A fuzzy optimisation model for decision making in a reverse logistics network design Presented By: Jyoti Darbari Lady Shri Ram College University of Delhi, New Delhi, India Supply Chain A Supply Chain consists of a series of activities involving many organizations through which the materials move from initial suppliers to final customers Reverse Supply Chain Reverse Logistics A reverse supply chain is a means of enhancing Process of planning, implementing, and controlling the efficient, cost effective flow of raw sustainability by retrieving products from customers. materials, in-process inventory, finished goods and related information from the point of consumption to the point of origin for the purpose of recapturing value or proper disposal. - Rogers and Tibben-Lembke Rl Processes and Recovery Options Direct Use C U S T O M E R S Collection Inspection Product Reprocessing Component Retrieval and Reprocessing Material Recovery Disposal Current Study

Location of Collection centers and potential RFCs in NCR Bawana(RFC5) Mayapuri Industrial Area(RFC1) Dwarka(RFC5) Badarpur(RFC2) EcoTech1(RFC3) Current Study In this study, evaluation of alternative locations for a recovery facility centre is done based on a number of economical and socio-environmental criteria to obtain the most suitable one. In the second stage, for the design of a economically and environmentally effective transportation network for flow of returns from CCs to the selected RFC, the set of CCs are grouped into zones. Finally, we formulate a Fuzzy Mixed Integer Linear Programming mathematical model or the planning of sustainable reverse logistics network with aim of minimizing the environmental impact (in terms of carbon emission) of the RL model. Proposed Methodology Fuzzy Cluster Analysis approach for allocation of CCs to zones Formulate a mathematical model to determine optimal routes for recovery flow network The Analytical Network Process(ANP) The analytic network process (ANP) is a more general form of the analytic

hierarchy process (AHP) used in multi-criteria decision analysis. ANP structures a decision problem into a network with a goal, decision criteria, and alternatives which makes it possible for one to deal systematically with all kinds of dependence and feedback. The power of the Analytic Network Process (ANP) lies in its use of ratio scales to capture all kinds of interactions and make accurate predictions, and, even further, to make better decisions. Flow chart of Fuzzy ANP Factors for selection of Recovery Facility Center(RFC) Triangular Judgement Matrix ~ ~ TFNs 1 9 are used to represent the subjective pair wise comparisons equal importance=1, moderate importance=3,strong importance=5, very strong importance=7 extremely strong importance=9. A triangular fuzzy number can be characterized as: M 0 , 1 m l , m u ( m l ) l , ( u m ) u with the interval of confidence level . For example: 7 5 2 , 9 2 1 and 7 1 , 1 If 0.5 we get 7 6, 8 9 2 5 2 1

and 7 1 1 8 , 6 And we get the following fuzzy judgement matrix: Transportation-TC Eco-Tech-1 Badarpur Mayapuri Dwarka Bawana Eco-Tech-1 1 [1,3] [3,5] [1,2] [2,4] Badarpur [1/3,1] 1 [1,3] [1,2] [2,4] Mayapuri [1/5,1/3] [1/3,1] 1

[1/5,1/3] [1/3,1] Dwarka [1/2,1] [1/2,1] [3,5] 1 [1,3] Bawana [1/4,1/2] [1/4,1/2] [1,3] [1/3,1] 1 Defuzzification of judgement matrix and deriving local priority vector Degree of satisfaction for the judgement matrix is estimated by the index of optimism defined as (Lee 1999): a a (1 )a 0,1 ij iju the local priority vector is calculated using the following equation Aw max w

ijl max where is the largest eigenvalue of A For consistency of the matrix, max n ratio CR is to be less than 0.1 where CI the consistency CR= RI , CI n 1 Transportation TC Eco-Tech-1 Badarpur Mayapuri Dwarka Bawana Eigenvector(w) The judgement matrix and the priority vector are hence obtained: Eco-Tech-1 1 2 4 1 3 0.32 Badarpur 0.5 1 2 0.5

3 0.18 Mayapuri 0.25 0.5 1 0.25 0.5 0.07 Dwarka 1 2 4 1 2 0.30 Bawana 0.333333 0.333333 2 0.5 1 0.11 Super-matrix for locations before convergence CL LCA

IC TC FLT RA SM SCD ILE PI SUE SD RFC1 RFC2 RFC3 RFC4 RFC5 CL LC A IC TC FLT RA SM SCD ILE PI SUE SD 0.00 0.00 0.00 0.00 0.00 0.16 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.67 0.28 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.33 0.08 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.09 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.39 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.50 0.40 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.33 0.00 0.50 0.60 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 1.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 RFC1 RFC2 RFC3 RFC4 RFC5 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Super-matrix for locations after convergence (A64) CL CL LCA IC TC FLT RA SM SCD ILE PI SUE SD RFC1 RFC2 RFC3 RFC4 RFC5 LCA IC

TC FLT RA SM SCD ILE PI SUE SD RFC1 RFC2 RFC3 RFC4 RFC5 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.06 0.06

0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.06

0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03

0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03

0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.03 0.03 0.03 0.03 0.03 0.03 0.03

0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07

0.07 0.07 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.10 0.10 0.10 0.10 0.10 0.10

0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 Ideal value for locations based on economic factors Potential location Normalised weights Eco-Tech-1(RFC1) 0.699615

Badarpur (RFC2) 0.600138 Mayapuri Industrial Area 1 (RFC3) Dwarka (RFC4) 0.609388 Bawana (RFC5) 0.632196 Rank Location of Collection centres and selected RFC in NCR Maya Puri (RFC3) Objectives of Cluster Analysis Finding groups of objects such that the objects in a group will be similar (or related) to one another and different from (or unrelated to) the objects in other groups Thus, Clustering of data is a method by which large sets of data is grouped into clusters of smaller sets of similar data Competing objectives Intra-cluster distances are minimized Inter-cluster distances are maximized Wards method

Similarity of two clusters is based on the increase in squared error when two clusters are merged At each step, Ward's method calculates the within-cluster sum of squares (WCSS) for every cluster. WCSS is the squared Euclidean distance between an object x j in the cluster and the mean of that clusterx , summed over all(m) objects in that cluster and is given by the following Equation: m WCSS ( x j x ) 2 j 1 Dendogram Dendogram is a tree like diagram that records the sequence of merges or splits Dendogram shows how the clusters are merged heirarchically by decomposing data objects into a several levels of nested partitioning . A clustering of the data objects is obtained by cutting the dendrogram at the desired level, then each connected component forms a cluster. Construction of Collection Zones using Wards Method Location of Collection centers and RFC in NCR Rohini Model Town Punjabi B Janak Puri Rajouri G Karol Bagh Maya Puri CP Mayur Vihar Dwarka Mathura road

South Ex East of Kailash Vasant Kunj Sushant Lok Vaishali Vehicle Routing Problem 8 Nodes: physical locations Recovery Facility Centre Collection Centres. 7 6 RFC Arcs or Links Transportation links 5 9 4 3 10 1 2 Number on each arc represents cost, distance,or travel time. Routes:{1,2,3,4,5} and {a,b,c,d} VRP-Optimal Solution Route is as short as possible. No subtouring is allowed

Every customer (node) is visited once, including the depot. Each node has one arc in and one arc out. 1 1 3 2 4 5 depot 6 Vehicle Routing Problem-Current Study Vehicle Routing Problem (VRP) integrates the decisions of determining: An optimal selection of vehicles for collection of returns from collection centres An optimal assignment of routes to vehicles Best route chosen to minimum distance Optimization model Sets L V set of collection centers (CC) index by l, l=1, 2.., L set of vehicles index by v Parameters R l number of products returned at lth CC Lsetr of collection centres in the *

L th r r cluster zone rth cluster zone Lr* Lr 0 , where 0 represents the Recovery Facility centre (RFC) Ev per unit emission of CO2e per unit km by the vth truck Ov capacity (in terms of number of units of products) of vth truck dprqr distance between the pth and qth CCs of the rth cluster zone dmax maximum allowable distance per each route Decision Variables Y pv if the p th node of r th cluster zone is visited by v th truc k 1 = 0 1 Wv = 0 otherw ise

if the v th vehicle is selected for transportation 1 A pqrv = 0 e pr otherw ise if the v th vehicle travels arc(p, q) of the r th clus ter zone otherw ise real numbers used to avoid subtouring in the routes within each cluster Objective functions: Function Objective M in im ise vV r R p r L* r q r L* r E d A W v p r q r p r q r v v The objective minimises the environmental impact of the transportation network of the Reverse Flow. Constraints The total number of units collected by vth vehicle within each cluster zone must be less than its capacity and distance of travel must not exceed the maximum allowable limit RY l lv Ov

v, r l Lr d p q Ap q vWv d r r prL*r qrL*r r r max Each CC must be visited by exactly one truck A prLr* v pr qr A prLr* pr qr Y Wv 1 qr Lr pr qrv qrv prqrv Yqrv Y v pr v qr Lr , v V 1 pr Lr v, r Constraints

From each CC, exactly one vehicle exits A qrLr* t qr pr A pr qrv qrLr* pr qr Yprv pr Lr , v V The vehicle that visits a CC must also exit from the CC A prqrv prLr* Y Wv 1 pr Lr pr qrv qrv Aqr prv prLr* qr Lr , v V The total number of vehicles selected for collection does not exceed the availability W v v

V Constraints A selected vehicle must start from and end at the RFC A qrLr Y Wv 0qrv qrv A pr Lr pr 0 v Y prv Wv v V Only the selected vehicle must visit the RFC Y0 v v v V W v v 0 No subtouring is allowed by any vehicle epr eqr (Lr 1) Aprqvr Yqrv Lr The non-negativity restrictions vV, pr , qr Lr Wv , epr , eqr 0

Result and Discussion Routes within cluster 1 Rohini Model Town Punjabi B Janak Puri Maya Puri Rajouri G Dwarka Karol Bagh Routes within cluster 2 Maya Puri CP South Ex Mathura road East of Kailash Vasant Kunj Sushant Lok Routes within cluster 3 Maya Puri Mayur Vihar Vaishali Routes within clusters Conclusion

The main contribution of the paper lies in the development of a decision support tool for DMs for planning a sustainable RL model for an Electronics manufacturing company which includes locating a new RFC and determining the collection routes with optimal selection of vehicles. The recovery model proposed in the study allows for the selection of the best location for a recovery facility centre taking into account sustainable criteria and an optimization model for designing an efficient routing network. The opinions of the DMs are subjective and thus there is a possibility of ambiguity in the final decisions. In order to tackle this, fuzzy ANP is implemented. For future work, fuzzy ANP can be combined with other multi criteria approaches in order to reduce the possibility of biasness in the subjective inputs. References Anderberg, M. R. (1973). Cluster analysis for applications (No. OAS-TR-73-9). OFFICE OF THE ASSISTANT FOR STUDY SUPPORT KIRTLAND AFB N MEX. Barreto, S., Ferreira, C., Paixao, J., & Santos, B. S. (2007). Using clustering analysis in a capacitated locationrouting problem. European Journal of Operational Research, 179(3), 968-977. Chang, N. B., Parvathinathan, G., & Breeden, J. B. (2008). Combining GIS with fuzzy multicriteria decisionmaking for landfill siting in a fast-growing urban region. Journal of environmental management, 87(1), 139153. Choudhary, D., & Shankar, R. (2012). An STEEP-fuzzy AHP-TOPSIS framework for evaluation and selection of thermal power plant location: A case study from India. Energy, 42(1), 510-521. Guneri, A. F., Cengiz, M., & Seker, S. (2009). A fuzzy ANP approach to shipyard location selection. Expert Systems with Applications, 36(4), 7992-7999. Jain, A. K., & Dubes, R. C. (1988). Algorithms for clustering data. Prentice-Hall, Inc.. Kannan, G., Haq, A. N., & Sasikumar, P. (2008). An application of the analytical hierarchy process and fuzzy analytical hierarchy process in the selection of collecting centre location for the reverse logistics multicriteria

decision-making supply chain model. International Journal of Management and Decision Making, 9(4), 350365. Liang, Tien-Fu. "Fuzzy multi-objective production/distribution planning decisions with multi-product and multi-time period in a supply chain." Computers & Industrial Engineering 55, no. 3 (2008): 676-694. Min, H. (1989). The multiple vehicle routing problem with simultaneous delivery and pick-up points. Transportation Research Part A: General, 23(5), 377-386. References nt, S., & Soner, S. (2008). Transshipment site selection using the AHP and TOPSIS approaches under fuzzy environment. Waste Management, 28(9), 1552-1559. zdaolu, A. (2012). A multi-criteria decision-making methodology on the selection of facility location: fuzzy ANP. The International Journal of Advanced Manufacturing Technology, 59(5-8), 787-803. Saaty, T. L. (2000). Fundamentals of decision making and priority theory with the analytic hierarchy process (Vol. 6). Rws Publications. Tuzkaya, G., & Glsn, B. (2008). Evaluating centralized return centers in a reverse logistics network: An integrated fuzzy multi-criteria decision approach.International Journal of Environmental Science & Technology, 5, 339-352. Wadhwa, S., Madaan, J., & Chan, F. T. S. (2009). Flexible decision modeling of reverse logistics system: A value adding MCDM approach for alternative selection. Robotics and Computer-Integrated Manufacturing, 25(2), 460-469. Ward Jr, J. H. (1963). Hierarchical grouping to optimize an objective function.Journal of the American statistical association, 58(301), 236-244. Wu, C. R., Lin, C. T., & Chen, H. C. (2009). Integrated environmental assessment of the location selection with fuzzy analytical network process.Quality and Quantity, 43(3), 351-380. Yang, C. L., Chuang, S. P., Huang, R. H., & Tai, C. C. (2008, December). Location selection based on AHP/ANP approach. In Industrial Engineering and Engineering Management, 2008. IEEM 2008. IEEE International Conference on(pp. 1148-1153). IEEE. Zimmermann, H-J. "Fuzzy programming and linear programming with several objective functions." Fuzzy sets and systems 1, no. 1 (1978): 45-55. THANK YOU