# American Institute of Mathematical Sciences

## The study upon 4PL integration based on AHP and fuzzy mathematics

 1 Navigation College, Guangdong Ocean University, Zhanjiang 524088, China 2 Logistics College, Beijing Normal University, Zhuhai, Zhuhai 519087, China

*Corresponding author: Guohua Yang

Received  April 2019 Revised  May 2019 Published  February 2020

We focused on the fourth party logistics integration problem, establishing a multi-objective optimization model, while selecting the third-party logistics partner which includes four aspects: the cost of selecting the candidate, the time to complete the task, the matching degree of the candidate companies and other companies, and the ability of the candidate companies. By using the method of fuzzy mathematics and AHP to concretely express the matching degree between candidate companies and the ability evaluation of them, put the concrete data into the model, and calculate the optimal partner. Finally, a numerical example is given to verify the feasibility of the model established in this paper.

Citation: Kaixian Gao, Xinliang Liu, Guohua Yang, Xiaobo Sun. The study upon 4PL integration based on AHP and fuzzy mathematics. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020268
##### References:
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##### References:
 [1] J. F. Chen and Y. Yang, A fuzzy anp-based approach to evaluate region agricultural drought risk, Procedia Engineering, 23 (2011), 822-827.  doi: 10.1016/j.proeng.2011.11.2588.  Google Scholar [2] S.-Y. Chou, L. Q. Dat and V. F. Yu, A revised method for ranking fuzzy numbers using maximizing set and minimizing set, Computers and Industrial Engineering, 61 (2011), 1342-1348.  doi: 10.1016/j.cie.2011.08.009.  Google Scholar [3] Y.-C. Chou, C.-C. Sun and H.-Y. Yen, Evaluating the criteria for human resource for science and technology (HRST) based on an integrated fuzzy ahp and fuzzy dematel approach, Applied Soft Computing, 12 (2012), 64-71.  doi: 10.1016/j.asoc.2011.08.058.  Google Scholar [4] R. Cuerno, A. F. Rañada and J. J. Ruiz-Lorenzo, Deterministic chaos in the elastic pendulum: A simple laboratory for nonlinear dynamics, American Journal of Physics, 60 (1992), 73-79.  doi: 10.1119/1.17047.  Google Scholar [5] R. Desai and B. P. Patil, Adaptive routing based on predictive reinforcement learning, International Journal of Computers and Applications, 40 (2018), 73-81.  doi: 10.1080/1206212X.2017.1395106.  Google Scholar [6] D. Dubois, The role of fuzzy sets in decision sciences: Old techniques and new directions, Fuzzy Sets and Systems, 184 (2011), 3-28.  doi: 10.1016/j.fss.2011.06.003.  Google Scholar [7] J. H. Dyer and H. Singh, The relational view: Cooperative strategy and sources of interorganizational competitive advantage, Academy of Management Review, 23 (1998), 660-679.   Google Scholar [8] A. E. Ellinger, H. Chen and T. Yu, Third-party logistics provider customer orientation and customer firm logistics improvement in china, International Journal of Physical Distribution and Logistics Management, 40 (2010), 356-376.   Google Scholar [9] W. Gao and W. F. Wang, The fifth geometric-arithmetic index of bridge graph and carbon nanocones, Journal of Difference Equations and Applications, 23 (2017), 100-109.  doi: 10.1080/10236198.2016.1197214.  Google Scholar [10] W. Gao, L. L. Zhu and K. Y. Wang, Ontology sparse vector learning algorithm for ontology similarity measuring and ontology mapping via ADAL technology, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 25 (2015), 1540034, 12 pp. doi: 10.1142/S0218127415400349.  Google Scholar [11] M. I. Garcia-Planas and T. Klymchuk, Perturbation analysis of a matrix differential equation $\dot{x} = ABx$, Applied Mathematics and Nonlinear Sciences, 3 (2018), 97-103.  doi: 10.21042/AMNS.2018.1.00007.  Google Scholar [12] S. Y. Liu, J. H. Zhang, W. X. Liu and Y. Qian, A comprehensive decision-making method for wind power integration projects based on improved fuzzy AHP, Energy Procedia, 14 (2012), 937-942.  doi: 10.1016/j.egypro.2011.12.1036.  Google Scholar [13] H. C. Rajput, A. S. Milani and A. Labun, Including time dependency and anova in decision-making using the revised fuzzy ahp: A case study on wafer fabrication process selection, Applied Soft Computing, 11 (2011), 5099-5109.  doi: 10.1016/j.asoc.2011.05.049.  Google Scholar [14] T. L. Saaty and J. S. Shang, An innovative orders-of-magnitude approach to ahp-based mutli-criteria decision making: Prioritizing divergent intangible humane acts, European Journal of Operational Research, 214 (2011), 703-715.  doi: 10.1016/j.ejor.2011.05.019.  Google Scholar [15] A. Saeidifar, Application of weighting functions to the ranking of fuzzy numbers, Computers and Mathematics with Applications, 62 (2011), 2246-2258.  doi: 10.1016/j.camwa.2011.07.012.  Google Scholar [16] M. Sevkli, A. Oztekin, O. Uysal, G. Torlak, A. Turkyilmaz and D. Delen, Development of a fuzzy anp based swot analysis for the airline industry in turkey, Expert Systems with Applications, 39 (2012), 14-24.  doi: 10.1016/j.eswa.2011.06.047.  Google Scholar [17] A. Shvets and A. Makaseyev, Deterministic chaos in pendulum systems with delay, Applied Mathematics and Nonlinear Sciences, 4 (2019), 1-8.  doi: 10.2478/AMNS.2019.1.00001.  Google Scholar [18] H. Taşkin and C. Kubat, Evaluation of the hospital service in turkey using fuzzy decision making approach, Journal of Intelligent Manufacturing, 92 (2015), 1-12.   Google Scholar [19] S. Vakilinia, Energy efficient temporal load aware resource allocation in cloud computing datacenters, Journal of Cloud Computing, 7 (2018). doi: 10.1186/s13677-017-0103-2.  Google Scholar
The operation procedure of 4PL
The operation improvement model of 4PL
The program integration model of 4PL
4PL Industrial innovation model
Company capacity structure diagram
The comparison between the third-party service and the forth party service
 Project Third-party logistics Fourth-party logistics Purpose of service Reduce the cost of external logistics operation of a single enterprise. Reduce the operating costs of the whole supply chain, improve the ability of logistics service Content of service It is mainly the purchasing logistics of a single enterprise, or the whole or a part of the sales logistics. Strategic analysis of enterprise Business process reorganization Logistics strategic planning The integrated logistics scheme of upstream and downstream enterprises Grade of service It is mainly for the purchase logistics of a single enterprise, or the whole or part of the sales Provide logistics planning scheme based on supply chain, responsible for implementation and monitoring. Object of service Large/medium/small size enterprises Large/medium enterprises Characteristics of operation The specialization of a single function is high and the multi-function integration is low. Multi-function integration The single function operation specialization of logistics is low. Partnership with customers The relations of contract and contractual generally more than one year Long-term strategic partnership, there is usually a long-term cooperation agreement.
 Project Third-party logistics Fourth-party logistics Purpose of service Reduce the cost of external logistics operation of a single enterprise. Reduce the operating costs of the whole supply chain, improve the ability of logistics service Content of service It is mainly the purchasing logistics of a single enterprise, or the whole or a part of the sales logistics. Strategic analysis of enterprise Business process reorganization Logistics strategic planning The integrated logistics scheme of upstream and downstream enterprises Grade of service It is mainly for the purchase logistics of a single enterprise, or the whole or part of the sales Provide logistics planning scheme based on supply chain, responsible for implementation and monitoring. Object of service Large/medium/small size enterprises Large/medium enterprises Characteristics of operation The specialization of a single function is high and the multi-function integration is low. Multi-function integration The single function operation specialization of logistics is low. Partnership with customers The relations of contract and contractual generally more than one year Long-term strategic partnership, there is usually a long-term cooperation agreement.
Scale form
 Called Meaning 1 It is equally important that two factors are compared 3 Compared to two factors, one factor is slightly more important than the others. 5 Compared to two factors One factor is obviously more important than others. 7 Compared to two elements, one factor is strongly more important than other. 9 Compared to two elements, one factor is extremely more important than others. 2, 4, 6, 8 The median of these two adjacent judgments reciprocal Judgment of factor $i$ and factor $j$ called $a_{ij}$ means $a_{ij}=1/a_{ij}$
 Called Meaning 1 It is equally important that two factors are compared 3 Compared to two factors, one factor is slightly more important than the others. 5 Compared to two factors One factor is obviously more important than others. 7 Compared to two elements, one factor is strongly more important than other. 9 Compared to two elements, one factor is extremely more important than others. 2, 4, 6, 8 The median of these two adjacent judgments reciprocal Judgment of factor $i$ and factor $j$ called $a_{ij}$ means $a_{ij}=1/a_{ij}$
The cost and time of choosing each candidate company
 T1 T2 T3 T4 I1 I2 W1 W2 W3 Ci 65 75 70 68 18 15 41 44 43 Ti 5 4.3 4.5 6 0 0 1.2 1 0.7
 T1 T2 T3 T4 I1 I2 W1 W2 W3 Ci 65 75 70 68 18 15 41 44 43 Ti 5 4.3 4.5 6 0 0 1.2 1 0.7
The indirect cost of each candidate company
 A T1 T2 T3 T4 I1 I2 W1 W2 W3 A 0 3.4 5.6 1.4 2.5 3.7 2.6 1.1 2 1.7 T1 3.4 0 $\times$ $\times$ $\times$ 3.6 3.9 1.5 3.2 3.8 T2 5.6 $\times$ 0 $\times$ $\times$ 2 1.9 3.6 2.4 1.7 T3 1.4 $\times$ $\times$ 0 $\times$ 1.8 1.5 2.7 3.1 3 T4 2.5 $\times$ $\times$ $\times$ 0 3.3 3.6 2 1.7 1.4 I1 3.7 3.6 2 1.8 3.3 0 $\times$ 2 2.3 2.9 I2 2.6 3.9 1.9 1.5 3.6 $\times$ 0 1.9 3 1.4 W1 1.1 1.5 3.6 2.7 2 2 1.9 0 $\times$ $\times$ W2 2 3.2 2.4 3.1 1.7 2.3 3 $\times$ 0 $\times$ W3 1.7 3.8 1.7 3 1.4 2.9 1.4 $\times$ $\times$ 0
 A T1 T2 T3 T4 I1 I2 W1 W2 W3 A 0 3.4 5.6 1.4 2.5 3.7 2.6 1.1 2 1.7 T1 3.4 0 $\times$ $\times$ $\times$ 3.6 3.9 1.5 3.2 3.8 T2 5.6 $\times$ 0 $\times$ $\times$ 2 1.9 3.6 2.4 1.7 T3 1.4 $\times$ $\times$ 0 $\times$ 1.8 1.5 2.7 3.1 3 T4 2.5 $\times$ $\times$ $\times$ 0 3.3 3.6 2 1.7 1.4 I1 3.7 3.6 2 1.8 3.3 0 $\times$ 2 2.3 2.9 I2 2.6 3.9 1.9 1.5 3.6 $\times$ 0 1.9 3 1.4 W1 1.1 1.5 3.6 2.7 2 2 1.9 0 $\times$ $\times$ W2 2 3.2 2.4 3.1 1.7 2.3 3 $\times$ 0 $\times$ W3 1.7 3.8 1.7 3 1.4 2.9 1.4 $\times$ $\times$ 0
The results of similarity coefficient between candidate companies
 R T1 T2 T3 T4 I1 I2 W1 W2 W3 R 1 0.603 0.655 0.715 0.615 0.587 0.542 0.633 0.669 0.583 T1 0.603 1 $\times$ $\times$ $\times$ 0.759 0.575 0.751 0.7 0.757 T2 0.655 $\times$ 1 $\times$ $\times$ 0.325 0.492 0.512 0.449 0.443 T3 0.715 $\times$ $\times$ 1 $\times$ 0.468 0.629 0.575 0.584 0.542 T4 0.615 $\times$ $\times$ $\times$ 1 0.312 0.546 0.443 0.51 0.504 I1 0.587 0.759 0.325 0.468 0.312 1 $\times$ 0.65 0.667 0.657 I2 0.542 0.575 0.492 0.629 0.546 $\times$ 1 0.684 0.606 0.598 W1 0.633 0.751 0.512 0.575 0.443 0.65 0.684 1 $\times$ $\times$ W2 0.669 0.7 0.449 0.584 0.51 0.667 0.606 $\times$ 1 $\times$ W3 0.583 0.757 0.443 0.542 0.504 0.657 0.598 $\times$ $\times$ 1
 R T1 T2 T3 T4 I1 I2 W1 W2 W3 R 1 0.603 0.655 0.715 0.615 0.587 0.542 0.633 0.669 0.583 T1 0.603 1 $\times$ $\times$ $\times$ 0.759 0.575 0.751 0.7 0.757 T2 0.655 $\times$ 1 $\times$ $\times$ 0.325 0.492 0.512 0.449 0.443 T3 0.715 $\times$ $\times$ 1 $\times$ 0.468 0.629 0.575 0.584 0.542 T4 0.615 $\times$ $\times$ $\times$ 1 0.312 0.546 0.443 0.51 0.504 I1 0.587 0.759 0.325 0.468 0.312 1 $\times$ 0.65 0.667 0.657 I2 0.542 0.575 0.492 0.629 0.546 $\times$ 1 0.684 0.606 0.598 W1 0.633 0.751 0.512 0.575 0.443 0.65 0.684 1 $\times$ $\times$ W2 0.669 0.7 0.449 0.584 0.51 0.667 0.606 $\times$ 1 $\times$ W3 0.583 0.757 0.443 0.542 0.504 0.657 0.598 $\times$ $\times$ 1
The ability AHP results of the candidate companies
 Sub-criteria layer Financial position The quality of staff the level of technical update The influence of industry The ability of employee innovation The capability of technical development The ability of integrate The reputation of corporate Total sort weight Layer Scheme 0.025 0.233 0.054 0.098 0.114 0.057 0.229 0.2 T1 0.058 0.054 0.028 0.019 0.097 0.058 0.318 0.106 0.125252 T2 0.113 0.105 0.154 0.215 0.026 0.021 0.031 0.291 0.125086 T3 0.322 0.197 0.105 0.028 0.04 0.299 0.021 0.029 0.092607 T4 0.027 0.027 0.056 0.076 0.31 0.129 0.156 0.081 0.111785 I1 0.141 0.074 0.317 0.113 0.093 0.205 0.079 0.042 0.096997 I2 0.04 0.327 0.08 0.283 0.208 0.075 0.04 0.148 0.172722 W1 0.071 0.158 0.201 0.164 0.058 0.144 0.051 0.061 0.102634 W2 0.208 0.018 0.038 0.061 0.024 0.027 0.115 0.22 0.091854 W3 0.019 0.04 0.021 0.042 0.144 0.043 0.19 0.022 0.081422
 Sub-criteria layer Financial position The quality of staff the level of technical update The influence of industry The ability of employee innovation The capability of technical development The ability of integrate The reputation of corporate Total sort weight Layer Scheme 0.025 0.233 0.054 0.098 0.114 0.057 0.229 0.2 T1 0.058 0.054 0.028 0.019 0.097 0.058 0.318 0.106 0.125252 T2 0.113 0.105 0.154 0.215 0.026 0.021 0.031 0.291 0.125086 T3 0.322 0.197 0.105 0.028 0.04 0.299 0.021 0.029 0.092607 T4 0.027 0.027 0.056 0.076 0.31 0.129 0.156 0.081 0.111785 I1 0.141 0.074 0.317 0.113 0.093 0.205 0.079 0.042 0.096997 I2 0.04 0.327 0.08 0.283 0.208 0.075 0.04 0.148 0.172722 W1 0.071 0.158 0.201 0.164 0.058 0.144 0.051 0.061 0.102634 W2 0.208 0.018 0.038 0.061 0.024 0.027 0.115 0.22 0.091854 W3 0.019 0.04 0.021 0.042 0.144 0.043 0.19 0.022 0.081422
Each target weight table
 Compatibility Cost Time Quality Sort weights Compatibility 1 0.333333 0.333333 0.5 0.109326 Cost 3 1 1 2 0.350713 Time 3 1 1 2 0.350713 Quality 2 0.5 0.5 1 0.189245
 Compatibility Cost Time Quality Sort weights Compatibility 1 0.333333 0.333333 0.5 0.109326 Cost 3 1 1 2 0.350713 Time 3 1 1 2 0.350713 Quality 2 0.5 0.5 1 0.189245

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