Main Article Content
Abstract
In this paper, an inventory control problem is discussed using imprecise parameters. The fusion of geometric programming and fuzzy logic is used as imprecise parameters to solve inventory control problems. In inventory, holding costs, set-up costs, etc. may be flexible due to vague information. Fuzzy set theory is used to convert the inventory model crisp to fuzzy for producing flexible output. Compensatory operator is used to aggregate the fuzzy membership functions corresponding to fuzzy sets for fuzzy objectives and constraints. This aggregation gives the overall achievement function and the model known as fuzzy geometric programming model.
Keywords
Fuzzy objective
Fuzzy constraint
Compensatory operator
Achievement function
Geometric programming
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How to Cite
Kumari, N., Mandal, M. K., & Burnwal, A. P. (2018). MATHEMATICAL MODEL FOR INVENTORY CONTROL PROBLEM USING IMPRECISE PARAMETERS. International Journal of Students’ Research in Technology & Management, 6(2), 07–12. https://doi.org/10.18510/ijsrtm.2018.622
References
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[1] S. K. Das and S. Tripathi, “Energy efficient routing formation technique for hybrid ad hoc network using fusion of artificial intelligence techniques,†International Journal of Communication Systems, 2017, pp. 1-16, DOI: 10.1002/dac.3340.
[2] Joao Paulo Papa, Gustavo Henrique Rosa, Luciene Patrici Papa, “A binary-constrained Geometric Semantic Genetic Programming for feature selection purposes,†Pattern Recognition Letters, 2017, vol. 100, no. 1, pp. 59-66.
[3] Jia Liu, Abdel Lisser and Zhiping Chen, “Stochastic geometric programming with joint probabilistic constraints,†Electronic Notes in Discrete Mathematics, 2016, vol. 55, pp. 49-52.
[4] Gongxian Xu, “Global optimization of signomial geometric programming problems,†European Journal of Operational Research, 2014, vol. 233, no. 3, pp. 500-510.
[5] A. Burnwal, A. Kumar, and S. K. Das, “Assessment of fuzzy set theory in different paradigm,†International Journal of Advanced Technology & Engineering Research, 2013, vol. 3, no. 3, pp. 16-22.
[6] A. Burnwal, A. Kumar, and S. K. Das, “Assessment of Mathematical Modeling in Different Areas,†International Journal of Advanced Technology & Engineering Research, 2013, vol. 3, no. 3, pp. 23-26.
[7] S. K. Das and S. Tripathi, “Adaptive and intelligent energy efficient routing for transparent heterogeneous ad-hoc network by fusion of game theory and linear programming,†Applied Intelligence, 2017, pp. 1-21, https://doi.org/10.1007/s10489-017-1061-6.
[8] S. K. Das, A. Kumar, B. Das, and A. Burnwal, “Ethics of reducing power consumption in wireless sensor networks using soft computing techniques,†International Journal of Advanced Computer Research, 2013, vol. 3, no. 1, pp. 301-304.
[9] S. K. Das, B. Das, and A. Burnwal, “Intelligent energy competency routing scheme for wireless sensor networksâ€, International Journal of Research in Computer Applications and Robotics, 2014, vol. 2, no. 3, pp. 79-84.
[10] S. K. Das, S. Tripathi, and A. Burnwal, “Intelligent energy competency multipath routing in wanet,†in Information Systems Design and Intelligent Applications, Springer, 2015, pp. 535-543, DOI: 10.1007/978-81-322-2250-7_53.
[11] S. K. Das, S. Tripathi, and A. Burnwal, “Fuzzy based energy efficient multicast routing for ad-hoc network,†in Computer, Communication, Control and Information Technology (C3IT), 2015 Third International Conference on, IEEE, 2015, pp. 1-5, DOI: 10.1109/C3IT.2015.7060126.
[12] S. K. Das, S. Tripathi, and A. Burnwal, “Design of fuzzy based intelligent energy efficient routing protocol for WANET,†in Computer, Communication, Control and Information Technology (C3IT), 2015 Third International Conference on, IEEE, 2015, pp. 1-4, DOI: 10.1109/C3IT.2015.7060201.
[13] S. K. Das and S. Tripathi, “Energy efficient routing protocol for manet based on vague set measurement technique,†Procedia Computer Science, 2015, vol. 58, pp. 348-355, doi:10.1016/j.procs.2015.08.030.
[14] S. K. Das and S. Tripathi, “Energy Efficient Routing Protocol for MANET Using Vague Set,†in Proceedings of Fifth International Conference on Soft Computing for Problem Solving, Springer, 2016, pp. 235-245, DOI: 10.1007/978-981-10-0448-3_19.
[15] A. Burnwal, A. Kumar, and S. K. Das, “Survey on application of artificial intelligence techniques,†International Journal of Engineering Research & Management, 2014, vol. 1, no. 5, pp. 215-219.
[16] S. K. Das, A. Kumar, B. Das, and A. Burnwal, “On soft computing techniques in various areas,†Computer Science & Information Technology (CS & IT), 2013, vol. 3, pp. 59-68, DOI : 10.5121/csit.2013.3206.
[17] S. K. Das, S. Tripathi, and A. Burnwal, “Some relevance fields of soft computing methodology,†International Journal of Research in Computer Applications and Robotics, 2014, vol. 2, pp. 1-6.
[18] S. K. Das, B. Das, and A. Burnwal, “Intelligent energy competency routing scheme for wireless sensor networksâ€, International Journal of Research in Computer Applications and Robotics, 2014, vol. 2, no. 3, pp. 79-84.
[19] S. K. Das and S. Tripathi, “Intelligent energy-aware efficient routing for MANET,†Wireless Networks, 2016, pp. 1-21, DOI 10.1007/s11276-016-1388-7.
[20] S. K. Das, A. K. Yadav and S. Tripathi, “IE2M: Design of intellectual energy efficient multicast routing protocol for ad-hoc network,†Peer-to-Peer Networking and Applications, 2016, vol. 10, no. 3, pp. 670-687, DOI 10.1007/s12083-016-0532-6.
[21] A. K. Yadav, S. K. Das and S. Tripathi, “EFMMRP: Design of efficient fuzzy based multi-constraint multicast routing protocol for wireless ad-hoc network,†Computer Networks, 2017, vol. 118, pp. 15-23, https://doi.org/10.1016/j.comnet.2017.03.001.
References
[1] S. K. Das and S. Tripathi, “Energy efficient routing formation technique for hybrid ad hoc network using fusion of artificial intelligence techniques,†International Journal of Communication Systems, 2017, pp. 1-16, DOI: 10.1002/dac.3340.
[2] Joao Paulo Papa, Gustavo Henrique Rosa, Luciene Patrici Papa, “A binary-constrained Geometric Semantic Genetic Programming for feature selection purposes,†Pattern Recognition Letters, 2017, vol. 100, no. 1, pp. 59-66.
[3] Jia Liu, Abdel Lisser and Zhiping Chen, “Stochastic geometric programming with joint probabilistic constraints,†Electronic Notes in Discrete Mathematics, 2016, vol. 55, pp. 49-52.
[4] Gongxian Xu, “Global optimization of signomial geometric programming problems,†European Journal of Operational Research, 2014, vol. 233, no. 3, pp. 500-510.
[5] A. Burnwal, A. Kumar, and S. K. Das, “Assessment of fuzzy set theory in different paradigm,†International Journal of Advanced Technology & Engineering Research, 2013, vol. 3, no. 3, pp. 16-22.
[6] A. Burnwal, A. Kumar, and S. K. Das, “Assessment of Mathematical Modeling in Different Areas,†International Journal of Advanced Technology & Engineering Research, 2013, vol. 3, no. 3, pp. 23-26.
[7] S. K. Das and S. Tripathi, “Adaptive and intelligent energy efficient routing for transparent heterogeneous ad-hoc network by fusion of game theory and linear programming,†Applied Intelligence, 2017, pp. 1-21, https://doi.org/10.1007/s10489-017-1061-6.
[8] S. K. Das, A. Kumar, B. Das, and A. Burnwal, “Ethics of reducing power consumption in wireless sensor networks using soft computing techniques,†International Journal of Advanced Computer Research, 2013, vol. 3, no. 1, pp. 301-304.
[9] S. K. Das, B. Das, and A. Burnwal, “Intelligent energy competency routing scheme for wireless sensor networksâ€, International Journal of Research in Computer Applications and Robotics, 2014, vol. 2, no. 3, pp. 79-84.
[10] S. K. Das, S. Tripathi, and A. Burnwal, “Intelligent energy competency multipath routing in wanet,†in Information Systems Design and Intelligent Applications, Springer, 2015, pp. 535-543, DOI: 10.1007/978-81-322-2250-7_53.
[11] S. K. Das, S. Tripathi, and A. Burnwal, “Fuzzy based energy efficient multicast routing for ad-hoc network,†in Computer, Communication, Control and Information Technology (C3IT), 2015 Third International Conference on, IEEE, 2015, pp. 1-5, DOI: 10.1109/C3IT.2015.7060126.
[12] S. K. Das, S. Tripathi, and A. Burnwal, “Design of fuzzy based intelligent energy efficient routing protocol for WANET,†in Computer, Communication, Control and Information Technology (C3IT), 2015 Third International Conference on, IEEE, 2015, pp. 1-4, DOI: 10.1109/C3IT.2015.7060201.
[13] S. K. Das and S. Tripathi, “Energy efficient routing protocol for manet based on vague set measurement technique,†Procedia Computer Science, 2015, vol. 58, pp. 348-355, doi:10.1016/j.procs.2015.08.030.
[14] S. K. Das and S. Tripathi, “Energy Efficient Routing Protocol for MANET Using Vague Set,†in Proceedings of Fifth International Conference on Soft Computing for Problem Solving, Springer, 2016, pp. 235-245, DOI: 10.1007/978-981-10-0448-3_19.
[15] A. Burnwal, A. Kumar, and S. K. Das, “Survey on application of artificial intelligence techniques,†International Journal of Engineering Research & Management, 2014, vol. 1, no. 5, pp. 215-219.
[16] S. K. Das, A. Kumar, B. Das, and A. Burnwal, “On soft computing techniques in various areas,†Computer Science & Information Technology (CS & IT), 2013, vol. 3, pp. 59-68, DOI : 10.5121/csit.2013.3206.
[17] S. K. Das, S. Tripathi, and A. Burnwal, “Some relevance fields of soft computing methodology,†International Journal of Research in Computer Applications and Robotics, 2014, vol. 2, pp. 1-6.
[18] S. K. Das, B. Das, and A. Burnwal, “Intelligent energy competency routing scheme for wireless sensor networksâ€, International Journal of Research in Computer Applications and Robotics, 2014, vol. 2, no. 3, pp. 79-84.
[19] S. K. Das and S. Tripathi, “Intelligent energy-aware efficient routing for MANET,†Wireless Networks, 2016, pp. 1-21, DOI 10.1007/s11276-016-1388-7.
[20] S. K. Das, A. K. Yadav and S. Tripathi, “IE2M: Design of intellectual energy efficient multicast routing protocol for ad-hoc network,†Peer-to-Peer Networking and Applications, 2016, vol. 10, no. 3, pp. 670-687, DOI 10.1007/s12083-016-0532-6.
[21] A. K. Yadav, S. K. Das and S. Tripathi, “EFMMRP: Design of efficient fuzzy based multi-constraint multicast routing protocol for wireless ad-hoc network,†Computer Networks, 2017, vol. 118, pp. 15-23, https://doi.org/10.1016/j.comnet.2017.03.001.
[2] Joao Paulo Papa, Gustavo Henrique Rosa, Luciene Patrici Papa, “A binary-constrained Geometric Semantic Genetic Programming for feature selection purposes,†Pattern Recognition Letters, 2017, vol. 100, no. 1, pp. 59-66.
[3] Jia Liu, Abdel Lisser and Zhiping Chen, “Stochastic geometric programming with joint probabilistic constraints,†Electronic Notes in Discrete Mathematics, 2016, vol. 55, pp. 49-52.
[4] Gongxian Xu, “Global optimization of signomial geometric programming problems,†European Journal of Operational Research, 2014, vol. 233, no. 3, pp. 500-510.
[5] A. Burnwal, A. Kumar, and S. K. Das, “Assessment of fuzzy set theory in different paradigm,†International Journal of Advanced Technology & Engineering Research, 2013, vol. 3, no. 3, pp. 16-22.
[6] A. Burnwal, A. Kumar, and S. K. Das, “Assessment of Mathematical Modeling in Different Areas,†International Journal of Advanced Technology & Engineering Research, 2013, vol. 3, no. 3, pp. 23-26.
[7] S. K. Das and S. Tripathi, “Adaptive and intelligent energy efficient routing for transparent heterogeneous ad-hoc network by fusion of game theory and linear programming,†Applied Intelligence, 2017, pp. 1-21, https://doi.org/10.1007/s10489-017-1061-6.
[8] S. K. Das, A. Kumar, B. Das, and A. Burnwal, “Ethics of reducing power consumption in wireless sensor networks using soft computing techniques,†International Journal of Advanced Computer Research, 2013, vol. 3, no. 1, pp. 301-304.
[9] S. K. Das, B. Das, and A. Burnwal, “Intelligent energy competency routing scheme for wireless sensor networksâ€, International Journal of Research in Computer Applications and Robotics, 2014, vol. 2, no. 3, pp. 79-84.
[10] S. K. Das, S. Tripathi, and A. Burnwal, “Intelligent energy competency multipath routing in wanet,†in Information Systems Design and Intelligent Applications, Springer, 2015, pp. 535-543, DOI: 10.1007/978-81-322-2250-7_53.
[11] S. K. Das, S. Tripathi, and A. Burnwal, “Fuzzy based energy efficient multicast routing for ad-hoc network,†in Computer, Communication, Control and Information Technology (C3IT), 2015 Third International Conference on, IEEE, 2015, pp. 1-5, DOI: 10.1109/C3IT.2015.7060126.
[12] S. K. Das, S. Tripathi, and A. Burnwal, “Design of fuzzy based intelligent energy efficient routing protocol for WANET,†in Computer, Communication, Control and Information Technology (C3IT), 2015 Third International Conference on, IEEE, 2015, pp. 1-4, DOI: 10.1109/C3IT.2015.7060201.
[13] S. K. Das and S. Tripathi, “Energy efficient routing protocol for manet based on vague set measurement technique,†Procedia Computer Science, 2015, vol. 58, pp. 348-355, doi:10.1016/j.procs.2015.08.030.
[14] S. K. Das and S. Tripathi, “Energy Efficient Routing Protocol for MANET Using Vague Set,†in Proceedings of Fifth International Conference on Soft Computing for Problem Solving, Springer, 2016, pp. 235-245, DOI: 10.1007/978-981-10-0448-3_19.
[15] A. Burnwal, A. Kumar, and S. K. Das, “Survey on application of artificial intelligence techniques,†International Journal of Engineering Research & Management, 2014, vol. 1, no. 5, pp. 215-219.
[16] S. K. Das, A. Kumar, B. Das, and A. Burnwal, “On soft computing techniques in various areas,†Computer Science & Information Technology (CS & IT), 2013, vol. 3, pp. 59-68, DOI : 10.5121/csit.2013.3206.
[17] S. K. Das, S. Tripathi, and A. Burnwal, “Some relevance fields of soft computing methodology,†International Journal of Research in Computer Applications and Robotics, 2014, vol. 2, pp. 1-6.
[18] S. K. Das, B. Das, and A. Burnwal, “Intelligent energy competency routing scheme for wireless sensor networksâ€, International Journal of Research in Computer Applications and Robotics, 2014, vol. 2, no. 3, pp. 79-84.
[19] S. K. Das and S. Tripathi, “Intelligent energy-aware efficient routing for MANET,†Wireless Networks, 2016, pp. 1-21, DOI 10.1007/s11276-016-1388-7.
[20] S. K. Das, A. K. Yadav and S. Tripathi, “IE2M: Design of intellectual energy efficient multicast routing protocol for ad-hoc network,†Peer-to-Peer Networking and Applications, 2016, vol. 10, no. 3, pp. 670-687, DOI 10.1007/s12083-016-0532-6.
[21] A. K. Yadav, S. K. Das and S. Tripathi, “EFMMRP: Design of efficient fuzzy based multi-constraint multicast routing protocol for wireless ad-hoc network,†Computer Networks, 2017, vol. 118, pp. 15-23, https://doi.org/10.1016/j.comnet.2017.03.001.