innovative bike-sharing in china: solving faulty bike-sharing recycling...

Research ArticleInnovative Bike-Sharing in China Solving Faulty Bike-SharingRecycling Problem

Shan Chang Rui Song Shiwei He and Guo Qiu

MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology Beijing Jiaotong University Beijing China

Correspondence should be addressed to Rui Song rsongbjtueducn

Received 13 January 2018 Revised 15 April 2018 Accepted 10 May 2018 Published 27 June 2018

Academic Editor Samiul Hasan

Copyright copy 2018 Shan Chang 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

In China based on the mobile Internet technology and global positioning system (GPS) innovative bike-sharing is different fromtraditional bike-sharing system with docking station for its flexibility and convenience However innovative bike-sharing systemfaces operational challenges especially in faulty bike-sharing recycling (FBSR) problem In this paper a framework is designedbased on the optimization method to solve the FBSR problem so that it can minimize the total recycling costs by taking the routeoptimization and loading capacity ratio as constraintsThe FBSRmethod combines the K-means method for clustering faulty bike-sharing with planning recycling route for operational decisions Moreover CPLEX solver is used to obtain the desired result of theFBSR model Finally a case study based on a certain area in Beijing China is used to verify the validity and applicability of themodelThe results show that the value of loading capacity ratio and the number of clustering points greatly affect the results of FBSRproblem Four vehicles are designated to execute FBSR tasks required by different clustering points This study is of considerablesignificance for the bike-sharing promotion in the last-mile situation to the real problems arising in the initial period

1 Introduction

Bike-sharing systems are becoming increasingly popular incities around the world because they are cheap efficienthealthy and green In recent years with the developmentof mobile Internet and global positioning system (GPS)becoming increasingly affordable [1] an innovative bike-sharing system without docking station emerged in 2015 inChina Bike-sharing system can effectively solve the last-mileproblem in multimodal transportation in addition manyChinese cities showmore cycling than the other internationalcities [2] which leads to wide spread of bike-sharing systemsacross China now Spatial distribution of main dockless bike-sharing systems in China is shown in Figure 1

Compared with traditional bike-sharing [3 4] docklessbike-sharing is more flexible and more convenient for theusers Bicycles of bike-sharing systems are widely distributedthus reducing travel distance from traveler to bicycle dockingstation It is convenient for users to use bike-sharing whenusers use bike-sharing for the first time first users should

register directly in the app and scan their identification andgive a deposit Then the smart bike-sharing app will showa map of all the bicycles around users and locate the closestbike After that users scan the Quick Response code with theapp and within 10 seconds they can hear the click and hiton the road However with all the benefits of this innovativebike-sharing system here come operational challenges

It is worth noting that there are a large number ofpeople cycling every day It is unavoidable that bike-sharingmay malfunction in its routine use and accidents mighttake place due to its faults According to some statisticsthere are more than 10 million bicycles in bike-sharingsystems and faulty bicycles rate slightly less than 1 If wecalculate with rate of 1 faulty bicycles there will be 100000faulty bicycles in China Meanwhile lots of bicycles willbe scrapped usually in three years in China These factorscould cause the following (a) the presence of the faultybike-sharing severely threatens usersrsquo safety (b) the servicequality of bike-sharing system will affect the reputation ofthe companies (c) faulty bicycles in the city have a very

HindawiJournal of Advanced TransportationVolume 2018 Article ID 4941029 10 pageshttpsdoiorg10115520184941029

2 Journal of Advanced Transportation

Figure 1 Spatial distribution of main dockless bike-sharing systemsin China

bad effect on the city appearance Therefore faulty bike-sharing recycling (FBSR) is a very significant issue thatshould be solved Moreover the distribution of bicyclesof innovative bike-sharing system is rather dispersed sincebike-sharing can park without docking station whereas fortraditional bike-sharing system faulty bicycles are readilydiscovered and easily processed at bicycle docking stationComparatively speaking it is more difficult for the innovativebike-sharing system to recycle faulty bicycle than traditionalbike-sharing Thus solving the FBSR problem is the key toreduce recycling costs for the authorities and operators withthe means

Therefore this paper presents a framework design andoptimization method to solve FBSR problem Firstly the K-means clustering method is used to divide the faulty bike-sharing into different service points Then a FBSR model isestablished to minimize the total recycling costs with loadingcapacity ratio as a constraint At last this method is verifiedbased on a case study in Beijing China

The remaining part of this paper is organized as followsThe relevant literature is reviewed in Section 2 The frame-work design of faulty bike-sharing recycling is presentedin Section 3 Section 4 describes the modeling methodolo-gies and model specifications In Section 5 the empiricalresults of the models and the effects of the explanatoryvariables are presentedThe final section provides a summaryof the research findings with possible extensions of theresearch

2 Literature Review

Since a bike-sharing system was first introduced in the 1960s[5] lots of bike-sharing systems have been implementedthroughout the world [6 7] and now the bike-sharing systemhas become a necessary for city transportation According toresearch by different scholars the bike-sharing system haspotentials due to the following reasons (a) reducing traffic

congestion and fuel use [8] (b) behavioral shifts towardsincreased bicycle use for daily mobility [9] (c) a growingperception of the bicycle as a convenient transportationmode[1]

The existing literature on bike-sharing systems is mainlyfocused on the traditional bike-sharing system with dockingstations including development policies and safety issues [10ndash12] operation scales and the operator[8 13] and benefiton the environment [14ndash18] In order to improve the userexperience for bicycle use and reduce the operating costsmany researchers study rebalancing operations Chemla etal [19] were the first to introduce rebalancing operations forbike-sharing system and proposed tabu search algorithmsfor solving it Schuijbroek et al [20] presented unifieddual-bounded service level constraints that add inventoryflexibility and vehicle routing for static rebalancing in bike-sharing systems Ghosh et al [21] developed an optimizationformulation to reposition bikes using vehicles while consid-ering the routes for vehicles and future expected demandto improve bike-sharing availability and reduce the usage ofprivate vehicles Pfrommer et al [22] proposed a heuristicalgorithm for solving the dynamic rebalancing problem withmultiple vehicles and presented a dynamic pricing strategythat encouraged users to return bikes to empty stationsHowever the bike-sharing system in a city does not have therestriction of fixed docking stations So the existing studiescannot solve the FBSR in China

Recently the new bike-sharing system without dockingstation has attracted attention from a few scholars Reissand Bogenberger [23] created a demand model to obtainan optimal distribution of bikes within the operating areabased on a detailed GPS-data analysis for the bike-sharingsystem Caggiani et al [24] suggested a method to use therevenue collected by a congestion price policy to implementa bike-sharing system Pal and Zhang [25] proposed a hybridnested large neighborhood search with variable neighbor-hood descent algorithm which can solve static rebalancingproblems for bike-sharing system Caggiani et al [26] pro-posed an operator-based bike redistribution methodologythat started from the prediction of the number and positionof bikes over operating area and ended with a decisionsupport system for the relocation process Cheng and Gao[27] studied the revenue changes of the platform after thebike-sharing platform adopted the monthly strategy andobtained the best monthly subscription pricing to maximizethe platform revenue However compared with bike-sharingscale in China these studies were based on case studies thatare of much smaller scale Therefore FBSR problem deservesmore attention

In addition Cervero et al [28] found that the singlestrongest predictor for bicycle use is the availability of abike The FBSR is one of the important means to ensure theavailability of bike-sharing However up to now there is noresearch on faulty bike-sharing recycling in the literatureThus this study bridges this gap by reporting a solutionalgorithm that addresses this issue and helps bike-sharingcompanies to reduce operating costs particularly in Chinesecities

Journal of Advanced Transportation 3

Service point

Upper network

Recycling route

Faulty bike-sharing

Lower network

A

B

C

O

D E

G

F

Handling line

Maintenance station

Figure 2 Multilevel faulty bike-sharing recycling network

3 Framework Design of FBSR

31 Faulty Bike-Sharing Definition and Classification In thispaper three types of bicycle as faulty bicycles are defined asfollows

(i) Fault of cycling it happens when the users unlockthe bicycles and find that the bicycle cannot be used thenthe users will send the information through the mobilephone appWhen the bike-sharing system server receives theinformation of the faulty bicycle status and location the bike-sharing company will have it repaired

(ii) Fault of communication it happens when bicyclesare identified as faulty bike-sharing owing to GPS equipmentdamage and the system server will prohibit users from usingthis bicycle (ignoring GPS equipment lost contact whilecycling)

(iii) End of the service life if a bicycle has reached thestatersquos mandatory write-off standard (generally three yearsin China) the bike-sharing system server will identify thebicycle as faulty bike-sharingThen this bicycle will be forcedto scrap prohibiting users from cycling

32 Recycling Rules Multilevel faulty bike-sharing recyclingnetwork is shown in Figure 2 which is divided into uppernetwork and lower network The lower network shows thatfaulty bike-sharing in multiple locations within a certain areawill be concentrated at clustering service point in the areawhere blue dots indicate faulty bike-sharing in some locationsand the lines among some dots stand for handing line Theupper network indicates that the clustering service points ofeach area are obtained where dots indicate service point redline shows the line direction and the green one representsmaintenance station The FBSR model can be applied to thebest routes so that total recycling costs are minimized

For the description ground rules are established asfollows

(1) A number of maintenance stations are established ina city Each maintenance station is in a fixed location The

maintenance station provides faulty bicycles maintenanceservice in a certain area and faulty bicycles are recycled oncea day It should be noted that the faulty bicycles will not beclassified The faulty bike-sharing information is collected ata fixed time every day if there are any updates about faultybike-sharing they will be dealt with the next day

(2)Within each local area faulty bicycles are clustered fordifferent service points according to their locations whichare made in lower network such as point A in Figure 2To perform a task a service vehicle will be parked in theclustering service point where the faulty bicycles are carriedback by hands Then service vehicle will move on to the nextservice point such as point B in Figure 2 after the task iscompleted at point A Finally the faulty bike-sharings of eachclustering service point are sent to maintenance point alongthe planned best line

(3) There are a number of recycling vehicles in mainte-nance station These vehicles traverse all service points frommaintenance station in order to recycle all faulty bicycles Itis worth noting that the service point is not fixed and theservice point should have enough space for recycling vehicleto park

Therefore there are two key issues to deal with tocomplete one FBSR in an area

(i)How to determine the number and the location of bike-sharing service points that are available for recycling vehicles

(ii) How to determine routes for recycling vehicles totraverse all service points from maintenance station

33 Recycling Framework Based on the analysis of faultybike-sharing definition classification and recycling rulesthe flowchart of faulty bike-sharing recycling is shown inFigure 3 There are four steps in the framework of FBSRwhich are the data collection and processing the faultybike-sharing clustering the planning of recycling route andthe performing of recycling task The details of recyclingframework can be described as follows


Data Collection and Processing

Clustering Faulty Bike-sharing

Planning Recycling Route

PerformingRecycling Task

Fault of cycling Fault of communication End of the service life

Maintenance station

Service points

Route optimization constraint

Loading capacity constraint

Recycling Route Handling information

Faulty bike-sharing of each service point

K-means algorithm

Vehicle terminal Driver of recycling

CPLEX

Figure 3 Flowchart of faulty bike-sharing recycling

Step 1 (data collection and processing) There are three typesof faulty bike-sharing in the section above For type 1 thesystem server will directly set it as faulty bike-sharing to beprocessed For type 2 when the location information of bike-sharing is lost the system needs to record the last receivedlocation information Type 1 and type 2 bicycles will be storedin the faulty bike-sharing database For type 3 when a bike-sharing company launches bicycles in the city every time thesystem server will set the time of the bicyclesrsquo service lifeafter which the time of service life of these bicycles will bestored in the faulty bike-sharing database by system server Byconfirmation and processing of three types above the bike-sharing company will have these faulty bikes fixed

Step 2 (faulty bike-sharing clustering) Faulty bike-sharingclustering is represented by lower network as shown inFigure 2The systemwill use theK-means algorithm to clusterthe faulty bicycles to different service points in each areaaccording to the result of data collection and processingBased on the different service point the faulty bicycles arecarried to this location by manual handling and wait forcompany trucks to carry them in each clustering service pointalong the planned route driving to maintenance point

Step 3 (planning recycling route) Planning recycling routeis represented by the upper network as shown in Figure 2Every recycling route is planned based on the result offaulty bike-sharing clustering Meanwhile recycling routeoptimization tries to achieve minimum total recycling costswith route optimization and vehicle capacity as constraintsThe recycling vehicles start from the maintenance stationcollect all the faulty bicycles and finally return to thestation

Step 4 (performing recycling task) According to the resultof Step 2 and Step 3 the recycling route and the faulty bike-sharing location information are sent to the vehicle terminalso that every driver of recycling vehicle can perform the taskof recycling faulty bicycles

It is worth noting that Step 2 and Step 3 are the keyscientific problems The FBSR aims at recycling all faultybicycles and traversing all service points while optimizing theroutes for recycling vehicles in order to reduce the costs ofrecycling

4 Model Formulation

Based on framework design of faulty bike-sharing recyclingthe FBSR model in this paper mainly consists of two partsfaulty bike-sharing clustering and recycling route modeling

41 Faulty Bike-Sharing Clustering K-means algorithm [27]is a method commonly used to automatically partition adataset into 119896 groups We use it to cluster the faulty bicyclesto different service points in an area Suppose that a dataset 1199091 119909119873 consists of 119873 observations of a random 2-dimensional Euclidean variable119909Theobjective is to partitionthe dataset into some number 119870 of clusters given the valueof119870 First introduce a set of 2-dimensional vectors 119888119896 where119862 = 119888119896 119896 = 1 119870 119888119896 represents the center of the 119896thcluster Second find an assignment of data points to clustersso that the sum of the squares of the distances of each datathat points to its closest vector 119888119896 is a minimum

min 119878119878119864 =119873

sum119899=1

119870

sum119896=1

119903119899119896 1003817100381710038171003817119909119899 minus 11988811989610038171003817100381710038172 (1)


119903119899119896 =

1 119909119899 isin 1198881198960 119909119899 notin 119888119896

(2)

where SSE (sum of squares for error) is the sum of thedistances from the data points to the clustering points binaryindicator variables 119903119899119896 isin 0 1 and 119896 describes which clusterthe data point 119909119899 is assigned to so that if 119909119899 is assigned tocluster 119896 then 119903119899119896 = 1 and 119903119899119895 = 0 for 119895 = 119896

42 Recycling Route Modeling We develop a recycling routemodel where the decision-maker (the transit authority oroperator) wishes to determine recycling routewhileminimiz-ing total recycling costs It is assumed that the result of faultybike-sharing clustering remains unchanged throughout thatperiod Consider a network rooted at depot (themaintenancestation) named 0 and let the depot be denoted as node0 1198780 is the set of nodes including the maintenance stationand service points that is 119878 = 11987800 We suppose thattravel time of recycling vehicles retains their characteristicsthroughout that period Consider a maintenance station thatconsists of119867 vehicles ℎ = 1 H Identical recycling vehicleswith capacity 119888119886119901ℎ serve the route for all service points forall119894 isin1198780 forall119895 isin 1198780 119894 = 119895 starting from depot (119894 = 0) and ending atdepot (119895 = 0) The travel time (ignoring dwell time) of eachvehicle between successive points 119894 and 119895 is denoted by 119905119894119895In order to model FBSR problem we make assumptions asfollows

(i) All route cycles are repeated with identical character-istics

(ii) The round-trip distance between the two servicepoints is the same

(iii) The location of the faulty bicycle without positioningis accurate

Thus the optimization problem is

119909119894119895ℎ

1 if vehicle ℎ traverses arc (119894 119895)0 otherwise

119910119894ℎ

1 if vehicle ℎ serves node 1198940 otherwise

(3)

Minimize 119862119898sum119894isin1198780

sum119895isin1198780

sum119896isin119867

119905119894119895119909119894119895ℎ (4)

Subject to sum119894isin1198780

119909119894119895ℎ = 119910ℎ119895 forall119895 isin 1198780 ℎ isin 119867 (5)

sum119895isin1198780


sum119896isin119867

119910ℎ119894 = 1 forall119894 isin 119878 (7)

sum119894

119910ℎ119894119889119894 le 119888119886119901ℎ ℎ isin 119867 (8)

119910ℎ119894 isin 0 1 forall119894 isin 1198780 ℎ isin 119867 (9)

119909119894119895ℎ isin 0 1 forall119894 119895 isin 1198780 ℎ isin 119867 (10)

The objective function minimizes the total recyclingcosts It is multiplied by 119862119898 which indicates recyclingvehicles operating costs per unit time119889119894 indicates the numberof bicycles handled by hands at node 119894Constraint (6) statesthat if a vehicle ℎ decides to serve node 119895which is serviced byonly one vehicle then it should travel along the arc from thatnode 119894 that is arc(119894 119895) Constraint (7) states that a vehicle ℎhas traversed arc(119894 119895) from node 119894 which is serviced by onlyone vehicle then it should travel along the arc leading to node119895 Constraint (6) and constraint (7) ensure that the path ofeach vehicle is successive Constraint (8) ensures that everynode is serviced by only one vehicle whereas constraint (9)ensures that the vehicle capacity is not exceeded In order tomodel the entire process of FBSR the formulation can easilyaccommodate fixed costs by modification of the objectivefunction as follows

119862119898sum119894isin1198780

sum119895isin1198780

sumℎisin119867

119905119894119895119909119894119895ℎ + 119862119899sum119894isin1198780

119905119899119894 (11)

The objective includes two components The first refersto the objective function (5) The second refers to theexpectation of the sum of manual handling costs where 119862119899indicates faulty bicycles manual handling costs per unit time119905 is the average time of handling each faulty bicycle andbased on formula (1) 119899119894 is the number of faulty bicycles inthe 119894th service points

Let us define

119905 = 2 times 119878119878119864Vsum119894isin119878 119899119894

(12)

where V is the average velocity of handling each faultybicycle It is multiplied by 2 because each vehicle must returnto the clustering points after service Objective function (11)is now

119862119898sum119894isin1198780

sum119895isin1198780

sumℎisin119867

119905119894119895119909119894119895ℎ + 1198621198992 times 119878119878119864

V (13)

In order to improve the utilization rate of recyclingvehicles we propose a constraint to restrict load capacity asfollows

sum119894isin119878

119910ℎ119894119899119894 ge 120582119888119886119901ℎ forallℎ isin 119867 (14)

where 120582 is the coefficient of load capacity ratioBesides in order to avoid the loop in the route it

is sufficient that problem includes the following bondingconstraint

119880119894ℎ minus 119880119895ℎ + |119878| sdot 119909119894119895ℎ le |119878| minus 1 forall119894 119895 isin 1198780 ℎ isin 119867 (15)

where 119880119894ℎ is the auxiliary variable to eliminate theconstraint of loop for ℎth vehicle


(a) (b)

Figure 4 Heat map of bike-sharing

In the process of problem solving the recycling routemodel belongs to 0-1 integer programming model Consid-ering the scale of the problem it can be solved by CPLEXsolver with branch and bound approach for its advantages ofthe direct and concise input and strong computation ability

5 Case Study

In this section a real-world bike-sharing from an areaof Beijing China was selected as a case study The testarea is a square area that has a side length of 26 km andHaidian Huang Zhuang subway station is selected as arealmaintenance station We set the number of recycling vehiclesin amaintenance station as 4 and the capacity of each vehicleis 30 bicyclesThere are 1900 bicycles (Figure 4(a)) in this areaand we randomly select 95 bicycles (5 of the total) as faultybike-sharing which is shown in Figure 4(b) Red indicatesthat faulty bicycles are dense followed by orange and bluemeans fewer bicycles in heat map

51 Result of Faulty Bike-Sharing Clustering We set up 1 to 14groups clustering experiment The times of iterations of eachclustering algorithm are not more than 20 which proves thatthe computation is highly efficientThe SSE graph of K-meansis shown in Figure 5 We show different clustering points inthe 119909-axis and SSE of different clustering points in the 119910-axisFrom the chart it can be seen that the SSE of the clustering isstable when we select 12 clustering points which is 17531 kmWe first select 12 clustering points for experimental analysis

Latitude and longitude coordinates of the clusteringcenters are obtained by the K-means algorithm and theirlocations on a map are shown in Figure 6 From the diagramit can be seen that the clustering points distribute relativelyequally in this area due to the fact that faulty bikes aredistributed relatively evenly

52 Recycling Route Analysis Considering the result of faultybike-sharing clustering by K-means algorithm of 12 servicepoints |119878| = 12 Travel time 119905119894119895 between every clusteringpoint is obtained by Google Maps (see Tables 4 5 and 6)which is calculated based on the shortest time of drivingThecoefficient of load capacity ratio 120582 is 07The recycling vehicle

Figure 5 The SSE graph of K-means

operating costs 119862119898 are 55 Renminbi (RMB) per minute andthe faulty bicycles manual handling costs 119862119899 are 05 RMB perminuteThe average velocity of handling each faulty bicycle Vis 60mminTheoptimal results of the FBSRmodel are solvedwith the CPLEX solver as shown in Table 1

In this example we can see that the total costs are 677RMB from the FBSR model In Table 1 travel time is derivedfrom the recycling route model carrying time is derivedfrom the clustering results for each service point It can beseen clearly that each route of total time is between 112 minand 206 min which demonstrates that the results of faultybike-sharing clustering and recycling route are reasonable Inaddition the number of bicycles loaded is 24 23 25 and 23for each vehicle capacity ratio of each vehicle is more than767 According to the FBSR model each vehicle achievesan optimized recycling route of FBSR with the vehicle loadcapacity constraint

The comparison experiment for the coefficient of loadcapacity ratio was conducted Figure 7 shows the number ofbicycles loaded for the different capacity ratio and the higherthe coefficient of load capacity ratio is the more average


Table 1 The optimal result of FBSP model

Vehicle Capacityratio Route Travel

timeminCarryingtimemin

Totaltimemin

TotalcostsRMB

1 80 0 rarr 1 rarr 4 rarr 2 rarr10 rarr 0 17 95 112 141

2 767 0 rarr 5 rarr 9 rarr 7 rarr0 17 176 193 1815

3 83 0 rarr 11 rarr 3 rarr12 rarr 0 24 182 206 223

4 767 0 rarr 6 rarr 8 rarr 0 12 131 143 1315Total 70 584 654 677

Figure 6 The graph of clustering centers by K-means

Figure 7 The number of bicycles loaded for the coefficient of loadcapacity ratio

number of bicycles is loaded It means that the load capacityconstraint has an impact on the result of the FBSR modelIn Table 2 we may observe travel time carrying time andtotal cost in several coefficients of load capacity ratios whichshows the optimal result of FBSP model for the differentcapacity ratio We can find that travel time and capacity ratiohave a positive correlation that is the lower the value of the

capacity ratio is the lower the travel time is and the lower thecosts are The lowest value of the capacity ratio is 04 whichresponds to the lowest travel time 67 and the lowest costs6605 And the highest value of the capacity ratio is 07 whichresponds to the highest travel time 70 and the highest costs677However the value of capacity ratiowill affect the fairnessof the recycling task and the utilization rate of the recyclingvehicles as a result decision-makers can consider adding themaximum coefficient as objective to FBSR model accordingto the actual situation of recycling

Table 3 shows that different clustering points are selectedfor contrast experiments According to the experimentalresults we can see that the total costs of 10-node clusteringpoints are always the highest with different load capacityrates Then the results show that the total costs of 12 nodesare more than the total costs of 14 nodes when the coefficientof load capacity ratio is nomore than 06 and the total costs of14 nodes are more than those of 12 nodes when the coefficientof load capacity ratio is equal to 07 When the number ofclustering points is less the increase in manual operationtime will lead to high cost In addition the increase in servicepoints will result in an increase of the recycling distance andthe higher costs of recycling vehicles operating Hence theappropriate recycling scheme should be selected according tothe costs changes of 119862119898 and 119862119899


Table 2 The optimal result of FBSP model for the different capacity ratio

120582 Vehicle route Traveltimemin

Carryingtimemin

TotalcostsRMB

04

1 0 rarr 11 rarr 2 rarr 4 rarr 1 rarr 067 584 66052 0 rarr 5 rarr 12 rarr 3 rarr 0

3 0 rarr 10 rarr 9 rarr 04 0 rarr 8 rarr 6 rarr 7 rarr 0

05

1 0 rarr 1 rarr 4 rarr 2 rarr 068 584 6662 0 rarr 5 rarr 9 rarr 10 rarr 0

3 0 rarr 8 rarr 6 rarr 7 rarr 04 0 rarr 12 rarr 3 rarr 11 rarr 0

06


3 0 rarr 10 rarr 7 rarr 9 rarr 04 0 rarr 8 rarr 6 rarr 0

07



Table 3 The effects of the number of clustering points

Network 120582 Travel timemin

Carrying timemin

Total timemin

Total costsRMB

10-node

04 65 710 775 712505 65 710 775 712506 65 710 775 712507 65 710 775 7125

12-node

04 67 584 651 660505 68 584 652 66606 69 584 653 671507 70 584 654 677

14-node

04 69 546 615 652505 71 546 617 663506 72 546 618 66907 74 546 620 680

6 Conclusions

This paper introduces the framework design and optimiza-tion method to solve FBSR problem In China the numberof bike-sharing systems grows rapidly due to its flexibilityand convenience for the users However they face opera-tional challenges such as FBSR problem For this reasonwe presented a framework design of FBSR to solve theproblem of recycling faulty bike-sharing Then we proposeFBSR optimization model that is able to minimize the totalrecycling costs through the K-means clustering method thatis used to divide the faulty bike-sharing into different servicepoints It can provide bike-sharing companyrsquos managerswith good insight into the design of a FBSR problemThe comparison among different service points can help

decision-makers to choose the best solution In addition thevehicle capacity restriction should be included in a FBSRoptimizationmodel to improve the number of bicycles loadedfor each vehicle

A typical example solved by CPLEX solver was createdto illustrate the proposed model The results of a casestudy show that the model works well It is indicated thatthe best route recycles the faulty bicycles according to theclustering points Compared with the values of capacityratio models in the FBRS model we can find that traveltime and capacity ratio have positive correlation And thecomparison experiment has shown that the number ofclustering points has a significant impact on total recyclingcosts which needs to be considered carefully in the FBSRmodel


Table 4 10-node travel time matrix for each point (unit min)

119905119894119895 0 1 2 3 4 5 6 7 8 9 100 0 2 6 9 12 4 7 4 7 3 41 2 0 4 14 2 6 6 5 12 6 72 6 4 0 17 1 12 8 9 16 13 83 9 14 17 0 13 7 8 10 7 4 124 12 2 1 13 0 12 9 11 13 11 75 4 6 12 7 12 0 8 6 8 4 76 7 6 8 8 9 8 0 5 4 7 67 4 5 9 10 11 6 5 0 7 6 58 7 12 16 7 13 8 4 7 0 9 119 3 6 13 4 11 4 7 6 9 0 610 4 7 8 12 7 7 6 5 11 6 0


119905119894119895 0 1 2 3 4 5 6 7 8 9 10 11 120 0 2 6 7 12 4 4 3 5 5 4 5 111 2 0 4 13 2 6 5 4 6 12 7 6 162 6 4 0 15 1 12 6 13 13 14 8 6 193 7 13 15 0 17 11 5 9 4 7 14 3 54 12 2 1 17 0 12 12 11 12 12 7 10 165 4 6 12 11 12 0 6 6 5 4 7 9 56 4 5 6 5 12 6 0 3 3 9 8 6 87 3 4 13 9 11 6 3 0 5 6 5 6 128 5 6 13 4 12 5 3 5 0 8 7 7 99 5 12 14 7 12 4 9 6 8 0 7 8 1210 4 7 8 14 7 7 8 5 7 7 0 7 1111 5 6 6 3 10 9 6 6 7 8 7 0 1012 11 16 19 5 16 5 8 12 9 12 11 10 0


119905119894119895 0 1 2 3 4 5 6 7 8 9 10 11 12 13 140 0 2 6 8 12 4 4 2 4 5 4 6 6 8 71 2 0 4 13 2 6 11 10 12 12 7 11 15 17 162 6 4 0 14 1 12 8 8 13 12 8 8 16 18 173 8 13 14 0 17 11 6 9 6 7 14 5 9 5 44 12 2 1 17 0 12 9 8 13 11 5 9 15 17 165 4 6 12 11 12 0 5 6 5 4 7 8 4 5 46 4 11 8 6 9 5 0 3 3 8 8 5 7 10 77 2 10 8 9 8 6 3 0 4 8 4 5 8 10 98 4 12 13 6 13 5 3 4 0 8 7 7 8 8 79 5 12 12 7 11 4 8 8 8 0 6 8 3 6 610 4 7 8 14 5 7 8 4 7 6 0 6 9 10 1011 6 11 8 5 9 8 5 5 7 8 6 0 10 9 812 6 15 16 9 15 4 7 8 8 3 9 10 0 3 213 8 17 18 5 17 5 10 10 8 6 10 9 3 0 214 7 16 17 4 16 4 7 9 7 6 10 8 2 2 0


In the future with bike-sharing systems growing inChina we will present a solution model for dealing withdynamic faulty bike-sharing recycling In addition randomsearching for faulty bicycle without GPS should also beconsidered by the researchers

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This research is supported by the National Natural ScienceFoundation of China (no U1434207 and no U1734204)

References

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[2] Y Tang H Pan and Q Shen ldquoBike-sharing systems in BeijingShanghai and Hangzhou and their impact on travel behaviourrdquoinProceedings of the Transportation Research Board 90thAnnualMeeting 2010

[3] S A Shaheen H Zhang E Martin and S Guzman ldquoChinarsquosHangzhou Public Bicycle Understanding early adoption andbehavioral response to bikesharingrdquo Transportation ResearchRecord no 2247 pp 33ndash41 2011

[4] Q Chen and T Sun ldquoA model for the layout of bike stations inpublic bike-sharing systemsrdquo Journal of Advanced Transporta-tion vol 49 no 8 pp 884ndash900 2015

[5] P Demaio ldquoBike-sharing history impacts models of provisionand futurerdquo Journal of Public Transportation vol 12 no 4 pp41ndash56 2009

[6] P J Demaio ldquoSmart bikes Public transportation for the 21stcenturyrdquo Transportation Quarterly vol 57 no 1 pp 9ndash11 2003

[7] S A Shaheen S H Guzaman and H Zhang ldquoBikesharingin Europe the Americas and Asia past present and futurerdquoTransportation Research Record vol 2143 Article ID 1316350pp 159ndash167 2010

[8] A Audikana E Ravalet V Baranger andV Kaufmann ldquoImple-menting bikesharing systems in small cities Evidence from theSwiss experiencerdquo Transport Policy vol 55 pp 18ndash28 2017

[9] Y T Hsu L Kang and Y H Wu ldquouser behavior of bikeshar-ing systems under demandndashsupply imbalancerdquo TransportationResearch Record vol 2587 pp 117ndash124 2016

[10] L Aultman-Hall and M G Kaltenecker ldquoToronto bicyclecommuter safety ratesrdquo Accident Analysis amp Prevention vol 31no 6 pp 675ndash686 1999

[11] E Fishman S Washington and N Haworth ldquoBike Share asynthesis of the literaturerdquo Transport Reviews vol 33 no 2 pp148ndash165 2013

[12] K Martens ldquoPromoting bike-and-ride The Dutch experiencerdquoTransportation Research Part A Policy and Practice vol 41 no4 pp 326ndash338 2007

[13] H Nakamura and N Abe ldquoEvaluation of the hybrid modelof public bicycle-sharing operation and private bicycle parkingmanagementrdquo Transport Policy vol 35 pp 31ndash41 2014

[14] K Martens ldquoThe bicycle as a feedering mode experiencesfrom three European countriesrdquo Transportation Research PartD Transport and Environment vol 9 no 4 pp 281ndash294 2004

[15] AKaltenbrunner RMeza J Grivolla J Codina andR BanchsldquoUrban cycles and mobility patterns Exploring and predictingtrends in a bicycle-based public transport systemrdquo Pervasiveand Mobile Computing vol 6 no 4 pp 455ndash466 2010

[16] J Pucher R Buehler and M Seinen ldquoBicycling renaissancein North America An update and re-appraisal of cyclingtrends and policiesrdquo Transportation Research Part A Policy andPractice vol 45 no 6 pp 451ndash475 2011

[17] S Kaplan FManca T A SNielsen andCG Prato ldquoIntentionsto use bike-sharing for holiday cycling an application of thetheory of planned behaviorrdquo Tourism Management vol 47 pp34ndash46 2015

[18] S-Y Chen ldquoGreen helpfulness or fun Influences of greenperceived value on the green loyalty of users and non-users ofpublic bikesrdquo Transport Policy vol 47 pp 149ndash159 2016

[19] D Chemla F Meunier and R W Calvo ldquoBike sharing systemssolving the static rebalancing problemrdquo Discrete Optimizationvol 10 no 2 pp 120ndash146 2013

[20] J Schuijbroek R C Hampshire and W-J van Hoeve ldquoInven-tory rebalancing and vehicle routing in bike sharing systemsrdquoEuropean Journal of Operational Research vol 257 no 3 pp992ndash1004 2017

[21] S Ghosh P Varakantham Y Adulyasak and P JailletldquoDynamic repositioning to reduce lost demand in bike sharingsystemsrdquo Journal of Artificial Intelligence Research vol 58 pp387ndash430 2017

[22] J Pfrommer J Warrington G Schildbach and M MorarildquoDynamic vehicle redistribution and online price incentivesin shared mobility systemsrdquo IEEE Transactions on IntelligentTransportation Systems vol 15 no 4 pp 1567ndash1578 2014

[23] S Reiss and K Bogenberger ldquoGPS-Data Analysis of MunichrsquosFree-Floating Bike Sharing System and Application of anOperator-based Relocation Strategyrdquo in Proceedings of the 18thIEEE International Conference on Intelligent TransportationSystems pp 584ndash589 September 2015

[24] L Caggiani R Camporeale and M Ottomanelli ldquoPlanningand design of equitable free-floating bike-sharing systemsimplementing a road pricing strategyrdquo Journal of AdvancedTransportation vol 2017 Article ID 3182387 18 pages 2017

[25] A Pal and Y Zhang ldquoFree-floating bike sharing Solving real-life large-scale static rebalancing problemsrdquo TransportationResearch Part C Emerging Technologies vol 80 pp 92ndash116 2017

[26] L Caggiani R Camporeale M Ottomanelli and W Y SzetoldquoA modeling framework for the dynamic management of free-floating bike-sharing systemsrdquo Transportation Research Part CEmerging Technologies vol 87 pp 159ndash182 2018

[27] X Cheng and Y Gao ldquoThe optimal monthly strategy pricingof free-floating bike sharing platformrdquoModern Economy vol 9no 2 pp 318ndash338 2018

[28] R Cervero O Lsarmiento E Jacoby L F Gomez A Nei-Manand G Xue ldquoInfluences of built environments on walking andcycling lessons from Bogotardquo Urban Transport of China vol 3no 4 pp 203ndash226 2016

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Submit your manuscripts atwwwhindawicom


Figure 1 Spatial distribution of main dockless bike-sharing systemsin China

bad effect on the city appearance Therefore faulty bike-sharing recycling (FBSR) is a very significant issue thatshould be solved Moreover the distribution of bicyclesof innovative bike-sharing system is rather dispersed sincebike-sharing can park without docking station whereas fortraditional bike-sharing system faulty bicycles are readilydiscovered and easily processed at bicycle docking stationComparatively speaking it is more difficult for the innovativebike-sharing system to recycle faulty bicycle than traditionalbike-sharing Thus solving the FBSR problem is the key toreduce recycling costs for the authorities and operators withthe means

Therefore this paper presents a framework design andoptimization method to solve FBSR problem Firstly the K-means clustering method is used to divide the faulty bike-sharing into different service points Then a FBSR model isestablished to minimize the total recycling costs with loadingcapacity ratio as a constraint At last this method is verifiedbased on a case study in Beijing China

The remaining part of this paper is organized as followsThe relevant literature is reviewed in Section 2 The frame-work design of faulty bike-sharing recycling is presentedin Section 3 Section 4 describes the modeling methodolo-gies and model specifications In Section 5 the empiricalresults of the models and the effects of the explanatoryvariables are presentedThe final section provides a summaryof the research findings with possible extensions of theresearch

2 Literature Review

Since a bike-sharing system was first introduced in the 1960s[5] lots of bike-sharing systems have been implementedthroughout the world [6 7] and now the bike-sharing systemhas become a necessary for city transportation According toresearch by different scholars the bike-sharing system haspotentials due to the following reasons (a) reducing traffic

congestion and fuel use [8] (b) behavioral shifts towardsincreased bicycle use for daily mobility [9] (c) a growingperception of the bicycle as a convenient transportationmode[1]

The existing literature on bike-sharing systems is mainlyfocused on the traditional bike-sharing system with dockingstations including development policies and safety issues [10ndash12] operation scales and the operator[8 13] and benefiton the environment [14ndash18] In order to improve the userexperience for bicycle use and reduce the operating costsmany researchers study rebalancing operations Chemla etal [19] were the first to introduce rebalancing operations forbike-sharing system and proposed tabu search algorithmsfor solving it Schuijbroek et al [20] presented unifieddual-bounded service level constraints that add inventoryflexibility and vehicle routing for static rebalancing in bike-sharing systems Ghosh et al [21] developed an optimizationformulation to reposition bikes using vehicles while consid-ering the routes for vehicles and future expected demandto improve bike-sharing availability and reduce the usage ofprivate vehicles Pfrommer et al [22] proposed a heuristicalgorithm for solving the dynamic rebalancing problem withmultiple vehicles and presented a dynamic pricing strategythat encouraged users to return bikes to empty stationsHowever the bike-sharing system in a city does not have therestriction of fixed docking stations So the existing studiescannot solve the FBSR in China

Recently the new bike-sharing system without dockingstation has attracted attention from a few scholars Reissand Bogenberger [23] created a demand model to obtainan optimal distribution of bikes within the operating areabased on a detailed GPS-data analysis for the bike-sharingsystem Caggiani et al [24] suggested a method to use therevenue collected by a congestion price policy to implementa bike-sharing system Pal and Zhang [25] proposed a hybridnested large neighborhood search with variable neighbor-hood descent algorithm which can solve static rebalancingproblems for bike-sharing system Caggiani et al [26] pro-posed an operator-based bike redistribution methodologythat started from the prediction of the number and positionof bikes over operating area and ended with a decisionsupport system for the relocation process Cheng and Gao[27] studied the revenue changes of the platform after thebike-sharing platform adopted the monthly strategy andobtained the best monthly subscription pricing to maximizethe platform revenue However compared with bike-sharingscale in China these studies were based on case studies thatare of much smaller scale Therefore FBSR problem deservesmore attention

In addition Cervero et al [28] found that the singlestrongest predictor for bicycle use is the availability of abike The FBSR is one of the important means to ensure theavailability of bike-sharing However up to now there is noresearch on faulty bike-sharing recycling in the literatureThus this study bridges this gap by reporting a solutionalgorithm that addresses this issue and helps bike-sharingcompanies to reduce operating costs particularly in Chinesecities


Service point

Upper network

Recycling route

Faulty bike-sharing

Lower network

A

B

C

O

D E

G

F

Handling line

Maintenance station























Maintenance station

Service points





K-means algorithm


CPLEX







4 Model Formulation



min 119878119878119864 =119873

sum119899=1

119870

sum119896=1

119903119899119896 1003817100381710038171003817119909119899 minus 11988811989610038171003817100381710038172 (1)


119903119899119896 =

1 119909119899 isin 1198881198960 119909119899 notin 119888119896

(2)







119909119894119895ℎ


119910119894ℎ


(3)


sum119895isin1198780

sum119896isin119867

119905119894119895119909119894119895ℎ (4)



sum119895isin1198780


sum119896isin119867

119910ℎ119894 = 1 forall119894 isin 119878 (7)

sum119894

119910ℎ119894119889119894 le 119888119886119901ℎ ℎ isin 119867 (8)




119862119898sum119894isin1198780

sum119895isin1198780

sumℎisin119867

119905119894119895119909119894119895ℎ + 119862119899sum119894isin1198780

119905119899119894 (11)


Let us define

119905 = 2 times 119878119878119864Vsum119894isin119878 119899119894

(12)


119862119898sum119894isin1198780

sum119895isin1198780

sumℎisin119867

119905119894119895119909119894119895ℎ + 1198621198992 times 119878119878119864

V (13)


sum119894isin119878







(a) (b)



5 Case Study













Totaltimemin

TotalcostsRMB













Carryingtimemin

TotalcostsRMB

04



05



06



07





Carrying timemin

Total timemin

Total costsRMB

10-node

04 65 710 775 712505 65 710 775 712506 65 710 775 712507 65 710 775 7125

12-node

04 67 584 651 660505 68 584 652 66606 69 584 653 671507 70 584 654 677

14-node

04 69 546 615 652505 71 546 617 663506 72 546 618 66907 74 546 620 680

6 Conclusions






119905119894119895 0 1 2 3 4 5 6 7 8 9 100 0 2 6 9 12 4 7 4 7 3 41 2 0 4 14 2 6 6 5 12 6 72 6 4 0 17 1 12 8 9 16 13 83 9 14 17 0 13 7 8 10 7 4 124 12 2 1 13 0 12 9 11 13 11 75 4 6 12 7 12 0 8 6 8 4 76 7 6 8 8 9 8 0 5 4 7 67 4 5 9 10 11 6 5 0 7 6 58 7 12 16 7 13 8 4 7 0 9 119 3 6 13 4 11 4 7 6 9 0 610 4 7 8 12 7 7 6 5 11 6 0


119905119894119895 0 1 2 3 4 5 6 7 8 9 10 11 120 0 2 6 7 12 4 4 3 5 5 4 5 111 2 0 4 13 2 6 5 4 6 12 7 6 162 6 4 0 15 1 12 6 13 13 14 8 6 193 7 13 15 0 17 11 5 9 4 7 14 3 54 12 2 1 17 0 12 12 11 12 12 7 10 165 4 6 12 11 12 0 6 6 5 4 7 9 56 4 5 6 5 12 6 0 3 3 9 8 6 87 3 4 13 9 11 6 3 0 5 6 5 6 128 5 6 13 4 12 5 3 5 0 8 7 7 99 5 12 14 7 12 4 9 6 8 0 7 8 1210 4 7 8 14 7 7 8 5 7 7 0 7 1111 5 6 6 3 10 9 6 6 7 8 7 0 1012 11 16 19 5 16 5 8 12 9 12 11 10 0


119905119894119895 0 1 2 3 4 5 6 7 8 9 10 11 12 13 140 0 2 6 8 12 4 4 2 4 5 4 6 6 8 71 2 0 4 13 2 6 11 10 12 12 7 11 15 17 162 6 4 0 14 1 12 8 8 13 12 8 8 16 18 173 8 13 14 0 17 11 6 9 6 7 14 5 9 5 44 12 2 1 17 0 12 9 8 13 11 5 9 15 17 165 4 6 12 11 12 0 5 6 5 4 7 8 4 5 46 4 11 8 6 9 5 0 3 3 8 8 5 7 10 77 2 10 8 9 8 6 3 0 4 8 4 5 8 10 98 4 12 13 6 13 5 3 4 0 8 7 7 8 8 79 5 12 12 7 11 4 8 8 8 0 6 8 3 6 610 4 7 8 14 5 7 8 4 7 6 0 6 9 10 1011 6 11 8 5 9 8 5 5 7 8 6 0 10 9 812 6 15 16 9 15 4 7 8 8 3 9 10 0 3 213 8 17 18 5 17 5 10 10 8 6 10 9 3 0 214 7 16 17 4 16 4 7 9 7 6 10 8 2 2 0



Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Service point

Upper network

Recycling route

Faulty bike-sharing

Lower network

A

B

C

O

D E

G

F

Handling line

Maintenance station























Maintenance station

Service points





K-means algorithm


CPLEX







4 Model Formulation



min 119878119878119864 =119873

sum119899=1

119870

sum119896=1

119903119899119896 1003817100381710038171003817119909119899 minus 11988811989610038171003817100381710038172 (1)


119903119899119896 =

1 119909119899 isin 1198881198960 119909119899 notin 119888119896

(2)







119909119894119895ℎ


119910119894ℎ


(3)


sum119895isin1198780

sum119896isin119867

119905119894119895119909119894119895ℎ (4)



sum119895isin1198780


sum119896isin119867

119910ℎ119894 = 1 forall119894 isin 119878 (7)

sum119894

119910ℎ119894119889119894 le 119888119886119901ℎ ℎ isin 119867 (8)




119862119898sum119894isin1198780

sum119895isin1198780

sumℎisin119867

119905119894119895119909119894119895ℎ + 119862119899sum119894isin1198780

119905119899119894 (11)


Let us define

119905 = 2 times 119878119878119864Vsum119894isin119878 119899119894

(12)


119862119898sum119894isin1198780

sum119895isin1198780

sumℎisin119867

119905119894119895119909119894119895ℎ + 1198621198992 times 119878119878119864

V (13)


sum119894isin119878







(a) (b)



5 Case Study













Totaltimemin

TotalcostsRMB













Carryingtimemin

TotalcostsRMB

04



05



06



07





Carrying timemin

Total timemin

Total costsRMB

10-node

04 65 710 775 712505 65 710 775 712506 65 710 775 712507 65 710 775 7125

12-node

04 67 584 651 660505 68 584 652 66606 69 584 653 671507 70 584 654 677

14-node

04 69 546 615 652505 71 546 617 663506 72 546 618 66907 74 546 620 680

6 Conclusions






119905119894119895 0 1 2 3 4 5 6 7 8 9 100 0 2 6 9 12 4 7 4 7 3 41 2 0 4 14 2 6 6 5 12 6 72 6 4 0 17 1 12 8 9 16 13 83 9 14 17 0 13 7 8 10 7 4 124 12 2 1 13 0 12 9 11 13 11 75 4 6 12 7 12 0 8 6 8 4 76 7 6 8 8 9 8 0 5 4 7 67 4 5 9 10 11 6 5 0 7 6 58 7 12 16 7 13 8 4 7 0 9 119 3 6 13 4 11 4 7 6 9 0 610 4 7 8 12 7 7 6 5 11 6 0


119905119894119895 0 1 2 3 4 5 6 7 8 9 10 11 120 0 2 6 7 12 4 4 3 5 5 4 5 111 2 0 4 13 2 6 5 4 6 12 7 6 162 6 4 0 15 1 12 6 13 13 14 8 6 193 7 13 15 0 17 11 5 9 4 7 14 3 54 12 2 1 17 0 12 12 11 12 12 7 10 165 4 6 12 11 12 0 6 6 5 4 7 9 56 4 5 6 5 12 6 0 3 3 9 8 6 87 3 4 13 9 11 6 3 0 5 6 5 6 128 5 6 13 4 12 5 3 5 0 8 7 7 99 5 12 14 7 12 4 9 6 8 0 7 8 1210 4 7 8 14 7 7 8 5 7 7 0 7 1111 5 6 6 3 10 9 6 6 7 8 7 0 1012 11 16 19 5 16 5 8 12 9 12 11 10 0


119905119894119895 0 1 2 3 4 5 6 7 8 9 10 11 12 13 140 0 2 6 8 12 4 4 2 4 5 4 6 6 8 71 2 0 4 13 2 6 11 10 12 12 7 11 15 17 162 6 4 0 14 1 12 8 8 13 12 8 8 16 18 173 8 13 14 0 17 11 6 9 6 7 14 5 9 5 44 12 2 1 17 0 12 9 8 13 11 5 9 15 17 165 4 6 12 11 12 0 5 6 5 4 7 8 4 5 46 4 11 8 6 9 5 0 3 3 8 8 5 7 10 77 2 10 8 9 8 6 3 0 4 8 4 5 8 10 98 4 12 13 6 13 5 3 4 0 8 7 7 8 8 79 5 12 12 7 11 4 8 8 8 0 6 8 3 6 610 4 7 8 14 5 7 8 4 7 6 0 6 9 10 1011 6 11 8 5 9 8 5 5 7 8 6 0 10 9 812 6 15 16 9 15 4 7 8 8 3 9 10 0 3 213 8 17 18 5 17 5 10 10 8 6 10 9 3 0 214 7 16 17 4 16 4 7 9 7 6 10 8 2 2 0



Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








Maintenance station

Service points





K-means algorithm


CPLEX







4 Model Formulation



min 119878119878119864 =119873

sum119899=1

119870

sum119896=1

119903119899119896 1003817100381710038171003817119909119899 minus 11988811989610038171003817100381710038172 (1)


119903119899119896 =

1 119909119899 isin 1198881198960 119909119899 notin 119888119896

(2)







119909119894119895ℎ


119910119894ℎ


(3)


sum119895isin1198780

sum119896isin119867

119905119894119895119909119894119895ℎ (4)



sum119895isin1198780


sum119896isin119867

119910ℎ119894 = 1 forall119894 isin 119878 (7)

sum119894

119910ℎ119894119889119894 le 119888119886119901ℎ ℎ isin 119867 (8)




119862119898sum119894isin1198780

sum119895isin1198780

sumℎisin119867

119905119894119895119909119894119895ℎ + 119862119899sum119894isin1198780

119905119899119894 (11)


Let us define

119905 = 2 times 119878119878119864Vsum119894isin119878 119899119894

(12)


119862119898sum119894isin1198780

sum119895isin1198780

sumℎisin119867

119905119894119895119909119894119895ℎ + 1198621198992 times 119878119878119864

V (13)


sum119894isin119878







(a) (b)



5 Case Study













Totaltimemin

TotalcostsRMB













Carryingtimemin

TotalcostsRMB

04



05



06



07





Carrying timemin

Total timemin

Total costsRMB

10-node

04 65 710 775 712505 65 710 775 712506 65 710 775 712507 65 710 775 7125

12-node

04 67 584 651 660505 68 584 652 66606 69 584 653 671507 70 584 654 677

14-node

04 69 546 615 652505 71 546 617 663506 72 546 618 66907 74 546 620 680

6 Conclusions






119905119894119895 0 1 2 3 4 5 6 7 8 9 100 0 2 6 9 12 4 7 4 7 3 41 2 0 4 14 2 6 6 5 12 6 72 6 4 0 17 1 12 8 9 16 13 83 9 14 17 0 13 7 8 10 7 4 124 12 2 1 13 0 12 9 11 13 11 75 4 6 12 7 12 0 8 6 8 4 76 7 6 8 8 9 8 0 5 4 7 67 4 5 9 10 11 6 5 0 7 6 58 7 12 16 7 13 8 4 7 0 9 119 3 6 13 4 11 4 7 6 9 0 610 4 7 8 12 7 7 6 5 11 6 0


119905119894119895 0 1 2 3 4 5 6 7 8 9 10 11 120 0 2 6 7 12 4 4 3 5 5 4 5 111 2 0 4 13 2 6 5 4 6 12 7 6 162 6 4 0 15 1 12 6 13 13 14 8 6 193 7 13 15 0 17 11 5 9 4 7 14 3 54 12 2 1 17 0 12 12 11 12 12 7 10 165 4 6 12 11 12 0 6 6 5 4 7 9 56 4 5 6 5 12 6 0 3 3 9 8 6 87 3 4 13 9 11 6 3 0 5 6 5 6 128 5 6 13 4 12 5 3 5 0 8 7 7 99 5 12 14 7 12 4 9 6 8 0 7 8 1210 4 7 8 14 7 7 8 5 7 7 0 7 1111 5 6 6 3 10 9 6 6 7 8 7 0 1012 11 16 19 5 16 5 8 12 9 12 11 10 0


119905119894119895 0 1 2 3 4 5 6 7 8 9 10 11 12 13 140 0 2 6 8 12 4 4 2 4 5 4 6 6 8 71 2 0 4 13 2 6 11 10 12 12 7 11 15 17 162 6 4 0 14 1 12 8 8 13 12 8 8 16 18 173 8 13 14 0 17 11 6 9 6 7 14 5 9 5 44 12 2 1 17 0 12 9 8 13 11 5 9 15 17 165 4 6 12 11 12 0 5 6 5 4 7 8 4 5 46 4 11 8 6 9 5 0 3 3 8 8 5 7 10 77 2 10 8 9 8 6 3 0 4 8 4 5 8 10 98 4 12 13 6 13 5 3 4 0 8 7 7 8 8 79 5 12 12 7 11 4 8 8 8 0 6 8 3 6 610 4 7 8 14 5 7 8 4 7 6 0 6 9 10 1011 6 11 8 5 9 8 5 5 7 8 6 0 10 9 812 6 15 16 9 15 4 7 8 8 3 9 10 0 3 213 8 17 18 5 17 5 10 10 8 6 10 9 3 0 214 7 16 17 4 16 4 7 9 7 6 10 8 2 2 0



Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



119903119899119896 =

1 119909119899 isin 1198881198960 119909119899 notin 119888119896

(2)







119909119894119895ℎ


119910119894ℎ


(3)


sum119895isin1198780

sum119896isin119867

119905119894119895119909119894119895ℎ (4)



sum119895isin1198780


sum119896isin119867

119910ℎ119894 = 1 forall119894 isin 119878 (7)

sum119894

119910ℎ119894119889119894 le 119888119886119901ℎ ℎ isin 119867 (8)




119862119898sum119894isin1198780

sum119895isin1198780

sumℎisin119867

119905119894119895119909119894119895ℎ + 119862119899sum119894isin1198780

119905119899119894 (11)


Let us define

119905 = 2 times 119878119878119864Vsum119894isin119878 119899119894

(12)


119862119898sum119894isin1198780

sum119895isin1198780

sumℎisin119867

119905119894119895119909119894119895ℎ + 1198621198992 times 119878119878119864

V (13)


sum119894isin119878







(a) (b)



5 Case Study













Totaltimemin

TotalcostsRMB













Carryingtimemin

TotalcostsRMB

04



05



06



07





Carrying timemin

Total timemin

Total costsRMB

10-node

04 65 710 775 712505 65 710 775 712506 65 710 775 712507 65 710 775 7125

12-node

04 67 584 651 660505 68 584 652 66606 69 584 653 671507 70 584 654 677

14-node

04 69 546 615 652505 71 546 617 663506 72 546 618 66907 74 546 620 680

6 Conclusions






119905119894119895 0 1 2 3 4 5 6 7 8 9 100 0 2 6 9 12 4 7 4 7 3 41 2 0 4 14 2 6 6 5 12 6 72 6 4 0 17 1 12 8 9 16 13 83 9 14 17 0 13 7 8 10 7 4 124 12 2 1 13 0 12 9 11 13 11 75 4 6 12 7 12 0 8 6 8 4 76 7 6 8 8 9 8 0 5 4 7 67 4 5 9 10 11 6 5 0 7 6 58 7 12 16 7 13 8 4 7 0 9 119 3 6 13 4 11 4 7 6 9 0 610 4 7 8 12 7 7 6 5 11 6 0


119905119894119895 0 1 2 3 4 5 6 7 8 9 10 11 120 0 2 6 7 12 4 4 3 5 5 4 5 111 2 0 4 13 2 6 5 4 6 12 7 6 162 6 4 0 15 1 12 6 13 13 14 8 6 193 7 13 15 0 17 11 5 9 4 7 14 3 54 12 2 1 17 0 12 12 11 12 12 7 10 165 4 6 12 11 12 0 6 6 5 4 7 9 56 4 5 6 5 12 6 0 3 3 9 8 6 87 3 4 13 9 11 6 3 0 5 6 5 6 128 5 6 13 4 12 5 3 5 0 8 7 7 99 5 12 14 7 12 4 9 6 8 0 7 8 1210 4 7 8 14 7 7 8 5 7 7 0 7 1111 5 6 6 3 10 9 6 6 7 8 7 0 1012 11 16 19 5 16 5 8 12 9 12 11 10 0


119905119894119895 0 1 2 3 4 5 6 7 8 9 10 11 12 13 140 0 2 6 8 12 4 4 2 4 5 4 6 6 8 71 2 0 4 13 2 6 11 10 12 12 7 11 15 17 162 6 4 0 14 1 12 8 8 13 12 8 8 16 18 173 8 13 14 0 17 11 6 9 6 7 14 5 9 5 44 12 2 1 17 0 12 9 8 13 11 5 9 15 17 165 4 6 12 11 12 0 5 6 5 4 7 8 4 5 46 4 11 8 6 9 5 0 3 3 8 8 5 7 10 77 2 10 8 9 8 6 3 0 4 8 4 5 8 10 98 4 12 13 6 13 5 3 4 0 8 7 7 8 8 79 5 12 12 7 11 4 8 8 8 0 6 8 3 6 610 4 7 8 14 5 7 8 4 7 6 0 6 9 10 1011 6 11 8 5 9 8 5 5 7 8 6 0 10 9 812 6 15 16 9 15 4 7 8 8 3 9 10 0 3 213 8 17 18 5 17 5 10 10 8 6 10 9 3 0 214 7 16 17 4 16 4 7 9 7 6 10 8 2 2 0



Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



(a) (b)



5 Case Study













Totaltimemin

TotalcostsRMB













Carryingtimemin

TotalcostsRMB

04



05



06



07





Carrying timemin

Total timemin

Total costsRMB

10-node

04 65 710 775 712505 65 710 775 712506 65 710 775 712507 65 710 775 7125

12-node

04 67 584 651 660505 68 584 652 66606 69 584 653 671507 70 584 654 677

14-node

04 69 546 615 652505 71 546 617 663506 72 546 618 66907 74 546 620 680

6 Conclusions






119905119894119895 0 1 2 3 4 5 6 7 8 9 100 0 2 6 9 12 4 7 4 7 3 41 2 0 4 14 2 6 6 5 12 6 72 6 4 0 17 1 12 8 9 16 13 83 9 14 17 0 13 7 8 10 7 4 124 12 2 1 13 0 12 9 11 13 11 75 4 6 12 7 12 0 8 6 8 4 76 7 6 8 8 9 8 0 5 4 7 67 4 5 9 10 11 6 5 0 7 6 58 7 12 16 7 13 8 4 7 0 9 119 3 6 13 4 11 4 7 6 9 0 610 4 7 8 12 7 7 6 5 11 6 0


119905119894119895 0 1 2 3 4 5 6 7 8 9 10 11 120 0 2 6 7 12 4 4 3 5 5 4 5 111 2 0 4 13 2 6 5 4 6 12 7 6 162 6 4 0 15 1 12 6 13 13 14 8 6 193 7 13 15 0 17 11 5 9 4 7 14 3 54 12 2 1 17 0 12 12 11 12 12 7 10 165 4 6 12 11 12 0 6 6 5 4 7 9 56 4 5 6 5 12 6 0 3 3 9 8 6 87 3 4 13 9 11 6 3 0 5 6 5 6 128 5 6 13 4 12 5 3 5 0 8 7 7 99 5 12 14 7 12 4 9 6 8 0 7 8 1210 4 7 8 14 7 7 8 5 7 7 0 7 1111 5 6 6 3 10 9 6 6 7 8 7 0 1012 11 16 19 5 16 5 8 12 9 12 11 10 0


119905119894119895 0 1 2 3 4 5 6 7 8 9 10 11 12 13 140 0 2 6 8 12 4 4 2 4 5 4 6 6 8 71 2 0 4 13 2 6 11 10 12 12 7 11 15 17 162 6 4 0 14 1 12 8 8 13 12 8 8 16 18 173 8 13 14 0 17 11 6 9 6 7 14 5 9 5 44 12 2 1 17 0 12 9 8 13 11 5 9 15 17 165 4 6 12 11 12 0 5 6 5 4 7 8 4 5 46 4 11 8 6 9 5 0 3 3 8 8 5 7 10 77 2 10 8 9 8 6 3 0 4 8 4 5 8 10 98 4 12 13 6 13 5 3 4 0 8 7 7 8 8 79 5 12 12 7 11 4 8 8 8 0 6 8 3 6 610 4 7 8 14 5 7 8 4 7 6 0 6 9 10 1011 6 11 8 5 9 8 5 5 7 8 6 0 10 9 812 6 15 16 9 15 4 7 8 8 3 9 10 0 3 213 8 17 18 5 17 5 10 10 8 6 10 9 3 0 214 7 16 17 4 16 4 7 9 7 6 10 8 2 2 0



Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






Totaltimemin

TotalcostsRMB













Carryingtimemin

TotalcostsRMB

04



05



06



07





Carrying timemin

Total timemin

Total costsRMB

10-node

04 65 710 775 712505 65 710 775 712506 65 710 775 712507 65 710 775 7125

12-node

04 67 584 651 660505 68 584 652 66606 69 584 653 671507 70 584 654 677

14-node

04 69 546 615 652505 71 546 617 663506 72 546 618 66907 74 546 620 680

6 Conclusions






119905119894119895 0 1 2 3 4 5 6 7 8 9 100 0 2 6 9 12 4 7 4 7 3 41 2 0 4 14 2 6 6 5 12 6 72 6 4 0 17 1 12 8 9 16 13 83 9 14 17 0 13 7 8 10 7 4 124 12 2 1 13 0 12 9 11 13 11 75 4 6 12 7 12 0 8 6 8 4 76 7 6 8 8 9 8 0 5 4 7 67 4 5 9 10 11 6 5 0 7 6 58 7 12 16 7 13 8 4 7 0 9 119 3 6 13 4 11 4 7 6 9 0 610 4 7 8 12 7 7 6 5 11 6 0


119905119894119895 0 1 2 3 4 5 6 7 8 9 10 11 120 0 2 6 7 12 4 4 3 5 5 4 5 111 2 0 4 13 2 6 5 4 6 12 7 6 162 6 4 0 15 1 12 6 13 13 14 8 6 193 7 13 15 0 17 11 5 9 4 7 14 3 54 12 2 1 17 0 12 12 11 12 12 7 10 165 4 6 12 11 12 0 6 6 5 4 7 9 56 4 5 6 5 12 6 0 3 3 9 8 6 87 3 4 13 9 11 6 3 0 5 6 5 6 128 5 6 13 4 12 5 3 5 0 8 7 7 99 5 12 14 7 12 4 9 6 8 0 7 8 1210 4 7 8 14 7 7 8 5 7 7 0 7 1111 5 6 6 3 10 9 6 6 7 8 7 0 1012 11 16 19 5 16 5 8 12 9 12 11 10 0


119905119894119895 0 1 2 3 4 5 6 7 8 9 10 11 12 13 140 0 2 6 8 12 4 4 2 4 5 4 6 6 8 71 2 0 4 13 2 6 11 10 12 12 7 11 15 17 162 6 4 0 14 1 12 8 8 13 12 8 8 16 18 173 8 13 14 0 17 11 6 9 6 7 14 5 9 5 44 12 2 1 17 0 12 9 8 13 11 5 9 15 17 165 4 6 12 11 12 0 5 6 5 4 7 8 4 5 46 4 11 8 6 9 5 0 3 3 8 8 5 7 10 77 2 10 8 9 8 6 3 0 4 8 4 5 8 10 98 4 12 13 6 13 5 3 4 0 8 7 7 8 8 79 5 12 12 7 11 4 8 8 8 0 6 8 3 6 610 4 7 8 14 5 7 8 4 7 6 0 6 9 10 1011 6 11 8 5 9 8 5 5 7 8 6 0 10 9 812 6 15 16 9 15 4 7 8 8 3 9 10 0 3 213 8 17 18 5 17 5 10 10 8 6 10 9 3 0 214 7 16 17 4 16 4 7 9 7 6 10 8 2 2 0



Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Carryingtimemin

TotalcostsRMB

04



05



06



07





Carrying timemin

Total timemin

Total costsRMB

10-node

04 65 710 775 712505 65 710 775 712506 65 710 775 712507 65 710 775 7125

12-node

04 67 584 651 660505 68 584 652 66606 69 584 653 671507 70 584 654 677

14-node

04 69 546 615 652505 71 546 617 663506 72 546 618 66907 74 546 620 680

6 Conclusions






119905119894119895 0 1 2 3 4 5 6 7 8 9 100 0 2 6 9 12 4 7 4 7 3 41 2 0 4 14 2 6 6 5 12 6 72 6 4 0 17 1 12 8 9 16 13 83 9 14 17 0 13 7 8 10 7 4 124 12 2 1 13 0 12 9 11 13 11 75 4 6 12 7 12 0 8 6 8 4 76 7 6 8 8 9 8 0 5 4 7 67 4 5 9 10 11 6 5 0 7 6 58 7 12 16 7 13 8 4 7 0 9 119 3 6 13 4 11 4 7 6 9 0 610 4 7 8 12 7 7 6 5 11 6 0


119905119894119895 0 1 2 3 4 5 6 7 8 9 10 11 120 0 2 6 7 12 4 4 3 5 5 4 5 111 2 0 4 13 2 6 5 4 6 12 7 6 162 6 4 0 15 1 12 6 13 13 14 8 6 193 7 13 15 0 17 11 5 9 4 7 14 3 54 12 2 1 17 0 12 12 11 12 12 7 10 165 4 6 12 11 12 0 6 6 5 4 7 9 56 4 5 6 5 12 6 0 3 3 9 8 6 87 3 4 13 9 11 6 3 0 5 6 5 6 128 5 6 13 4 12 5 3 5 0 8 7 7 99 5 12 14 7 12 4 9 6 8 0 7 8 1210 4 7 8 14 7 7 8 5 7 7 0 7 1111 5 6 6 3 10 9 6 6 7 8 7 0 1012 11 16 19 5 16 5 8 12 9 12 11 10 0


119905119894119895 0 1 2 3 4 5 6 7 8 9 10 11 12 13 140 0 2 6 8 12 4 4 2 4 5 4 6 6 8 71 2 0 4 13 2 6 11 10 12 12 7 11 15 17 162 6 4 0 14 1 12 8 8 13 12 8 8 16 18 173 8 13 14 0 17 11 6 9 6 7 14 5 9 5 44 12 2 1 17 0 12 9 8 13 11 5 9 15 17 165 4 6 12 11 12 0 5 6 5 4 7 8 4 5 46 4 11 8 6 9 5 0 3 3 8 8 5 7 10 77 2 10 8 9 8 6 3 0 4 8 4 5 8 10 98 4 12 13 6 13 5 3 4 0 8 7 7 8 8 79 5 12 12 7 11 4 8 8 8 0 6 8 3 6 610 4 7 8 14 5 7 8 4 7 6 0 6 9 10 1011 6 11 8 5 9 8 5 5 7 8 6 0 10 9 812 6 15 16 9 15 4 7 8 8 3 9 10 0 3 213 8 17 18 5 17 5 10 10 8 6 10 9 3 0 214 7 16 17 4 16 4 7 9 7 6 10 8 2 2 0



Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




119905119894119895 0 1 2 3 4 5 6 7 8 9 100 0 2 6 9 12 4 7 4 7 3 41 2 0 4 14 2 6 6 5 12 6 72 6 4 0 17 1 12 8 9 16 13 83 9 14 17 0 13 7 8 10 7 4 124 12 2 1 13 0 12 9 11 13 11 75 4 6 12 7 12 0 8 6 8 4 76 7 6 8 8 9 8 0 5 4 7 67 4 5 9 10 11 6 5 0 7 6 58 7 12 16 7 13 8 4 7 0 9 119 3 6 13 4 11 4 7 6 9 0 610 4 7 8 12 7 7 6 5 11 6 0


119905119894119895 0 1 2 3 4 5 6 7 8 9 10 11 120 0 2 6 7 12 4 4 3 5 5 4 5 111 2 0 4 13 2 6 5 4 6 12 7 6 162 6 4 0 15 1 12 6 13 13 14 8 6 193 7 13 15 0 17 11 5 9 4 7 14 3 54 12 2 1 17 0 12 12 11 12 12 7 10 165 4 6 12 11 12 0 6 6 5 4 7 9 56 4 5 6 5 12 6 0 3 3 9 8 6 87 3 4 13 9 11 6 3 0 5 6 5 6 128 5 6 13 4 12 5 3 5 0 8 7 7 99 5 12 14 7 12 4 9 6 8 0 7 8 1210 4 7 8 14 7 7 8 5 7 7 0 7 1111 5 6 6 3 10 9 6 6 7 8 7 0 1012 11 16 19 5 16 5 8 12 9 12 11 10 0


119905119894119895 0 1 2 3 4 5 6 7 8 9 10 11 12 13 140 0 2 6 8 12 4 4 2 4 5 4 6 6 8 71 2 0 4 13 2 6 11 10 12 12 7 11 15 17 162 6 4 0 14 1 12 8 8 13 12 8 8 16 18 173 8 13 14 0 17 11 6 9 6 7 14 5 9 5 44 12 2 1 17 0 12 9 8 13 11 5 9 15 17 165 4 6 12 11 12 0 5 6 5 4 7 8 4 5 46 4 11 8 6 9 5 0 3 3 8 8 5 7 10 77 2 10 8 9 8 6 3 0 4 8 4 5 8 10 98 4 12 13 6 13 5 3 4 0 8 7 7 8 8 79 5 12 12 7 11 4 8 8 8 0 6 8 3 6 610 4 7 8 14 5 7 8 4 7 6 0 6 9 10 1011 6 11 8 5 9 8 5 5 7 8 6 0 10 9 812 6 15 16 9 15 4 7 8 8 3 9 10 0 3 213 8 17 18 5 17 5 10 10 8 6 10 9 3 0 214 7 16 17 4 16 4 7 9 7 6 10 8 2 2 0



Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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