Fuzzy Solution Model for Multi-Objective Multi-Resource Knapsack Problem

Purnima Raj; Nitish Kumar Bharadwaj; Ranjana

doi:https://doi.org/10.14445/22315373/IJMTT-V69I1P509

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 69 | Issue 1 | Year 2023 | Article Id. IJMTT-V69I1P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I1P509

Fuzzy Solution Model for Multi-Objective Multi-Resource Knapsack Problem

Purnima Raj, Nitish Kumar Bharadwaj, Ranjana

Received	Revised	Accepted	Published
01 Dec 2022	02 Jan 2023	15 Jan 2023	26 Jan 2023

Citation :

Purnima Raj, Nitish Kumar Bharadwaj, Ranjana, "Fuzzy Solution Model for Multi-Objective Multi-Resource Knapsack Problem," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 1, pp. 62-66, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I1P509

Abstract

Wholesaling vegetables stands as a major problem in the business market. The main role of the wholesaler is to supply the vegetables raw and fresh to retail supermarkets on a daily basis. The challenge here lies in getting done with this task efficiently with minimum time and maximum profit. The wholesaler has to collect different kinds of vegetables (objects) from different sources (resources), in order to sell the vegetables in different marketplaces (objects). Mathematically, this problem can be viewed as a multi-objective multi-resource (MOMR) problem, in which the ultimate goal is to reduce the time and increase the profit attained. For such a MOMR Knapsack problem, the Fuzzy solution model is applied in this work to present efficient wholesaling of vegetables. The defined objective function for the Fuzzy solution model considers possible profit, demand, and cost of travel. This work is proceeded with an assumption that all the vegetables are available for all the resources. The performance of the proposed model is then evaluated and compared with the existing works for validation.

Keywords

Knapsack problem, Fuzzy, Machine learning, Multi-objective problem, Vegetable wholesaling.

References

[1] Boris Kuzman, Nedeljko Prdic, and Zoran Dobras, “The Importance of the Wholesale Markets for Trade in Agricultural Products,” Economics of Agriculture, vol. 64, no. 3, pp. 1177-1190, 2019. Crossref, http://dx.doi.org/10.5937/ekoPolj1703177K
[2] Prdić Nedeljko, “Competitive Advantage of the Wholesale Market as a Distribution Channel,” Agricultural Economics, Faculty of Agriculture, University of Novi Sad, vol. 72, pp. 51-63, 2016.
[3] Viktoriia Boiko et al., “Competitive Advantages of Wholesale Markets of Agricultural Products as a Type of Entrepreneurial Activity: The Experience of Ukraine and Poland,” Economics Journal, vol. 175, no. 1-2, pp. 68-72, 2019. Crossref, http://dx.doi.org/10.21003/ea.V175-12
[4] MacDonald et al., “Demand Response Providing Ancillary Services: A Comparison of Opportunities and Challenges in US Wholesale Markets,” Lawrence Berkeley National Laboratory, 2023.
[5] Rahul Vaze, “Online Knapsack Problem Under Expected Capacity Constraint,” IEEE INFOCOM 2018-IEEE Conference on Computer Communications, IEEE, pp. 2159-2167, 2018. Crossref, https://doi.org/10.1109/INFOCOM.2018.8485980
[6] Chiranjit Changdar et al., “A Genetic Algorithm Based Approach to Solve Multi-Resource Multi-Objective Knapsack Problem for Vegetable Wholesalers in Fuzzy Environment,” Operational Research, vol. 20, pp. 1321-1352, 2020. Crossref, https://doi.org/10.1007/s12351-018-0392-3
[7] Ananta Raj Devkota et al., “Assessment of Fruit and Vegetable Losses at Major Wholesale Markets in Nepal,” International Journal of Applied Sciences and Biotechnology, vol. 2, no. 4, pp. 559-562, 2014. Crossref, http://dx.doi.org/10.3126/ijasbt.v2i4.11551
[8] S. Nagabhushana, Narahari Seetharam Nuggenahalli, and C.K. Nagendra Guptha, “Modeling Vegetable Food Supply Chain by the Prediction of Yield and Demand for A City to Reduce Food Waste,” Indian Journal of Science and Technology, vol. 9, no. 45, 2016. Crossref, http://dx.doi.org/10.17485/ijst/2016/v9i45/105954
[9] Raghad O. Bahebshi, and Abdulaziz T. Almaktoom, “Dynamical Modeling of Fresh Vegetables While Considering Degradation Effect on Pricing,” 7 th Annual International Conference on Industrial Engineering and Operations Management, pp. 1817-1825, 2020.
[10] Brian Lee, Jhih-Yun Liu, and Hung-Hao Chang, “The Choice of Marketing Channel and Farm Profitability: Empirical Evidence From Small Farmers,” Agribusiness, vol. 36, no. 3, pp. 402-421, 2020. Crossref, https://doi.org/10.1002/agr.21640
[11] Mauro Dell’Amico et al., “Mathematical Models and Decomposition Methods for the Multiple Knapsack Problem,” European Journal of Operational Research, vol. 274, no. 3, pp. 886-899, 2019. Crossref, https://doi.org/10.1016/j.ejor.2018.10.043
[12] Bingyu Song et al., “A Repair-Based Approach for Stochastic Quadratic Multiple Knapsack Problem,” Knowledge-Based Systems, vol. 145, pp. 145-155, 2018. Crossref, https://doi.org/10.1016/j.knosys.2018.01.012
[13] Jayanthi Manicassamy et al., “GPS: A Constraint-Based Gene Position Procurement in Chromosome for Solving Large-Scale Multiobjective Multiple Knapsack Problems,” Frontiers of Computer Science, vol. 12, pp. 101-121, 2018. Crossref, https://doi.org/10.1007/s11704-016-5195-1
[14] Paolo Detti, “A New Upper Bound for the Multiple Knapsack Problem,” Computers & Operations Research, vol. 129, p. 105210, 2021. Crossref, https://doi.org/10.1016/j.cor.2021.105210
[15] D. Hamlin, “Process Systems Engineering for Pharmaceutical Manufacturing,” Johnson Matthey Technology Review, vol. 63, no. 4, pp. 292-298, 2019. Crossref, https://doi.org/10.1595/205651319X15680343765046
[16] David Pisinger, “Heuristics for the Container Loading Problem,” European Journal of Operational Research, vol. 141, no. 2, pp. 382- 392, 2002. Crossref, https://doi.org/10.1016/S0377-2217(02)00132-7
[17] Daniel C. Vanderster et al., “Resource Allocation on Computational Grids Using A Utility Model and the Knapsack Problem,” Future Generation Computer Systems, vol. 25, no. 1, pp. 35-50, 2009. Crossref, https://doi.org/10.1016/j.future.2008.07.006
[18] Brianna Christian, and Selen Cremaschi, “Planning Pharmaceutical Clinical Trials under Outcome Uncertainty,” Computer Aided Chemical Engineering, vol. 41, pp. 517-550, 2018. Crossref, https://doi.org/10.1016/B978-0-444-63963-9.00021-X
[19] Debasis Samanta, Fuzzy Membership Function Formulation and Parameterization, 2018. [Online]. Available:https://cse.iitkgp.ac.in/~dsamanta/courses/archive/sca/Archives/Chapter%203%20Fuzzy%20Membership%
[20] Witold Pedrycz, “Why Triangular Membership Functions?,” Fuzzy Sets and Systems, vol. 64, no. 1, pp. 21-30, 1994. Crossref, https://doi.org/10.1016/0165-0114(94)90003-5
[21] K.O. Willis, and D.F. Jones, “Multi-Objective Simulation Optimization through Search Heuristic & Relation Database Analysis,” Decision Support System, vol. 46, no. 1, pp. 277-286, 2008. Crossref, https://doi.org/10.1016/j.dss.2008.06.012
[22] Jose Ramon San Cristobal, “A Goal Programming Model for Vessel Dry Docking,” Journal on Ship Production, vol. 25, no. 2, pp. 95- 98, 2009. Crossref, http://dx.doi.org/10.5957/jsp.2009.25.2.95
[23] Fernando García et al., “A Goal Programming Approach to Estimating Performance Weights for Ranking Firms,” Computers and Operations Research, vol. 37, no. 7, pp. 1597-1609, 2010. Crossref, https://doi.org/10.1016/j.cor.2009.11.018
[24] Dipti Dubay, Suresh Chandra, and Aparna Mehra, “Fuzzy Linear Programming Under Interval Uncertainty based on Intuitionistic Fuzzy Set Representation,” Fuzzy Sets and Systems, vol. 188, no. 1, pp. 68-87, 2012. Crossref, https://doi.org/10.1016/j.fss.2011.09.008
[25] Seyed Hadi Nasseri et al., “A Novel Approach for Solving Fully Fuzzy Linear Programming Problems Using Membership Function Concepts,” Annals of Fuzzy Mathematics and Informatics, vol. 7, no. pp. 355-368, 2014.
[26] Yusuf Tansel İç, Melis Özel, and İmdat Kara, “An Integrated Fuzzy TOPSIS-Knapsack Problem Model for Order Selection in A Bakery,” Arabian Journal for Science and Engineering, vol. 42, pp. 5321-5337, 2017. Crossref, https://doi.org/10.1007/s13369-017-2809-3