Optimizing the Routing of Urban Logistics by ContextBased Social Network and MultiCriteria Decision Analysis
Abstract
:1. Introduction
 To solve the product delivery delay problems in the urban logistics areas, this work proposes a novel approach of using symmetry/asymmetry traffic context data and multicriteria decision analysis to optimize vehicleroute selection as part of urbanlogistical planning.
 The paper uses data mining technologies to process the traffic context data from official urban transportation databases and metadata of Google Maps route planning in order to construct a contextbased social network. Since the traffic features and routing criteria have symmetry/asymmetry properties to influence the decision of path selection, we adopt multicriteria decision analysis to generate a ranking of candidate paths based on an evaluation of traffic data in contextbased social networks to recommend to the deliveryman. The deliveryman can select a reasonable path for delivering products according to the ranking of candidate paths.
 The experimental results show that the work’s precision is 79.65%, recall is 80.70%, and F1score is 80.17% in order to prove the vehicleroute recommendation effectiveness. It helps deliverymen send products as soon as possible to customers to retain the quality, especially in coldchain logistics. The paper optimizes trafficrouting solutions for improved service quality of urban logistics in smart cities.
2. Related Work
2.1. PointsofInterest (POI) Recommendations in LocationBased Social Networks (LBSNs)
2.2. MultiCriteria Decision Analysis (MCDA)
3. Problem Definition
3.1. Routing Problems in Urban Logistics
3.2. A Novel System to Optimize TrafficRoute Selection in Urban Logistics
Data extraction algorithm: collects the symmetry/asymmetry information on the logistics destination, referred to as pointsofinterest (POI), which is required by the deliveryman. Parameter definition is shown as follows.  
OpenDataUrl  The URL of open data website. 
UrbantransportationUrl  The URL of urban transportation website. 
GoogleMapUrl  The URL of Google Maps website. 
POI  Data extraction from cloud servers. 
urlSet  A URL set of the open data websites. 
POISet  A set of the POI. 
POIInformation  Information on POI. 
POIData  A set of POI data. 
JSONKey  The key of JSON. 
JSONKeySet  A set of JSONKey. 
Input: OpenDataUrl, UrbantransportationUrl, GoogleMapUrl Output: POIData

Data preprocessing algorithm: analyzes the POI description and relevant symmetry/asymmetry attributes to remove meaningless information. Parameter definition is shown as follows.  
POIData  A set of POI data. 
DCPOIDataSet  A set of POI data after data cleaning. 
DCPOIData  POI data after data cleaning. 
UrbantransportationData  Urban transportation POI data after data cleaning. 
GoogleMapData  Google Maps POI data after data cleaning. 
DIPOIDataSet  A set of POI data after data integration. 
DIPOIData  Symmetry/asymmetry POI data after data integration. 
Input: POIData Output: DIPOIDataSet

Multicriteria decision analysis algorithm: generates a ranking of candidate paths based on the evaluation of criteria in the context of traffic conditions. Parameter definition is shown as follows.  
CandidatePathSet  A data set of the candidate path with traffic context values regarding issues for a deliveryman. 
RCandidatePathSet  A data set of the candidate path with normalized traffic context values. 
WeightSet  A criteria weight set by the deliveryman configuration. 
RankingOrder  Ranking order from use of a multicriteria decision method. 
MCDACandidatePathSet  A data set of the paths from use of multicriteria decision analysis. 
Input: CandidatePathSet, WeightSet Output: MCDACandidatePathSet

3.3. Utility Model for Candidate Paths
3.4. Discovering a Selection Order via the VIKOR Method
 Step 1: Construct the initial matrix $P$, as shown in Equation (2).$$P={\left[{p}_{ij}\right]}_{m\times n}=\left[\begin{array}{c}\begin{array}{ccc}{U}_{{p}_{1},c{i}_{1}}& \dots & {U}_{{p}_{1},c{i}_{j}}\\ \vdots & \ddots & \vdots \end{array}\\ \begin{array}{ccc}{U}_{{p}_{i},c{i}_{1}}& \dots & {U}_{{p}_{i},c{i}_{j}}\\ \vdots & \ddots & \vdots \end{array}\\ \begin{array}{ccc}{U}_{{p}_{m},c{i}_{1}}& \dots & {U}_{{p}_{m},c{i}_{j}}\end{array}\end{array}\begin{array}{c}\begin{array}{cc}\dots & {U}_{{p}_{1},c{i}_{n}}\\ \ddots & \vdots \end{array}\\ \begin{array}{cc}\dots & {U}_{{p}_{i},c{i}_{n}}\\ \ddots & \vdots \end{array}\\ \begin{array}{cc}\dots & {U}_{{p}_{m},c{i}_{n}}\end{array}\end{array}\right]$$
 Step 2: Calculate the column vector by Equation (3) and normalize the matrix $P$ to obtain a normalized matrix ${P}^{\prime}$.$${P}^{\prime}={\left[{p}_{ij}\right]}_{m\times n},{f}_{ij}=\frac{{p}_{ij}}{\sqrt{{{\displaystyle \sum}}_{i=1}^{m}{p}_{ij}^{2}}}$$
 Step 3: Determine the ideal ${f}_{i}^{*}$ value by Equation (4) and the worst ${f}_{i}^{}$ value by Equation (5). If the $i$th function represents a benefit then:$${f}_{i}^{*}=\left\{\left(ma{x}_{j}{f}_{ij}\parallel i\in {I}_{1}\right),\left(mi{n}_{j}{f}_{ij}\parallel i\in {I}_{2}\right)\right\}$$$${f}_{i}^{}=\left\{\left(mi{n}_{j}{f}_{ij}\parallel i\in {I}_{1}\right),\left(ma{x}_{j}{f}_{ij}\parallel i\in {I}_{2}\right)\right\}$$
 Step 4: Set the weight of the evaluation criteria by Equation (6). The weight matrix $W$ is configured by the user in this work.$$W={\left[\begin{array}{ccc}{w}_{1}& \cdots & 0\\ \vdots & \ddots & \vdots \\ 0& \cdots & {w}_{n}\end{array}\right]}_{n\times n}$$
 Step 5: Calculate the group utility ${S}_{i}$ of candidate path $i$ by Equation (7) and the individual regret ${R}_{i}$ of candidate path $i$ by Equation (8) where ${w}_{j}$ are the weights of criteria, expressing their relative importance.$${S}_{i}={{\displaystyle \sum}}_{j}^{n}{W}_{j}\left({f}_{j}^{*}{f}_{ij}\right)/\left({f}_{j}^{*}{f}_{j}^{}\right)$$$${R}_{i}=Ma{x}_{j}\left[{W}_{j}\left({f}_{j}^{*}{f}_{ij}\right)/\left({f}_{j}^{*}{f}_{j}^{}\right)\right]$$
 Step 6: Compute the values ${Q}_{i}$ by Equation (9) where $v$ is introduced as weight of the strategy of the maximum group utility, here $v$ = 0.5.$${Q}_{i}=v\left({S}_{j}{S}^{*}\right)/\left({S}^{}{S}^{*}\right)+\left(1v\right)\left({R}_{j}{R}^{*}\right)/\left({R}^{}{R}^{*}\right)$$
 Step 7: Rank the candidate paths, sorting by the values $S$, R, and $Q$, in decreasing order. The results are three ranking lists.
 Step 8: Propose as a compromise solution the candidate path (${a}^{\prime}$) which is ranked the best by the measure $Q$ (minimum) if the following two conditions are satisfied:
 Condition 1: Acceptable advantage.
 where ${a}^{\u2033}$ is the candidate path with the second position in the ranking list by $Q$; $DQ=1/\left(J1\right)$; $J$ is the number of candidate paths.
 Condition 2: Acceptable stability in decisionmaking.
 Candidate path ${a}^{\prime}$ must also be the best ranked by $S$ and/or $R$. This compromise solution is stable within a decisionmaking process, which could be: “voting by majority rule” (when $v>0.5$ is needed), or “by consensus” $v\approx 0.5$, or “with veto” ($v<0.5$). Here, $v$ is the weight of the decisionmaking strategy of the maximum group utility.
3.5. Evaluation of System Framework
4. Case Study on TrafficRouting Recommendation for Deliverymen
 Step 1: Construct the initial matrix $P$ where 10 indicates the number of candidate paths and 4 indicates the number of candidate path items.$$P=\left[\begin{array}{cccc}33& 6& 2.08& 5\\ 42& 2& 1.65& 7\\ 30& 8& 1.79& 4\\ 44& 2& 2.62& 6\\ 25& 4& 1.74& 8\\ 46& 3& 4.02& 2\\ 38& 4& 1.24& 4\\ 43& 6& 3.58& 6\\ 46& 9& 1.93& 7\\ 52& 1& 3.9& 8\end{array}\right]$$
 Step 2: Calculate the column vector by Equation (3) and normalize the matrix $P$ to obtain a normalized matrix ${P}^{\prime}$.$${P}^{\prime}=\left[\begin{array}{cccc}0.25627& 0.38490& 0.24933& 0.26389\\ 0.32654& 0.12830& 0.19779& 0.36945\\ 0.23325& 0.51320& 0.21457& 0.21111\\ 0.34209& 0.12830& 0.31406& 0.31667\\ 0.19437& 0.51320& 0.20858& 0.42222\\ 0.35764& 0.19245& 0.48188& 0.10556\\ 0.29544& 0.25660& 0.14864& 0.21111\\ 0.33432& 0.38490& 0.42914& 0.31667\\ 0.35764& 0.19245& 0.23135& 0.36945\\ 0.40429& 0.06415& 0.46750& 0.42222\end{array}\right]$$
 Step 3: Determine the ideal ${f}_{i}^{*}$ value by Equation (4) and the worst ${f}_{i}^{}$ value by Equation (5). If the $i$th function represents a benefit, then:$$\begin{array}{c}{f}_{i}^{*}=\left\{\left(0.40429,0.06415,0.14864,0.42222\right)\right\}\\ {f}_{i}^{}=\left\{\left(0.19437,0.51320,0.48188,0.10556\right)\right\}\end{array}$$
 Step 4: Set the weight of the evaluation criteria by Equation (6). The weight matrix $W$ is configured by the user in this work.$$W=\left[\begin{array}{cccc}0.3& 0& 0& 0\\ 0& 0.2& 0& 0\\ 0& 0& 0.1& 0\\ 0& 0& 0& 0.4\end{array}\right]$$
 Step 5: Calculate the group utility ${S}_{i}$ of candidate path $i$ by Equation (7) and the individual regret ${R}_{i}$ of candidate path $i$ by Equation (8) where ${w}_{j}$ are the weights of criteria, expressing their relative importance.$$\begin{array}{c}{S}_{1}=0.58418{S}_{2}=0.22109{S}_{3}=0.73089{S}_{4}=0.30043{S}_{5}=0.51799\\ {S}_{6}=0.62381{S}_{7}=0.50794{S}_{8}=0.46036{S}_{9}=0.21529{S}_{10}=0.09568\\ {R}_{1}=0.21111{R}_{2}=0.11111{R}_{3}=0.26667{R}_{4}=0.13333{R}_{5}=0.30000\\ {R}_{6}=0.40000{R}_{7}=0.26667{R}_{8}=0.14286{R}_{9}=0.06667{R}_{10}=0.09568\end{array}$$
 Step 6: Compute the values ${Q}_{i}$ by Equation (9) where $v$ is introduced as the weight of the strategy of the maximum group utility, here $v$ = 0.5.$$\begin{array}{l}{S}^{*}=Mi{n}_{j}{S}_{j}=0.09568,{S}^{}=Ma{x}_{j}{S}_{j}=0.58418,\\ {R}^{*}=Mi{n}_{j}{R}_{j}=0.09568,{R}^{}=Ma{x}_{j}{R}_{j}=0.21111,v=0.5\\ {Q}_{1}=0.60118{Q}_{2}=0.16538{Q}_{3}=0.80000{Q}_{4}=0.26116{Q}_{5}=0.68242\\ {Q}_{6}=0.91571{Q}_{7}=0.62451{Q}_{8}=0.40134{Q}_{9}=0.09415{Q}_{10}=0.04352\end{array}$$
 Step 7: Rank the candidate paths, sorting by the values S, R, and Q, in decreasing order. The results are three ranking lists.
 Step 8: Propose as a compromise solution the candidate path (${a}^{\prime}$), which is ranked the best by the measure $Q$ (minimum) if the following two conditions are satisfied: in the case study, the topk ranking order “P10→P09→P02→P04→P08→P01→P07→P05→P03→P06” is produced. The traffic path P10 is a reasonable path for the deliveryman because its ranking order is the first.
5. Experimental Results
5.1. Path Rankings from Different MCDA Methods
5.2. Evaluations and Discussions
6. Conclusions
 To solve the product delivery delay problems in the urban logistics areas, this work proposes a novel systematic framework of using symmetry/asymmetry traffic context data and multicriteria decision analysis to optimize vehicleroute selection as part of urbanlogistical planning.
 The paper uses data mining technologies to process the huge amount of traffic context data from official urban transportation databases and metadata of Google Maps route planning in order to construct a contextbased social network. Since the traffic features and routing criteria have symmetry/asymmetry properties to influence the decision of path selection, we adopt multicriteria decision analysis to generate a ranking of candidate paths based on an evaluation of traffic data in contextbased social networks to recommend to the deliveryman. The deliveryman can select a reasonable path for delivering products according to the ranking of candidate paths.
 The experimental results show the path recommendation of the work’s precision is 79.65%, recall is 80.70%, and F1score is 80.17% to prove the vehicleroute recommendation effectiveness. It helps deliverymen send products as soon as possible to customers to retain the quality, especially in coldchain logistics. The paper optimizes trafficrouting solutions for improved service quality of urban logistics in smart cities.
 Expiry of collected data may cause the recommendation to have unexpected results. The open data in official urban transportation databases may update regularly but not immediately.
 If the traffic features are not contained in official urban transportation databases and metadata of Google Maps route planning, we cannot design the comprehensive criteria to evaluate, e.g., weather influence, traffic incidents, temporary road construction, etc. This work cannot handle complex realtime traffic features.
 This work does not consider the adaptive mechanism to adjust the weight configuration of criteria in multicriteria decision analysis. The weight configuration of criteria may influence the path recommendation.
 As for now, the proposed approach is functional modularity but it lacks the space and time complexity analysis of each algorithm to identify its pros and cons.
 Using more comprehensive criteria with symmetry/asymmetry concepts, such as traffic status, logistics vehicle, deliverymen habits, and customer requirement features, in an effort to analyze usage scenarios more realistically.
 The human emotional analysis and deep learning models can be explored to strengthen the effectiveness of the proposed approach.
 Using the unified theory of acceptance and use of technology (UTAUT) to verify the user acceptance of this paper’s novel approach.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
 Schafer, J.B.; Konstan, J.A.; Riedl, J. Ecommerce recommendation applications. Data Min. Knowl. Discov. 2001, 5, 115–153. [Google Scholar] [CrossRef]
 Mulvenna, M.D.; Anand, S.S.; Büchner, A.G. Personalization on the Net using Web mining: Introduction. Commun. ACM 2000, 43, 122–125. [Google Scholar] [CrossRef]
 Abbas, A.; Zhang, L.; Khan, S.U. A survey on contextaware recommender systems based on computational intelligence techniques. Computing 2015, 97, 667–690. [Google Scholar] [CrossRef]
 Wei, L.Y.; Zheng, Y.; Peng, W.C. Constructing popular routes from uncertain trajectories. In Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Beijing, China, 12–16 August 2012; pp. 195–203. [Google Scholar]
 Zhang, Z.; Che, O.; Cheang, B.; Lim, A.; Qin, H. A memetic algorithm for the multiperiod vehicle routing problem with profit. Eur. J. Oper. Res. 2013, 229, 573–584. [Google Scholar] [CrossRef]
 Liu, B.; Xiong, H. PointofInterest recommendation in location based social networks with topic and location awareness. In Proceedings of the 2013 Siam International Conference on Data Mining (SDM), Austin, TX, USA, 2–4 May 2013; pp. 396–404. [Google Scholar]
 Borris, J.; Moreno, A.; Valls, A. Intelligent tourism recommender systems: A survey. Expert Syst. Appl. 2014, 41, 7370–7389. [Google Scholar] [CrossRef]
 Bao, J.; Zheng, Y.; Wilkie, D.; Mokbel, M. Recommendations in locationbased social networks: A survey. GeoInformatica 2015, 19, 525–565. [Google Scholar] [CrossRef]
 Liu, B.; Xiong, H.; Papadimitriou, S.; Fu, Y.J.; Yao, Z.J. A general geographical probabilistic factor model for point of interest recommendation. IEEE Trans. Knowl. Data Eng. 2014, 27, 1167–1179. [Google Scholar] [CrossRef]
 Sheng, l.Z.; Irwin, K.; Michael, R.L. A survey of Pointofinterest Recommendation in Locationbased social network. arXiv 2016, arXiv:1607.00647v1[cs.IR]. [Google Scholar]
 Ishizaka, A.; Nemery, P. MultiCriteria Decision Analysis: Methods and Software; Wiley: New York, NY, USA, 2013. [Google Scholar]
 Aruldoss, M.; Lakshmi, T.M.; Venkatesan, V.P. A survey on multi criteria decision making methods and its applications. Am. J. Inf. Syst. 2013, 1, 31–43. [Google Scholar]
 Sojahrood, Z.B.; Taleai, M. A POI group recommendation method in locationbased social networks based on user influence. Expert Syst. Appl. 2021, 171, 114593. [Google Scholar] [CrossRef]
 Pablo, S.; Alejandro, B. Pointofinterest recommender systems based on locationbased social networks: A survey from an experimental perspective. ACM Comput. Surv. 2022, 1–35. [Google Scholar]
 Wang, Z.S.; Juang, J.F.; Teng, W.G. Predicting poi visits with a heterogeneous information network. In Proceedings of the 2015 Conference on Technologies and Applications of Artificial Intelligence (TAAI), IEEE, Tainan, Taiwan, 20–22 November 2015; pp. 388–395. [Google Scholar]
 Yu, Z.; Xu, H.; Yang, Z.; Guo, B. Personalized travel package with multipointofinterest recommendation based on crowdsourced user footprints. IEEE Trans. Hum.Mach. Syst. 2016, 46, 151–158. [Google Scholar] [CrossRef]
 Abeer, A.N.; Norah, A.; Hend, A. Recommendation system algorithms on locationbased social networks: Comparative study. Information 2022, 13, 188. [Google Scholar]
 Ke, C.K.; Lai, S.C.; Huang, L.T. Developing a Contextaware POI Network of Adaptive Vehicular Traffic Routing for Urban Logistics. In Proceedings of the 11th EAI International Wireless Internet Conference (WiCON 2018), Taipei, Taiwan, 15–16 October 2018. [Google Scholar]
 Ke, C.K.; Wu, M.Y.; Ho, W.C.; Lai, S.C.; Huang, L.T. Intelligent PointofInterest Recommendation for Tourism Planning via Densitybased Clustering and Genetic Algorithm. In Proceedings of the 22nd Pacific Asia Conference on Information Systems (PACIS 2018), Yokohama, Japan, 26–30 June 2018. [Google Scholar]
 Nassereddine, M.; Eskandari, H. An integrated MCDM approach to evaluate public transportation systems in Tehran. Transp. Res. Part A Policy Pract. 2017, 106, 427–439. [Google Scholar] [CrossRef] [Green Version]
 Safavi, S.; Jalali, M.; Houshmand, M. Toward pointofinterest recommendation systems: A critical review on deeplearning Approaches. Electronics 2022, 11, 1998. [Google Scholar] [CrossRef]
 Griesner, J.B.; Abdessalem, T.; Naacke, H. POI Recommendation: Towards Fused Matrix Factorization with Geographical and Temporal Influences. In Proceedings of the 9th ACM Conference on Recommender Systems, Vienna, Austria, 16–20 September 2015; pp. 301–304. [Google Scholar]
 Cheng, C.; Yang, H.Q.; Lyu, M.R.; King, I. Where You Like to Go Next: Successive PointofInterest Recommendation. In Proceedings of the TwentyFourth International Joint Conference on Artificial Intelligence, Buenos Aires, Argentina, 25–31 July 2015; pp. 2605–2611. [Google Scholar]
 Feng, S.S.; Li, X.T.; Zeng, Y.F.; Cong, G.; Chee, Y.M.; Yuan, Q. Personalized Ranking Metric Embedding for Next New POI Recommendation. In Proceedings of the TwentyFourth International Joint Conference on Artificial Intelligence, Buenos Aires, Argentina, 25–31 July 2015; pp. 2069–2075. [Google Scholar]
 Han, J.K.; Yamana, H. Geographical Diversification in POI Recommendation: Toward Improved Coverage on Interested Areas. In Proceedings of the ACM Conference Series on Recommender Systems, Como, Italy, 27–31 August 2017; pp. 27–31. [Google Scholar]
 Liu, X.; Liu, Y.; Aberer, K. Personalized PointofInterest Recommendation by Mining Users’ Preference Transition. In Proceedings of the 22nd ACM International Conference on Information & Knowledge Management, San Francisco, CA, USA, 27 October–1 November 2013; pp. 733–738. [Google Scholar]
 Hu, B.; Ye, Y.; Zhong, Y.; Pan, J.; Hu, M. TransMKR: Translationbased knowledge graph enhanced multitask pointofinterest recommendation. Neurocomputing 2022, 474, 107–114. [Google Scholar] [CrossRef]
 Hossein, A.R.; Yashar, D.; Tommaso, D.N. The role of context fusion on accuracy, beyondaccuracy, and fairness of pointofinterest recommendation systems. Expert Syst. Appl. 2022, 205, 117700. [Google Scholar]
 Liu, X.; Yang, Y.; Xu, Y.; Yang, F.; Huang, Q.; Wang, H. Realtime POI recommendation via modeling long and shortterm user preferences. Neurocomputing 2022, 467, 454–464. [Google Scholar] [CrossRef]
 Xu, Z.; Xia, M. Identifying and eliminating dominated alternatives in multiattribute decision making with intuitionistic fuzzy information. Appl. Soft Comput. 2012, 12, 1451–1456. [Google Scholar] [CrossRef]
 Liou, J.J.; Chuang, Y.T. Developing a hybrid multicriteria model for selection of outsourcing providers. Expert Syst. Appl. 2010, 37, 3755–3761. [Google Scholar] [CrossRef]
 Tadić, S.; Zečević, S.; Krstić, M. A novel hybrid MCDM model based on fuzzy DEMATEL, fuzzy ANP and fuzzy VIKOR for city logistics concept selection. Expert Syst. Appl. 2014, 41, 8112–8128. [Google Scholar] [CrossRef]
 Liu, C.H.; Tzeng, G.H.; Lee, M.H.; Lee, P.Y. Improving metro–airport connection service for tourism development: Using hybrid MCDM models. Tour. Manag. Perspect. 2013, 6, 95–107. [Google Scholar] [CrossRef]
 Ke, C.K.; Chen, Y.L. A message negotiation approach to eservices by utility function and multicriteria decision analysis. Comput. Math. Appl. 2012, 64, 1056–1064. [Google Scholar] [CrossRef]
 Chen, Y.L.; Ke, C.K. Optimal mobile device selection for roundrobin data exchange via adaptive multicriteria decision analysis. Comput. Electr. Eng. 2016, 54, 119–130. [Google Scholar]
 Silaghi, G.C.; Arenas, A.E.; Silva, L.M. A UtilityBased Reputation Model for ServiceOriented Computing, towards Next Generation Grids; Springer: New York, NY, USA, 2007; pp. 63–72. [Google Scholar]
 Chen, M.C. A Comparative Study of MultiCriteria DecisionMaking Analysis Methods in the Application Recommendation Mechanism of Application Markets. Master’s Thesis, National Taichung University of Science and Technology, Taichung, Taiwan, 2016. [Google Scholar]
 García, J.M.; Junghans, M.; Ruiz, D.; Agarwal, S.; RuizCortés, A. Integrating semantic Web services ranking mechanisms using a common preference model. Knowl.Based Syst. 2013, 49, 22–36. [Google Scholar] [CrossRef]
 Lin, S.Y.; Lai, C.H.; Wu, C.H.; Lo, C.C. A trustworthy QoSbased collaborative filtering approach for web service discovery. J. Syst. Softw. 2014, 93, 217–228. [Google Scholar] [CrossRef]
Path No  Average Speed (Kilometer/Hour)  Congestion Degree (1 to 10)  Distance (Kilometer)  Personal Interest (1 to 10) 

P01  33  6  2.08  5 
P02  42  2  1.65  7 
P03  30  8  1.79  4 
P04  44  2  2.62  6 
P05  25  8  1.74  8 
P06  46  3  4.02  2 
P07  38  4  1.24  4 
P08  43  6  3.58  6 
P09  46  3  1.93  7 
P10  52  1  3.90  8 
MCDA Method  Candidate Path Ranking Order 

TOPSIS  P10→P02→P09→P04→P05→P08→P07→P01→P06→P03 
VIKOR  P10→P09→P02→P04→P08→P01→P07→P05→P03→P06 
ELECTRE  P02→P10→P09→P04→{P05, P08}→P07→P01→P06→P03 
PROMETHEE  P10→P02→P09→P04→P07→P05→P08→P06→P01→P03 
SAW  P10→P02→P09→P04→P07→P08→P05→P01→P06→P03 
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Wu, M.Y.; Ke, C.K.; Lai, S.C. Optimizing the Routing of Urban Logistics by ContextBased Social Network and MultiCriteria Decision Analysis. Symmetry 2022, 14, 1811. https://doi.org/10.3390/sym14091811
Wu MY, Ke CK, Lai SC. Optimizing the Routing of Urban Logistics by ContextBased Social Network and MultiCriteria Decision Analysis. Symmetry. 2022; 14(9):1811. https://doi.org/10.3390/sym14091811
Chicago/Turabian StyleWu, MeiYu, ChihKun Ke, and SzuCheng Lai. 2022. "Optimizing the Routing of Urban Logistics by ContextBased Social Network and MultiCriteria Decision Analysis" Symmetry 14, no. 9: 1811. https://doi.org/10.3390/sym14091811