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A genetic algorithm based approach to solve multi-resource multi-objective knapsack problem for vegetable wholesalers in fuzzy environment

Author

Listed:
  • Chiranjit Changdar

    (Raja N. L. Khan Women’s College)

  • Rajat Kumar Pal

    (University of Calcutta)

  • Ghanshaym Singha Mahapatra

    (National Institute of Technology)

  • Abhinandan Khan

    (University of Calcutta)

Abstract

Vegetable wholesaling problem has a vital role in the business system. In this problem, a vegetable wholesaler is supposed to supply raw, fresh vegetables to supermarkets in an efficient way by minimizing time but maximizing profit. In this paper, we have presented a multi-resource multi-objective knapsack problem (MRKP) for vegetable wholesalers. This model is beneficial for a vegetable wholesaler who collects different types of vegetables (objects) from different villages (resources) to a market for selling the vegetables (objects). MRKP is an extension of the classical concept of 0–1 multi-dimensional knapsack problem (KP). In this model, precisely a wholesaler has a limited capacity van/trolley by which he/she collects a set of vegetables from different villages/vegetable fields. In this model, we have assumed that all the vegetables are available for each resource. Each type of vegetable is associated with a weight, a corresponding profit, and a collection time (for a particular resource). The profit, weight, and collection time of objects is different for different resources. Here a time slice is considered for each object to collect it from different villages to a particular destination/market. Also, the profit and time are the two objectives. MRKP aims to find the amount of an object and the corresponding resource name from which it is collected. We have solved the proposed problem in the fuzzy environment. In this paper, we have explained two defuzzification techniques, namely fuzzy expectation and total $$\lambda$$ λ -integral value method to solve the proposed problem. We have explained a modified multi-objective genetic algorithm (NSGA-II by Deb et al. in IEEE Trans Evol Comput 6(2):192–197, 2002) that is to maximise the profit and minimise the time to collect the objects. We have considered a multi-objective benchmark test function to show the effectiveness of the proposed Genetic Algorithm. Modification is made by introducing refinement operation. An extensive computational experimentation has been executed that generates interesting results to establish the effectiveness of the proposed model.

Suggested Citation

  • Chiranjit Changdar & Rajat Kumar Pal & Ghanshaym Singha Mahapatra & Abhinandan Khan, 2020. "A genetic algorithm based approach to solve multi-resource multi-objective knapsack problem for vegetable wholesalers in fuzzy environment," Operational Research, Springer, vol. 20(3), pages 1321-1352, September.
    • Handle: RePEc:spr:operea:v:20:y:2020:i:3:d:10.1007_s12351-018-0392-3
    DOI: 10.1007/s12351-018-0392-3
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    References listed on IDEAS

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    1. Bagchi, Ansuman & Bhattacharyya, Nalinaksha & Chakravarti, Nilotpal, 1996. "LP relaxation of the two dimensional knapsack problem with box and GUB constraints," European Journal of Operational Research, Elsevier, vol. 89(3), pages 609-617, March.
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    4. Balev, Stefan & Yanev, Nicola & Freville, Arnaud & Andonov, Rumen, 2008. "A dynamic programming based reduction procedure for the multidimensional 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 186(1), pages 63-76, April.
    5. Cai Dai & Yuping Wang & Wei Yue, 2015. "A new orthogonal evolutionary algorithm based on decomposition for multi-objective optimization," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(10), pages 1686-1698, October.
    6. Oliveira, Jose Fernando & Wascher, Gerhard, 2007. "Cutting and Packing," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1106-1108, December.
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