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Multi-objective Inventory Model with Both Stock-Dependent Demand Rate and Holding Cost Rate Under Fuzzy Random Environment

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Abstract

In this paper, we investigated a multi-objective inventory model under both stock-dependent demand rate and holding cost rate with fuzzy random coefficients. Chance constrained fuzzy random multi-objective model and a traditional solution procedure based on an interactive fuzzy satisfying method are discussed. In addition, the technique of fuzzy random simulation is applied to deal with general fuzzy random objective functions and fuzzy random constraints which are usually difficult to converted into their crisp equivalents. The purposed of this study is to determine optimal order quantity and inventory level such that the total profit and wastage cost are maximized and minimize for the retailer respectively. Finally, illustrate example is given in order to show the application of the proposed model.

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Abbreviations

Pos:

Possibility measure

Nec:

Necessity measure

Cr:

Credibility measure

Pr:

Probability measure

Ch:

Chance measure

CCMOP:

Chance constrained multi-objective problem

FISM:

Interactive fuzzy satisfied method

\({\mathop {a}\limits ^{\simeq }}\) :

Fuzzy random variable

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Author notes

  1. In this article, Totan Garai, Dipankar Chakraborty and Tapan Kumar Roy have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Silda Chandra Sekhar College, Silda, Jhargram, 721515, West Bengal, India

    Totan Garai & Tapan Kumar Roy

  2. Department of Mathematics, Heritage Institute of Technology, Anandapur, Kolkata, 700107, West Bengal, India

    Dipankar Chakraborty

Authors
  1. Totan Garai
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  2. Dipankar Chakraborty
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  3. Tapan Kumar Roy
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Correspondence to Totan Garai.

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Garai, T., Chakraborty, D. & Roy, T.K. Multi-objective Inventory Model with Both Stock-Dependent Demand Rate and Holding Cost Rate Under Fuzzy Random Environment. Ann. Data. Sci. 6, 61–81 (2019). https://doi.org/10.1007/s40745-018-00186-0

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  • DOI: https://doi.org/10.1007/s40745-018-00186-0

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