Multi-objective linear fractional inventory problem under intuitionistic fuzzy environment

Abstract

In this paper, we have assumed an inventory multi-objective optimization model under intuitionistic fuzziness. In modelling, we have considered the situations where triangular intuitionistic fuzzy numbers used to express some of the input information which associated with decision variables. Further, a ranking function approach by considering linear and the nonlinear degree of membership functions have been used to obtain the crisp form of the fuzzy parameters. Finally, the fuzzy goal programming approach has been used to solve the resultant model to obtain the optimal ordering quantity. Also, a comparative study of the formulated problem under intuitionistic fuzziness has been done with a deterministic model of inventory. The concept of the paper is explained through a numerical example.

A Deterministic Multi-Objective Optimization Process of Multi-Item Inventory Management in Fmcg Industry

“…Table 1: Summary of Literature on Inventory Models Garai et al [1] They formulated inventory model base on demand rate and carrying cost with fuzzy concept. The paper determined optimal order quantity and inventory level with minimize total inventory cost for retailer Ali et al [2] They formulated multi-objective inventory optimization model to min. inventory cost and optimal order size under intuitionistic fuzziness.…”

“…Inventories deal with the management of sufficient inventory of products to guarantee a smooth functioning of a production system. Business and industry have traditionally viewed stock as aindispensable measure.Too little stock can cause an expensive process failure, and excessively inventory can destroy the economical edge of the company.Recently, Ali et al [2] proposed a multi-objective inventory model with in which they considered a theoretical process with deterministic parameters for the inventory model and used a fuzzy goal programming technique to achieve the optimum quantity.Dutta and Kumar [4,5] used LFP along with multi-criterion decision-making in inventory management.They consideredthe problemof without shortage, and formulated it as the multi-objective inventory problem of fractional objective function and extracting the ideal order quantity of commodities, respectively.Here, we discussed the modelling and optimization of a multiobjective inventory system with consideration of real set of data which has been collected from FMCG Company.The foregoing descriptions and premises used to develop the problem are as follows: 3. Constant level of production.…”

“…The accompanying quantitative example illustrates the solution that has been suggested.Ali et al [2] and Dutta and Kumar [4,5]have presented their inventory model with hypothetical information. Here we are considering the real case of inventory optimization in which the input information has been collected from the well-known FMCG Company.The information collected has been summarized in Table 2 The problem that has been formulated above cannot be solved instantly, so we must first figure out the individual optimum solution for each objective function.The obtained individual optimum value of each objective functions has been treated as their goal respectively.…”

“…Company may have to suffer huge losses in the organization. So it is important that we need to keep inventory and to reduce bullwhip effect so that demand information do not distort as it moves away from end-use customer.so, some companies are making use of the direct interface those days between the customer and the company [2]. These days the use of information technology is helping the companies to reduce this effect, but many times the demand gets distorted because of the bullwhip effect.…”

Multi‐objective linear fractional inventory model with possibility and necessity constraints under generalised intuitionistic fuzzy set environment

“…Garg [25] presented the fuzzy inventory model for deteriorating items under the different types of lead‐time distribution. Ali et al [26] formulated a fractional inventory management problem in intuitionistic fuzzy environment.…”