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      https://www.ias.ac.in/article/fulltext/sadh/046/0039

    • Keywords

       

      Differential equation; Caputo’s derivative; Riemann–Liouville integral; triangular dense fuzzy set; memory; learning experience.

    • Abstract

       

      Due to the involvement of human intelligence in the inventory planning procedures, memory and learning from repeated tasks in the planning horizon are two important facts that make great impressions on the decision taken in reality. However, the concepts of learning and memory related to the inventory theory are rarely illustrated in literature and till date we have not noticed any work where the effects of memory and system learning have been explored simultaneously. Making an attempt to close the gap, the present paper extends an economic order quantity (EOQ) model into a memory and learning sensitive set-up. The primary structure of the model is established on the assumption that the demand of the EOQ model is constant in inventory run period and the same is a decreasing function of time in the shortage period. Introducing fractional calculus as a replacement of integer one, the notion of memory is included in the proposed theory. Finally, using Zadeh’s extension principle, the fuzzzification of the fractional deterministic model is executed and ultimately the senseof learning based decision making is incorporated letting the demand to be a triangular dense fuzzy number. Here, considering different underlying scenarios, four different models have been illustrated and solved numerically. The a-cut method of defuzzification is used for the numerical simulation of two fuzzy models. It is worth mentioning that the joint impact of learning and memory creates positive results on the cost reduction objective of the proposed lot-sizing problem.

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    • Author Affiliations

       

      MOSTAFIJUR RAHAMAN1 SANKAR PRASAD MONDAL2 SHARIFUL ALAM1 ADRIJIT GOSWAMI3

      1. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, , Howrah 711103, India
      2. Department of Applied Science, Maulana Abul Kalam Azad University of Technology, West Bengal, Nadia 741249, India
      3. Department of Mathematics, Indian Institute of Technology, Kharagpur, Kharagpur, India
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