898

sum119894=1

119910119894119903119902119894 le 119876V 119903 = 1 2 119877 (9)

119904119894 + 120582119902119894 + 120590 +119889119894119895

Vminus 119872 (1 minus

119877

sum119903=1

119909119894119895119903) le 119904119895

119894 = 0 1 2 119898 119895 = 1 2 119898 + 1

(10)

119886119894 le 119904119894 le 119887119894 le 119879 119894 = 0 1 2 119898 + 1 (11)

119909119894119895119903 isin 0 1 119910119894119903 isin 0 1 (12)

Constraint (3) states that the sum of delivery pointsrsquodemand cannot be more than total daily demand in thisdistrict Constraints (4)ndash(6) state that every delivery pointshould be visited at most once Constraints (7)-(8) are flowconservation constraints that describe the individual routesConstraint (9) states that the total demand on a route cannotbemore than vehicle capacity Constraints (10) and (11) ensurethe feasibility of the time schedule

Real-coded genetic algorithm which is one of the mosteffective ways to solve VRPTW problems is employed inthis paper Sequence coding is used and each delivery pointis assigned a serial number and 0 represents the depot Achromosome consists of 119898 + 119877 + 1 genes for example (0

11989411 11989412 11989413 0 11989421 11989422 11989423 0 1198941198771 1198941198772 0) Differ-ent sequences represent different solutions The initial 100population is generated randomly and individuals that couldnot meet the requirements of delivery time windows shouldbe deleted and generated randomly again Parent chromo-somes are selected with roulette wheel selection accordingto the fitness function (13) The vehicle capacity constraint isintegrated into the objective function119872 a pretty big numberrepresents the penalty coefficient when orders on a vehicle aremore than 119876V

min 119911 =

119877

sum119903=1

119898+1

sum119894=0

119898+1

sum119895=0

119909119894119895119903 (119889119894119895

V)

+ 119872

119877

sum119903=1

max(

119898

sum119894=1

119910119894119903119902119894 minus 119876V 0)

(13)


Then partially matched crossover is adopted as crossoveroperator The crossing points are selected by using thecertain crossover probability and two children are generatedAfterwards a nonzero gene is generated mutation randomlywith the certain mutation probability and the gene generatedoriginally in the chromosomes changes to the one whichmutates Eligible children would substitute the parents whosefitness is very low and a new generation is formed Terminatethe algorithm when it updates the set generations

Since a delivery point has one reception box at least thecalculation of 119905

road119895 in RB is similar to that in AHD However

it is a VRP problem because RB has no limitation on deliverytimeThe formulas are all the same except the constraint (11)It should be altered to 119904119894 le 119879 The formulas will not belisted again A simple genetic algorithm is employed to solvethis VRP problem The programming of genetic algorithmis similar to that of AHD except the elimination of theconstraintmdashdeleting the individuals that could not meet therequirements of delivery time windows

The calculation of 119905road119895 in CDPs is very different from that

in AHD and RBThe reason is that a CDP could serve severaldelivery points at the same time as long as the distancesbetween them are acceptable to customers Besides CDPshave no capacity constraints Thus it is reasonable to clusterthe delivery points on the basis of Euclidean distance In reallife the choice of CDPs involves a lot of commercial andenvironmental factors To simplify the calculation processthe CDPs in the experiment are located in the centers ofclusters From this 119870-means clustering algorithm is appliedto this problem first

Objective function

119899

sum119894=1

min119895isin12119896

10038171003817100381710038171003817119900119894 minus 119875119895

10038171003817100381710038171003817

2(14)

subject to

119900119894 =1

1003816100381610038161003816119871 1198941003816100381610038161003816

sum119900isin119871 119894

119900 (15)

119864 =

119896

sum119894=1

sum119900isin119871 119894

1003816100381610038161003816119900 minus 11990011989410038161003816100381610038162 (16)

where 119900119894 denotes the locations of delivery points 119875119895 denotesthe average value of cluster 119871 119894 and 119864 is the sum of squarederrors Constraint (15) states the average value of updatedclusters constraint (16) states the calculation rule The clus-tering centers are recognized as delivery points and theshortest path among them is solved with VRP model In thisway a hierarchical procedure involving one heuristic and twoalgorithm phases is developed Phase I aims to identify a setof feasible clusters with 119896-means algorithm while phase IIassigns clusters to vehicles and sequences them on each tourby using VRP problem

In short conceptually AHDrsquos operation efficiency islowest because of the long time waiting for customers while

CDPsrsquo operation efficiency is the highest due to the simplestoperational process The average time per order is

119905119895 =119905sum119895

119902 (17)

Different modes lead to different operation efficiencieswhich result in different demands of equipment Appropriateamount of equipment helps express companies accomplishtasks with minimal cost The parameter 119899119895-number ofequipment is the intermediate variable between operationefficiency and total cost The relationship is

119902119905119895

119899119895le 119879 (18)

which indicates all the arrival orders should be distributedwithin working time of the same day

23 Cost Structure Different modes have different costcomponents There are some common cost componentssuch as investments of vehicles handheld terminals andmanagement expense However even these common com-ponents have different values because the most appropriatedevice type and commission are diverse in different modesonly management expenses of three modes are the sameNotice that fuel fee is ignored in the model because manyexpress companies provide couriers with vehicles but are notresponsible for their fuel fee in reality In AHD the total costis

119862 = 119872 + 119899 (119888 + 119908119891) + 119908119902 (19)

The total cost contains fixed administrative expense 119872short fixed cost and variable cost Short fixed cost consistsof the investment on devices 119899 lowast 119888 and welfare payment forlabors 119899 lowast 119908119891 An employee is assumed to operate a device119888 includes the price of a vehicle and a handheld terminal andtheir maintenance fee 119908 indicates the commission per orderpaid to couriers

In RB the total cost is

119862 = 119872 + 119899 (119888 + 119908119891) + 119908119902 + 119868 (20)

Total cost of RB should be added an item 119868mdashthe invest-ment of purchasing and maintaining reception boxes on thebasis of AHD

In CDPs the total cost is

119862 = 119872 + 119899 (119888 + 119908119891) + (119908 + 120574) 119902 + 119868 (21)

Total cost of CDPs has one more item that the commis-sions paid to the cooperators 120574 lowast 119902 119868 is the expenditure ofnegotiating and signing contracts with cooperators

From the formula above only labors and cooperatorscommission are proportional to the quantity of ordersAdministrative expense is a constant Short fixed cost whichincludes investments on devices and welfare payments is astep function This model reveals all detailed cost containedin the ldquolast milerdquo delivery activities


3 Numerical Experiments

It is difficult to obtain the delivery time of the three modesin real life On the one hand it is hard to put the three modesinto practice under the same circumstance tomake the resultscomparable on the other hand it involves express companiesrsquobusiness secrets In consequence simulation experiments aremade with the software Matlab The certain crossover andmutation probability of genetic algorithm are 08 and 02respectively and the algorithm is terminated when it updates200 generations

In the specific experimental 30 delivery points repre-sent 30 communities The locations of delivery points aregenerated randomly in the square of 25 kilometers and itis suitable for Chinarsquos condition Demand of every deliverypoint is generated randomly tooOther data of constants werecollected from the investigations on couriers and interviewswith middle-level managers from ShenTong Express Yuan-Tong Express ZTO Express YunDa Express and SF Expresswhich are the main e-commerce logistics providers in China

To simplify the simulation process the depot is set upin the centre of this area Every vehicle starts off and comesback here The roads between any two points are assumedto be straight-lines On the first scenario demands of allcommunities are set less than 36 orders to make sure settingup a reception box in a community is enough and thisscenario is regarded as the standard scenario

31 The Importance of Vehicle Choice To make the resultsof three modes comparable and show the significance ofemploying the most appropriate vehicles we compare theeffects of different vehicles applied to AHD In china seldomexpress companies offer delivery timewindows to choose andjust few customers ask for delivery time windows accordingto the investigation mentioned above Here are the limitingvalues of the vehicle fleet The first are the limiting values ofelectrotricycles in AHD

(1) maximum 300 orders per electrotricycle(2) average velocity 30 kmh(3) working time maximum 10 hours per electrotricycle(4) stopping and starting the electrotricycle 2min every

time(5) serving per customer 5min(6) 3 delivery points ask for an hour time window (1130-

1230 1400-1500 and 1730-1830 resp)

Second are the limiting values of light-weight vans whichare used in RB and CDPs

(1) maximum 800 orders per van(2) average velocity 60 kmh(3) working time maximum 10 hours per van(4) stopping and starting the van 2min every time(5) serving per customer 5min(6) 3 delivery points ask for an hour time window (1130-

1230 1400-1500 and 1730-1830 resp)

Table 1 Time spent situation in AHD with two kinds of vehicles

Items ModesElectrotricycle Light-weight van

Total distance (km) 4216 4165Number of orders 744 744Stopping times 30 30Number of vehicles 8 8119905road (min) 843 417119905119904 (min) 60 60

119905service (min) 3720 3720Buffering time (min) 20 20Total time (min) 3884 38417Average time per order (min) 522 516

The delivery situations with the two kinds of vehicles inAHD are displayed in Figure 1

Parameter values are displayed inTable 1The efficiency ofemploying light-weight vans is just a little bit higher than thatof electrotricycles because the former one has larger averagevelocity and spends less time on the road 119905

119904 and 119905service areexactly the same Time spent on serving customers occupiesthe largest proportion of total time Thus no matter how fastand how big the vehicle is delivery efficiency could not beimproved visibly That is why the routes in two cases aresimilar

Daily total cost of the two cases is calculated on the basisof the delivery efficiency and cost structure All the conditionsare set exactly the same as Section 33

The cost of using electrotricycles and light-weight vansin AHD is showed in Figure 2 It is found that the cost ofemploying light-weight vans is always higher because thedelivery efficiency of employing light-weight vans could notbe improved largely while the investment is much more Asthe increase of orders the gap between them is bigger andbigger That is mainly because the growth of orders makes119905service occupy a larger proportion of total time and leads tomore and more advantages of employing light-weight vansdisappeared but the investment of light-weight vans is moreand more greater than that of electrotricycles

From the foregoing the use of appropriate vehicles indifferent delivery modes is very important In AHD elec-trotricycle is suitable but in RB and CDPs light-weight vanis preferable

32 Delivery Efficiencies of Three Modes According to theanalysis of Section 31 light-weight vans are employed in RBThe limiting values of the vehicle fleet in RB are listed asfollows

(1) maximum 800 orders per van

(2) average velocity 60 kmh

(3) working time maximum 10 hours per van

(4) stopping and starting the van 2min every time

(5) serving per customer 1min


05 1 15 2 25 3 35 4 450

05

1

15

2

25

3

35

4

45

5

(km)

(km

)Delivery situation of mode of attended home delivery

(a) With electrotricycles

05 1 15 2 25 3 35 4 45

0

05

1

15

2

25

3

35

4

45

5

5

(km)

(km

)

(b) With light-weight vans

Figure 1 Delivery situation of AHD with two kinds of vehicles

0 500 1000 1500

1000

1500

2000

2500

3000

3500

4000

Orders per day

Tota

l cos

tyua

n

Different vehicles

ElectrotricyclesLight-weight vans

Figure 2 Total cost of AHD with two kinds of vehicles

It could be seen AHD needs much more vehicles andcouriers than RB by comparing Figure 1 with Figure 3

As mentioned above 30 delivery points should be clus-tered first in CDPs Since the scope is a square of 25kilometers itrsquos enough to set up 5 collection-and-deliverypoints The result is displayed in Figure 4 The points ofthe same shape are in the same cluster The big green dotrepresentsDCwhile the black crosses stand forCDPs It couldbe seen that the distance between every delivery point and itsnearest CDP is no more than 1 km (a reasonable distance thatconforms to the key successful rule [15]) The limiting valuesof the vehicle fleet in CDPs are listed as follows

05 1 15 2 25 3 35 4 45

0

05

1

15

2

25

3

35

4

45

5

5

(km)

(km

)

Figure 3 Delivery situation of RB

Cluster situation of communities

05 1 15 2 25 3 35 4 45

0

05

1

15

2

25

3

35

4

45

5

5

(km)

(km

)

Figure 4 Cluster situation of communities


0 50 100 150 200 250 300 350 400 4501000

1100

1200

1300

1400

1500

1600

1700

1800

Orders per day

Cos

tyua

n

AHDRBCDPs

Figure 5 Total cost of three modes

Table 2 Time spent situation in standard scenario

Items ModesAHD RB CDPs

Total distance (km) 4216 269 115Number of orders 744 744 744Stopping times 30 30 5Number of vehicles 8 2 1119905road (min) 843 269 115119905119904 (min) 60 60 20119905service (min) 3720 744 1488Buffering time (min) 20 20 20Total time (min) 3884 850 2003Average time per order (min) 522 115 027

(1) maximum 800 orders per van(2) average velocity 60 kmh(3) working time maximum 10 hours per van(4) stopping and starting the van 4min every time(5) serving per customer 02min

The result is displayed in Figure 4 as well As expectedtotal travel distance in CDPs decreases sharply compared tothat in AHD and RB

To all the three modes 20min is endowed as bufferingtime to make up for the time couriers spending doing otherthings The values of parameters in the three modes areshowed in Table 2

FromTable 2 CDPs have the highest operation efficiencyfollowed by RB and then AHD 119905

service occupies the largestproportion of total time That is mainly because every com-munityrsquos demand is relatively large and residential density inthis region is high

The distinct of operation efficiency reflected is evidentObviously CDPs need the least 119905

service while AHD needs themost Because of AHD couriers have to wait for the receiver

Table 3 Time spent situation with half orders compared withstandard scenario


Total distance (km) 4216 269 115Number of orders 372 372 372Stopping times 30 30 5Number of vehicles 8 2 1119905road (min) 843 269 115119905119904 (min) 60 60 20

119905service (min) 1860 372 744Buffering time (min) 20 20 20Total time (min) 20243 4789 1259Average time per order (min) 544 129 034

Table 4 Time spent situation with double orders compared withstandard scenario



to sigh for the goods and sometimes wait for longer till thereceiver checks the goods In RB couriers put the goods in thecorresponding boxes and scan them Apparently this wouldbe faster Furthermore couriers just unload and scan goodsBesides both CDPs and RB modes save couriersrsquo walkingtime because unified delivery points always locate on the firstfloor and enjoy convenient transportation

CDPs would cost the least 119905119904 due to its much less parking

times RB needs more 119905119904 than CDPs but less than AHD119905119904 is affected by residential density [4] and the ease ofparking For the growth of private cars in cities perhapsthe problem of parking would be another big obstacle to e-logistics increasingly From the perspective of this point RBand CDPs would be more advantageous in future

AHD spends much more 119905road than RB and CDPs That

happens mainly because the vehicles suitable for AHD goslower and vehicles have to go through extra way to satisfycustomersrsquo delivery time windows [29] Consequently 119905road

is closely connected with residential density and customersrsquodelivery time windows in AHD [5]

To study the influence of orders on operation efficiencythe parameters are calculated in half and double ordersrespectively The results are shown in Tables 3 and 4


0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n

Cost situation of reception box and CDPs

Reception boxCDPs

(a) 120574 = 05 119868each = 5000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(b) 120574 = 06 119868each = 5000

3500

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(c) 120574 = 07 119868each = 5000

Figure 6 Cost situation of RB and CDPs with changing third party commission

Visually the average time per order of eachmode changessynchronously with orders That is because 119905road and 119905119904 couldbe shared withmore orders when orders increaseWhen onlyorder quantity changes in the area 119905road would change but nottoo much resulting from the additional vehiclesrsquo extra wayconnected to the depot 119905

119904 would be relatively fixed 119905service

would increase or decrease in proportionwith order quantityIn three scenarios the ratios of average time per order in threemodes are 1 024 0063 1 022 0052 and 1 021 0045corresponding to 372 744 and 1488 orders respectively Theresult indicates that CDPsrsquo operation efficiency will be moreand more competitive as the increase of orders It mainlybenefits from the high efficiency of serving customers and nolimit to the CDPsrsquo capacity

33 Total Cost of Three Modes The total cost of every modeis showed in Figure 5 It clearly reflects higher operationefficiency does not mean lower cost through fair and foulFrom Figure 5 it could be concluded when daily demand isless than 50 orders in this region adopting AHD is wise Atthis time CDPs cost a little higher than AHD while RB costsa great deal That is because the initial fixed investment ofreception boxes is very large and the vehicles used in RB andCDPs cost a lot more than that in AHDOn account of AHDrsquoshigh variable cost and low operation efficiency its cost soarssharply as the increase of orders On the contrary the variablecost of RB and CDPs is much smaller

When orders are massive AHD definitely costs the mostbut which one costs the least still needs to be studied


0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(a) 120574 = 06 119868each = 4000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(b) 120574 = 06 119868each = 5000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

3500

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(c) 120574 = 06 119868each = 6000

Figure 7 Cost situation of RB and CDPs with changing reception box expense

further According to Figures 6 and 7 the choice of RB orCDPs depends on the expense of reception boxes and thecommission paid to the third party partners because whenorders increase the extra investment of new reception boxesis the main incremental cost in RB while the commissionpaid to third party partners is the main incremental cost inCDPs Figure 6 shows the cost situation with stable expenseof reception box and changing third party commission whileFigure 7 shows the cost situation on the contrary 119868each denotesthe expense of a reception box per year It could be concludedthat the higher the commission paid to third party partnersis the faster the cost of CDPs would exceed that of RBWhenthird party commission is small cost of CDPs will be always

less than that of RB However even when such thing happensit does not mean RB is utterly useless because it has someunique advantages such as providing refrigeration serviceand being set up in luxury residential where couriers are notallowed to enter

In general when orders are not many it is wise to adoptAHD when orders are massive enough it is wise to adopt RBand CDPs but which one to choose depends on the currentcontext In addition to this cooperating with e-logisticsproviders benefits third party partners as researchers pointout that one in four customers would make a purchase in thestore when collecting or returning their parcels [13] It meansCDPs are expected to become themost economical waywhen


orders are massive through cutting down commissions paidto third party partners counting on the benefits they havealready made

4 Conclusions

Despite the three ldquolast milerdquo delivery modes are concurrencein practice a little theoretical research aims at choosingthem according to different scenarios so far This papermakes the quantitative study of different delivery modesrsquocompetitiveness through analyzing ldquolast milerdquo activitiesrsquo coststructure and operation efficiency in different scenarios

The major conclusions of this paper are concluded asfollows (i) Total cost of ldquolast milerdquo delivery relies on theprice of manpower and material resources and operationefficiency Additionally different ldquolast milerdquo delivery modeshave different operation efficiencies Furthermore choosingthe most appropriate devices reduces cost effectively (ii)Operation efficiency is affected by order quantity and CDPsare more sensitive to the change of orders Also undernormal circumstances CDPsrsquo operation efficiency is thehighest followed by RB and then AHD (iii) When ordersare few AHD is the most suitable mode as the result of thelarger amount of equipment investment in RB and CDPsOn the contrary when there are plenty of orders in highresidential density areas with high reception box expense andlow commission of third party partners CDPs are optimummoreover when there are plenty of orders in sparse areas orhigh-grade district RB has the optimal advantage

In summary the paper extends the academic study ofldquolast milerdquo delivery puts forward the cost structure of eachmode then reveals the variation tendency of cost alongwith the change of order quantity and further analyzes thecompetitiveness of each mode in different scenarios It couldprovide some theoretical guidance for e-logistic providers

Given the fact that the use of RB and CDPs is still both atthe very beginning with excellent prospect for increasing useof these concepts in the future more quantitative researcheson this subject are necessary Customersrsquo satisfaction varieswith each individual and this should be taken into considera-tion in the near future research on this field Besides that thosemodes are considered separately in this paper in reality theycould be applied mixed in the same district and that shouldbe figured out by researchers

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank the anonymous referees andProfessor Kwok-Wo Wong for their useful comments andsuggestions which were very helpful in improving this paperThis work was supported by the National Natural ScienceFoundation of China under Grant (nos 71171029 7127103771201014 and 71301020) and the China Scholarship Council

References

[1] J-C Pai and C-H Yeh ldquoFactors affecting the implementationof e-business strategies an empirical study in TaiwanrdquoManage-ment Decision vol 46 no 5 pp 681ndash690 2008

[2] China Internet Network Information Center ldquoChinarsquos onlineshoppingmarket research report in 2012rdquo April 2007 (Chinese)httpwwwcnniccnhlwfzyjhlwxzbgdzswbg201304t2013041739290htm

[3] China Enterprise News ldquoOptimization of logistics distri-bution chain solve last mile delivery problemrdquo September2013 (Chinese) httpinfojctranscomnewssynthetic trans20139121967744shtml

[4] V Kupke P Rossini and S McGreal ldquoMeasuring the impactof higher density housing developmentrdquo PropertyManagementvol 30 no 3 pp 274ndash291 2012

[5] P J Smailes N Argent and T L C Griffin ldquoRural populationdensity its impact on social and demographic aspects of ruralcommunitiesrdquo Journal of Rural Studies vol 18 no 4 pp 385ndash404 2002

[6] K K Boyer A M Prudrsquohomme and W Chung ldquoThe lastmile challenge evaluating the effects of customer density anddelivery window patternsrdquo Journal of Business Logistics vol 30no 1 pp 185ndash201 2009

[7] N Agatz A Campbell M Fleischmann and M SavelsberghldquoTime slot management in attended home deliveryrdquo Trans-portation Science vol 45 no 3 pp 435ndash449 2011

[8] A V Hill J M Hays and E Naveh ldquoA model for optimaldelivery time guaranteesrdquo Journal of Service Research vol 2 no3 pp 254ndash264 2000

[9] M A Bushuev and A L Guiffrida ldquoOptimal position of sup-ply chain delivery window concepts and general conditionsrdquoInternational Journal of Production Economics vol 137 no 2 pp226ndash234 2012

[10] A M Campbell and M Savelsbergh ldquoIncentive schemes forattended home delivery servicesrdquo Transportation Science vol40 no 3 pp 327ndash341 2006

[11] M Punakivi H Yrjola and J Holmstrom ldquoSolving the last mileissue reception box or delivery boxrdquo International Journal ofPhysical Distribution amp Logistics Management vol 31 no 6 pp427ndash439 2001

[12] M Punakivi and K Tanskanen ldquoIncreasing the cost efficiencyof e-fulfilment using shared reception boxesrdquo InternationalJournal of Retail amp Distribution Management vol 30 no 10 pp498ndash507 2002

[13] J W J Weltevreden ldquoB2c e-commerce logistics the rise ofcollection-and-delivery points in The Netherlandsrdquo Interna-tional Journal of Retail amp Distribution Management vol 36 no8 pp 638ndash660 2008

[14] H L Lee and SWhang ldquoWinning the lastmile of e-commercerdquoMIT Sloan Management Review vol 42 no 4 pp 54ndash62 2001

[15] L Song T Cherrett F McLeod and W Guan ldquoAddressing thelast mile problem-the transport impacts of collectiondeliverypointsrdquo in Proceedings of the 88th Annual Meeting of theTransportation Research Board 2009

[16] FMcLeod T Cherrett and L Song ldquoTransport impacts of localcollectiondelivery pointsrdquo International Journal of Logisticsvol 9 no 3 pp 307ndash317 2006

[17] Y Yi and T Gong ldquoThe effects of customer justice perceptionand affect on customer citizenship behavior and customerdysfunctional behaviorrdquo Industrial MarketingManagement vol37 no 7 pp 767ndash783 2008


[18] Z Ursani D Essam D Cornforth and R Stocker ldquoLocalizedgenetic algorithm for vehicle routing problem with time win-dowsrdquoApplied SoftComputing vol 11 no 8 pp 5375ndash5390 2011

[19] R Liu X Xie V Augusto and C Rodriguez ldquoHeuristicalgorithms for a vehicle routing problem with simultaneousdelivery and pickup and time windows in home health carerdquoEuropean Journal of Operational Research vol 230 no 3 pp475ndash486 2013

[20] V Pureza R Morabito and M Reimann ldquoVehicle routing withmultiple deliverymen modeling and heuristic approaches fortheVRPTWrdquoEuropean Journal ofOperational Research vol 218no 3 pp 636ndash647 2012

[21] J Ruan X Wang Y Shi and Z Sun ldquoScenario-based pathselection in uncertain emergency transportation networksrdquoInternational Journal of Innovative Computing Information ampControl vol 9 no 8 pp 3293ndash3305 2013

[22] X Wang J Ruan and Y Shi ldquoA recovery model for com-binational disruptions in logistics delivery considering thereal-world participatorsrdquo International Journal of ProductionEconomics vol 140 no 1 pp 508ndash520 2012

[23] F P Goksal I Karaoglan and F Altiparmak ldquoA hybrid discreteparticle swarm optimization for vehicle routing problem withsimultaneous pickup and deliveryrdquo Computers amp IndustrialEngineering vol 65 no 1 pp 39ndash53 2013

[24] J Ruan X Wang and Y Shi ldquoDeveloping fast predictors forlarge-scale time series using fuzzy granular support vectormachinesrdquoApplied Soft Computing vol 13 no 9 pp 3981ndash40002012

[25] R Dondo and J Cerda ldquoA cluster-based optimization approachfor themulti-depot heterogeneous fleet vehicle routing problemwith time windowsrdquo European Journal of Operational Researchvol 176 no 3 pp 1478ndash1507 2007

[26] G di Fatta F Blasa S Cafiero and G Fortino ldquoFault tolerantdecentralised K-means clustering for asynchronous large-scalenetworksrdquo Journal of Parallel and Distributed Computing vol73 no 3 pp 317ndash329 2013

[27] F An and H J Mattausch ldquoK-means clustering algorithmfor multimedia applications with flexible HWSW co-designrdquoJournal of Systems Architecture vol 59 no 3 pp 155ndash164 2012

[28] J Ruan X Wang and Y Shi ldquoA clustering-based approachfor emergency medical supplies transportation in large-scaledisastersrdquo ICIC Express Letters vol 8 no 1 pp 187ndash193 2014

[29] M Punakivi and J Saranen ldquoIdentifying the success factorsin e-grocery home deliveryrdquo International Journal of Retail ampDistribution Management vol 29 no 4 pp 156ndash163 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


pick up goods at any time using messaged passwords In thisway couriers are released from time limitation while theirdelivery efficiencies are improved Moreover RB could beused as a refrigerated cabinet to store organic vegetables andfruits However the investment of reception boxes is largePunakivi et al compared AHD and RB from the perspectiveof cost and payback period They found that up to 60 costreductions are achievable by using RB and the operationalcost of delivery box is on the same level as the reception boxwhen delivery boxes are not picked up until the next deliverytime [11] Further Punakivi and Tanskanen found that costcan be saved as high as 55ndash60 by using shared receptionbox compared to the concept offering attended receptionwithtwo-hour timewindows However thismode is only suited tocustomers living in blocks of flats [12]

Collection-and-delivery points refer to conveniencestores plot properties and other institutions which belongto or cooperate with express companies as the place wherecustomers come to pick up goods Couriers just scan andput goods in certain places in CDPs Operation efficiency isimproved dramatically because a CDP could serve severaldelivery points at the same time When CDPs are located atareas that already generate consumer trips their satisfactionwill seldom or never be affected seriously because littleadditional travel by consumers will be required to collecta package [13] Lee and Whang suggested CDPs are one ofthe five best ways to solve ldquolast milerdquo delivery problem [14]Different distribution of the third institutions has importantinfluences on delivery cost and environment [15] Customermileage could be reduced by eighty percent by using CDPsfor failed first-time home shopping deliveries [16] BesidesCDPs is beneficial to the cooperating parties because about25 CDPs users would make a purchase when collecting orreturning their parcels [13]

Different delivery modes have different characteristicsand delivery efficiencies The choice of the most appropriateldquolast milerdquo delivery mode in different scenarios has no quan-titative guidance This paper reveals the variations of threedelivery modesrsquo cost and operation efficiencies in differentscenarios

The rest of the paper is organized as follows In Section 2the method is proposed to calculate the total cost of differentdelivery modes Each modersquos operation efficiency is solvedwith VPRmodels and genetic algorithmThen on the basis ofoperation efficiencies and cost structures analyzed the totalcost of each mode is calculated In Section 3 the specificexperiment is conducted and the competitiveness of eachmode is analyzed At last the conclusions are drawn andfurther research directions are raised

2 Method

This section proposes a method to calculate the total cost ofdifferent ldquolast milerdquo delivery modes First some assumptionsare made to define this problem Second VRP models arebuilt to achieve operation efficiencies according to eachmodersquos characteristics and genetic algorithm is adoptedto solve the VRP problems Last the cost structures are

proposed to calculate the total cost of each delivery modetogether with operation efficiencies

21 Assumptions Some assumptions are made according tothe status quo of ldquolast milerdquo operation in China as follows

(1) Packages will not be sent twice Couriers will get intouch with the receivers before they start to deliverthe customersrsquo goods Actually first-delivery failure israre in China

(2) Reception box employed in this paper is communalreception box with drawers of different sizes It usesluggage locker technology and PIN codes to controlthe delivery It is assumed all the goods could beloaded into the boxes In rural and suburban areasmost people live in single detached family Indepen-dent reception box and delivery box are desirable inthis case because an important advantage of RB is thatcustomers could get goods nearby However in high-density area most families live in blocks of flats thuscommunal reception box is preferable [12]

(3) The collection-and-delivery points employed in thispaper are convenience stores supermarkets subwaystations and some other institutions which cooper-ate with express companies In reality CDPs couldbe built in two ways setting up CDPs by expresscompanies themselves and collaborating with thirdparties [15]The former one requiresmore investmentand bears more risk Thus it is rational for expresscompanies to cooperate with other organizations inthe early stage

(4) CDPs and reception boxes are set up abiding strictlyby the principles listed below (i) CDPs should belocated within a five-minute driving distance by carfrom customer address [15] (ii) each community(a delivery point stands for a community in thispaper)mdasha group of peoplewho live in the same areamdashhas one reception box at least to guarantee customersatisfaction from the view of fair [17] (iii) CDPsshould be accessible to the major road network andparking should be permitted and easy

22 Delivery Efficiency Different ldquolast milerdquo delivery modeshave different delivery efficiencies Measuring the operationefficiency of each mode is fundamental for calculating itstotal cost Operation efficiency could be measured by averagedelivery time per order 119905119895 with 119895 distinguishing differentmodes The larger the 119905119895 is the lower the operation efficiencyis

According to delivery process no matter which modeit is total delivery time per day consists of three partsas formula (1) shows time spent on the road 119905

road119895 time

spent starting or stopping the vehicle 119905119904119895 and time spentserving customers 119905service119895 respectively 119905service119895 indicates timespent walking to customersrsquo doorstep waiting for consigneesrsquosignatures scanning bar codes unpacking and inspectinggoods in AHD time spent walking to the places putting




119905sum119895 = 119905

road119895 + 119905

119904119895 + 119905

service119895 (1)













V Average velocity







min 119905road

=

119877

sum119903=1

119898+1

sum119894=0

119898+1

sum119895=0

119909119894119895119903 (119889119894119895

V) (2)

subject to119898

sum119894=1

119902119894 = 119902 (3)

119877

sum119903=1

119910119894119903 = 1 119894 = 1 2 3 119898 (4)

119898

sum119894=0

119909119894119895119903 = 119910119895119903 119895 = 1 2 119898 + 1 119903 = 1 2 119877 (5)

119898+1

sum119895=1

119909119894119895119903 = 119910119894119903 119894 = 0 1 2 119898 119903 = 1 2 119877 (6)

119898+1

sum119895=1

1199090119895119903 = 1 119903 = 1 2 119877 (7)

119898

sum119894=0

119909119894(119898+1)119903 = 1 119903 = 1 2 119877 (8)

119898

sum119894=1

119910119894119903119902119894 le 119876V 119903 = 1 2 119877 (9)

119904119894 + 120582119902119894 + 120590 +119889119894119895


119877

sum119903=1

119909119894119895119903) le 119904119895

119894 = 0 1 2 119898 119895 = 1 2 119898 + 1

(10)

119886119894 le 119904119894 le 119887119894 le 119879 119894 = 0 1 2 119898 + 1 (11)

119909119894119895119903 isin 0 1 119910119894119903 isin 0 1 (12)




min 119911 =

119877

sum119903=1

119898+1

sum119894=0

119898+1

sum119895=0

119909119894119895119903 (119889119894119895

V)

+ 119872

119877

sum119903=1

max(

119898

sum119894=1

119910119894119903119902119894 minus 119876V 0)

(13)








Objective function

119899

sum119894=1

min119895isin12119896

10038171003817100381710038171003817119900119894 minus 119875119895

10038171003817100381710038171003817

2(14)

subject to

119900119894 =1

1003816100381610038161003816119871 1198941003816100381610038161003816

sum119900isin119871 119894

119900 (15)

119864 =

119896

sum119894=1

sum119900isin119871 119894

1003816100381610038161003816119900 minus 11990011989410038161003816100381610038162 (16)




119905119895 =119905sum119895

119902 (17)


119902119905119895

119899119895le 119879 (18)



119862 = 119872 + 119899 (119888 + 119908119891) + 119908119902 (19)



119862 = 119872 + 119899 (119888 + 119908119891) + 119908119902 + 119868 (20)



119862 = 119872 + 119899 (119888 + 119908119891) + (119908 + 120574) 119902 + 119868 (21)











1230 1400-1500 and 1730-1830 resp)



1230 1400-1500 and 1730-1830 resp)


















05 1 15 2 25 3 35 4 450

05

1

15

2

25

3

35

4

45

5

(km)

(km



05 1 15 2 25 3 35 4 45

0

05

1

15

2

25

3

35

4

45

5

5

(km)

(km

)



0 500 1000 1500

1000

1500

2000

2500

3000

3500

4000

Orders per day

Tota

l cos

tyua

n

Different vehicles





05 1 15 2 25 3 35 4 45

0

05

1

15

2

25

3

35

4

45

5

5

(km)

(km

)



05 1 15 2 25 3 35 4 45

0

05

1

15

2

25

3

35

4

45

5

5

(km)

(km

)



0 50 100 150 200 250 300 350 400 4501000

1100

1200

1300

1400

1500

1600

1700

1800

Orders per day

Cos

tyua

n

AHDRBCDPs



























0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(a) 120574 = 05 119868each = 5000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(b) 120574 = 06 119868each = 5000

3500

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(c) 120574 = 07 119868each = 5000








0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(a) 120574 = 06 119868each = 4000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(b) 120574 = 06 119868each = 5000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

3500

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(c) 120574 = 06 119868each = 6000







4 Conclusions







Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119905sum119895 = 119905

road119895 + 119905

119904119895 + 119905

service119895 (1)













V Average velocity







min 119905road

=

119877

sum119903=1

119898+1

sum119894=0

119898+1

sum119895=0

119909119894119895119903 (119889119894119895

V) (2)

subject to119898

sum119894=1

119902119894 = 119902 (3)

119877

sum119903=1

119910119894119903 = 1 119894 = 1 2 3 119898 (4)

119898

sum119894=0

119909119894119895119903 = 119910119895119903 119895 = 1 2 119898 + 1 119903 = 1 2 119877 (5)

119898+1

sum119895=1

119909119894119895119903 = 119910119894119903 119894 = 0 1 2 119898 119903 = 1 2 119877 (6)

119898+1

sum119895=1

1199090119895119903 = 1 119903 = 1 2 119877 (7)

119898

sum119894=0

119909119894(119898+1)119903 = 1 119903 = 1 2 119877 (8)

119898

sum119894=1

119910119894119903119902119894 le 119876V 119903 = 1 2 119877 (9)

119904119894 + 120582119902119894 + 120590 +119889119894119895


119877

sum119903=1

119909119894119895119903) le 119904119895

119894 = 0 1 2 119898 119895 = 1 2 119898 + 1

(10)

119886119894 le 119904119894 le 119887119894 le 119879 119894 = 0 1 2 119898 + 1 (11)

119909119894119895119903 isin 0 1 119910119894119903 isin 0 1 (12)




min 119911 =

119877

sum119903=1

119898+1

sum119894=0

119898+1

sum119895=0

119909119894119895119903 (119889119894119895

V)

+ 119872

119877

sum119903=1

max(

119898

sum119894=1

119910119894119903119902119894 minus 119876V 0)

(13)








Objective function

119899

sum119894=1

min119895isin12119896

10038171003817100381710038171003817119900119894 minus 119875119895

10038171003817100381710038171003817

2(14)

subject to

119900119894 =1

1003816100381610038161003816119871 1198941003816100381610038161003816

sum119900isin119871 119894

119900 (15)

119864 =

119896

sum119894=1

sum119900isin119871 119894

1003816100381610038161003816119900 minus 11990011989410038161003816100381610038162 (16)




119905119895 =119905sum119895

119902 (17)


119902119905119895

119899119895le 119879 (18)



119862 = 119872 + 119899 (119888 + 119908119891) + 119908119902 (19)



119862 = 119872 + 119899 (119888 + 119908119891) + 119908119902 + 119868 (20)



119862 = 119872 + 119899 (119888 + 119908119891) + (119908 + 120574) 119902 + 119868 (21)











1230 1400-1500 and 1730-1830 resp)



1230 1400-1500 and 1730-1830 resp)


















05 1 15 2 25 3 35 4 450

05

1

15

2

25

3

35

4

45

5

(km)

(km



05 1 15 2 25 3 35 4 45

0

05

1

15

2

25

3

35

4

45

5

5

(km)

(km

)



0 500 1000 1500

1000

1500

2000

2500

3000

3500

4000

Orders per day

Tota

l cos

tyua

n

Different vehicles





05 1 15 2 25 3 35 4 45

0

05

1

15

2

25

3

35

4

45

5

5

(km)

(km

)



05 1 15 2 25 3 35 4 45

0

05

1

15

2

25

3

35

4

45

5

5

(km)

(km

)



0 50 100 150 200 250 300 350 400 4501000

1100

1200

1300

1400

1500

1600

1700

1800

Orders per day

Cos

tyua

n

AHDRBCDPs



























0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(a) 120574 = 05 119868each = 5000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(b) 120574 = 06 119868each = 5000

3500

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(c) 120574 = 07 119868each = 5000








0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(a) 120574 = 06 119868each = 4000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(b) 120574 = 06 119868each = 5000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

3500

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(c) 120574 = 06 119868each = 6000







4 Conclusions







Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Objective function

119899

sum119894=1

min119895isin12119896

10038171003817100381710038171003817119900119894 minus 119875119895

10038171003817100381710038171003817

2(14)

subject to

119900119894 =1

1003816100381610038161003816119871 1198941003816100381610038161003816

sum119900isin119871 119894

119900 (15)

119864 =

119896

sum119894=1

sum119900isin119871 119894

1003816100381610038161003816119900 minus 11990011989410038161003816100381610038162 (16)




119905119895 =119905sum119895

119902 (17)


119902119905119895

119899119895le 119879 (18)



119862 = 119872 + 119899 (119888 + 119908119891) + 119908119902 (19)



119862 = 119872 + 119899 (119888 + 119908119891) + 119908119902 + 119868 (20)



119862 = 119872 + 119899 (119888 + 119908119891) + (119908 + 120574) 119902 + 119868 (21)











1230 1400-1500 and 1730-1830 resp)



1230 1400-1500 and 1730-1830 resp)


















05 1 15 2 25 3 35 4 450

05

1

15

2

25

3

35

4

45

5

(km)

(km



05 1 15 2 25 3 35 4 45

0

05

1

15

2

25

3

35

4

45

5

5

(km)

(km

)



0 500 1000 1500

1000

1500

2000

2500

3000

3500

4000

Orders per day

Tota

l cos

tyua

n

Different vehicles





05 1 15 2 25 3 35 4 45

0

05

1

15

2

25

3

35

4

45

5

5

(km)

(km

)



05 1 15 2 25 3 35 4 45

0

05

1

15

2

25

3

35

4

45

5

5

(km)

(km

)



0 50 100 150 200 250 300 350 400 4501000

1100

1200

1300

1400

1500

1600

1700

1800

Orders per day

Cos

tyua

n

AHDRBCDPs



























0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(a) 120574 = 05 119868each = 5000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(b) 120574 = 06 119868each = 5000

3500

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(c) 120574 = 07 119868each = 5000








0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(a) 120574 = 06 119868each = 4000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(b) 120574 = 06 119868each = 5000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

3500

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(c) 120574 = 06 119868each = 6000







4 Conclusions







Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra

















1230 1400-1500 and 1730-1830 resp)



1230 1400-1500 and 1730-1830 resp)


















05 1 15 2 25 3 35 4 450

05

1

15

2

25

3

35

4

45

5

(km)

(km



05 1 15 2 25 3 35 4 45

0

05

1

15

2

25

3

35

4

45

5

5

(km)

(km

)



0 500 1000 1500

1000

1500

2000

2500

3000

3500

4000

Orders per day

Tota

l cos

tyua

n

Different vehicles





05 1 15 2 25 3 35 4 45

0

05

1

15

2

25

3

35

4

45

5

5

(km)

(km

)



05 1 15 2 25 3 35 4 45

0

05

1

15

2

25

3

35

4

45

5

5

(km)

(km

)



0 50 100 150 200 250 300 350 400 4501000

1100

1200

1300

1400

1500

1600

1700

1800

Orders per day

Cos

tyua

n

AHDRBCDPs



























0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(a) 120574 = 05 119868each = 5000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(b) 120574 = 06 119868each = 5000

3500

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(c) 120574 = 07 119868each = 5000








0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(a) 120574 = 06 119868each = 4000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(b) 120574 = 06 119868each = 5000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

3500

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(c) 120574 = 06 119868each = 6000







4 Conclusions







Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










05 1 15 2 25 3 35 4 450

05

1

15

2

25

3

35

4

45

5

(km)

(km



05 1 15 2 25 3 35 4 45

0

05

1

15

2

25

3

35

4

45

5

5

(km)

(km

)



0 500 1000 1500

1000

1500

2000

2500

3000

3500

4000

Orders per day

Tota

l cos

tyua

n

Different vehicles





05 1 15 2 25 3 35 4 45

0

05

1

15

2

25

3

35

4

45

5

5

(km)

(km

)



05 1 15 2 25 3 35 4 45

0

05

1

15

2

25

3

35

4

45

5

5

(km)

(km

)



0 50 100 150 200 250 300 350 400 4501000

1100

1200

1300

1400

1500

1600

1700

1800

Orders per day

Cos

tyua

n

AHDRBCDPs



























0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(a) 120574 = 05 119868each = 5000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(b) 120574 = 06 119868each = 5000

3500

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(c) 120574 = 07 119868each = 5000








0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(a) 120574 = 06 119868each = 4000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(b) 120574 = 06 119868each = 5000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

3500

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(c) 120574 = 06 119868each = 6000







4 Conclusions







Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 50 100 150 200 250 300 350 400 4501000

1100

1200

1300

1400

1500

1600

1700

1800

Orders per day

Cos

tyua

n

AHDRBCDPs



























0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(a) 120574 = 05 119868each = 5000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(b) 120574 = 06 119868each = 5000

3500

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(c) 120574 = 07 119868each = 5000








0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(a) 120574 = 06 119868each = 4000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(b) 120574 = 06 119868each = 5000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

3500

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(c) 120574 = 06 119868each = 6000







4 Conclusions







Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(a) 120574 = 05 119868each = 5000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(b) 120574 = 06 119868each = 5000

3500

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(c) 120574 = 07 119868each = 5000








0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(a) 120574 = 06 119868each = 4000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(b) 120574 = 06 119868each = 5000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

3500

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(c) 120574 = 06 119868each = 6000







4 Conclusions







Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(a) 120574 = 06 119868each = 4000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(b) 120574 = 06 119868each = 5000

0 500 1000 1500 2000 2500 3000

1000

1500

2000

2500

3000

3500

Orders per day

Tota

l cos

tyua

n


Reception boxCDPs

(c) 120574 = 06 119868each = 6000







4 Conclusions







Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











4 Conclusions







Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article How to Choose Last Mile Delivery Modes...

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Transcript of Research Article How to Choose Last Mile Delivery Modes...