Granular Computing

, Volume 4, Issue 1, pp 71–88

# A fuzzy rough multi-objective multi-item inventory model with both stock-dependent demand and holding cost rate

• Totan Garai
• Dipankar Chakraborty
• Tapan Kumar Roy
Original Paper

## Abstract

In this paper, we developed a multi-objective multi-item inventory model with fuzzy rough coefficients. Here, we have considered both demand and holding cost which is a non-linear function of the instantaneous stock level. Chance-constrained fuzzy rough multi-objective model and a traditional solution procedure based on an interactive fuzzy satisfying method are discussed. By examining the various definitions and theoretical results of fuzzy rough variables, we have designed a Tr-Pos chance constrained technique to determine the optimal solutions of a fuzzy rough multi-objective inventory problem. Finally, a numerical example is provided to illustrate the present model, and a sensitivity analysis of the optimal solution with respect to the major parameters is carried out.

## Keywords

Multi-objective Multi-item inventory Stock-dependent demand Stock-dependent holding cost Fuzzy rough variable Chance measure

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© Springer International Publishing AG, part of Springer Nature 2018

## Authors and Affiliations

• Totan Garai
• 1
Email author
• Dipankar Chakraborty
• 1
• Tapan Kumar Roy
• 1
1. 1.Department of MathematicsIndian Institute of Engineering Science and Technology, ShibpurHowrahIndia