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Type-2 zigzag uncertain multi-objective fixed-charge solid transportation problem: time window vs. preservation technology

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Abstract

Urgency of fresh items is increasing day by day everywhere. During transportation over a long distance, the rate of deterioration is also increasing for perishable items, and if the items are not reaching at destination within a specified time, then they are no longer fresh. Based on the fact, the customers loose the quality and quantity of items; as a result, suppliers are penalized for the occurrence of any such a situation. This problem is resolved by introducing two criteria such as time window restrictions and preservation technology in the proposed study. To prevent the deterioration rate, we find a strategy by formulating a model for multi-objective fixed-charge solid transportation problem with two criteria and then finalize one of them. To ensure that the necessary fresh items are to reached at the destination just in time, we introduce several objectives such as transportation cost, transportation time, preservation cost, penalty charge for time window, carbon emission with cap policy, deterioration, etc., such that these are optimized simultaneously. Again source, demand and conveyance capacity are not precisely estimated for different real-life situations. Here, we address such situation by choosing type-2 zigzag uncertain variable. Expected value operator is initiated to convert such uncertainty into crisp form, and then three approaches, namely, fuzzy programming, Pythagorean hesitant fuzzy programming and global criterion method are utilized to find Pareto-optimal solution. Finally two numerical examples are put to check the appropriateness of the formulated study. The results along with discussions and conclusions are described at last. The main contribution is that the deterioration of transported perishable items is reduced by imposing one of the proposed criteria according to the economical or other conditions of systems.

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Author notes

  1. Shyamali Ghosh and Karl-Heinz Küfer have contributed equally to this work.

Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, West Bengal, India

    Shyamali Ghosh & Sankar Kumar Roy

  2. Department of Optimization and Operations Research, Fraunhofer-Institut für Techno-und Wirtschaftsmathematik ITWM, Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany

    Karl-Heinz Küfer

  3. Faculty of Engineering Management, Poznan University of Technology, Poznan, Poland

    Gerhard-Wilhelm Weber

Authors
  1. Shyamali Ghosh
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  2. Karl-Heinz Küfer
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  3. Sankar Kumar Roy
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  4. Gerhard-Wilhelm Weber
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Correspondence to Sankar Kumar Roy.

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Ghosh, S., Küfer, KH., Roy, S.K. et al. Type-2 zigzag uncertain multi-objective fixed-charge solid transportation problem: time window vs. preservation technology. Cent Eur J Oper Res 31, 337–362 (2023). https://doi.org/10.1007/s10100-022-00811-7

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  • DOI: https://doi.org/10.1007/s10100-022-00811-7

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