Optimization of Fuzzy Inventory Models under k-preference (original) (raw)

Comparison Between Kuhn – Tucker and Lagrangean Methods on Fuzzy Inventory Model

2021

In this paper deals with an production inventory model without shortages in a fuzzy environment with fuzzy constraints for crisp production quantity or for fuzzy production quantity are rooted in fuzzy inventory management . We have applied graded mean method for defuzzifying the fuzzy general production inventory cost in trapezoidal fuzzy numbers. The aim of our work is to find optimal solution of these models by using Lagrangean method and Kuhn-tucker method finally a numerical example explained to show the uniqueness obtained in both crisp and fuzzy inventory model.

Optimization of Fuzzy Inventory Model Without Shortages

European Journal of Molecular & Clinical Medicine, 2021

The goal of this undertaking is to discover the enhancement of EOQ model under uncertainty with no reasonable deficiencies for Pentagonal Fuzzy Numbers. Here the parameters like purchasing cost, storing cost and yearly interest are thought to be Pentagonal Fuzzy Numbers. The PFN can be defuzzify by utilizing the Graded Mean Integration Representation technique to get the advancement in the least difficult manner. The fuzzy optimal solution of the stock model is arrived by utilizing the expansion of Lagrangean strategy. To make this strategy progressively reasonable, numerical instances of both PFN is shown by utilizing the fuzzy values.

Optimization of Fuzzy Inventory Models under Fuzzy Demand and Fuzzy Lead Time

Inventory model under risk that demand is uncertain is recognized. In this paper, the fuzzy demand per day and fuzzy lead time on a cycle in fuzzy inventory control system are assumed to trapezoidal distribution, trapezoidal fuzzy number by decision maker. A fuzzy inventory model under manager's preference for order quantity is presented first. This model is given by fuzzy total annual inventory cost summating of total annual holding cost and fuzzy total annual setup cost. We obtain the optimal order quantity by using both Function Principle and Graded Mean Integration Representation method for both computing and representing fuzzy total annual inventory cost. The number of orders in a year, then, is getting by the above optimal order quantity. In addition, we get the reorder point and safety stock under a unit service level by manager. Furthermore, we also introduce a fuzzy inventory model under safety stock based on fuzzy total annual safety stock cost combined by total annual...

Fuzzy Optimal Production and Shortage Quantity for Fuzzy Production Inventory With Backorder

Abstract: This study aims at presenting fuzzy optimal production Q∗∗ and shortage quantity b∗∗ for fuzzy production inventory with backorder when setup, holding, and shortage costs are fuzzy. For this purpose, two different fuzzy models, one of which includes crisp production and crisp shortage quantity, and the other of which involves those that are fuzzy, have been presented by making use of trapezoidal fuzzy numbers. For each model, fuzzy total cost FTC has been attained via function principle. In order to defuzzfy the FTC, graded mean integration method has been used, and as to solve inequality constrain problems, Extension of the Lagrangean method has been applied.

A METHOD FOR SOLVING FUZZY INVENTORY WITH SHORTAGE UNDER THE SPACE AND INVESTMENT CONSTRAINTS

This paper discusses an Economic Order Quantity (EOQ) model with shortage under the space, investment constraints, where the setup cost, the holding cost, price per unit, the shortage cost, demand, storage area and the investment amount are considered as triangular fuzzy numbers. The fuzzy parameters in the constraints are then transformed into crisp using Robust’s ranking technique. The fuzzy parameters in the objective function are then transformed into corresponding interval numbers. Minimization of the interval objective function (obtained by using interval parameters) has been transformed into a classical multi-objective EOQ problem. The order relation that represents the decision maker’s preference among the interval objective function has been defined by the right limit, left limit, and center which is the half –width of an interval. This concept is used to minimize the interval objective function. The problem has been solved by fuzzy programming technique. Finally, the proposed method is illustrated with a numerical example.

A Fuzzy Inventory Model with Shortages Using Different Fuzzy Numbers

American Journal of Mathematics and Statistics, 2015

It is found from the literature that most of the authors have considered inventory problems without shortage in fuzzy environment and they also considered different costs as fuzzy numbers and defuzzified by using signed distance method. In our present investigation an attempt has been made to study inventory model with shortage by considering the associated costs involved as fuzzy numbers. In the present piece of work we have referred the work of Dutta and Kumar (2012). They have considered fuzzy inventory model without shortages using trapezoidal fuzzy number and for defuzzification signed distance method was used. Following their work we have extended it for purchasing inventory model with shortages using trapezoidal fuzzy number for different costs and signed distance method for defuzzification, and then for the same purchasing inventory model, the associated costs were considered as different fuzzy numbers like triangular fuzzy number, trapezoidal fuzzy number and parabolic fuzz...

Fuzzy order quantity inventory model with fuzzy shortage quantity and fuzzy promotional index

Economic Modelling, 2013

The article deals with a backorder EOQ (Economic Order Quantity) model with promotional index for fuzzy decision variables. Here, a profit function is developed where the function itself is the function of m-th power of promotional index (PI) and the order quantity, shortage quantity and the PI are the decision variables. The demand rate is operationally related to PI variables and the model has been split into two types for the multiplication and addition operation. First the crisp profit function is optimized, letting it free from fuzzy decision variable. Yager (1981) ranking index method is utilized here to have a best inventory policy for the fuzzy model. Finally, a graphical presentation of numerical illustrations and sensitivity analysis are done to justify the general model.

Optimization of fuzzy production inventory models

Information Sciences, 2002

⎯In this paper, we introduce a fuzzy Economic Production Quantity (EPQ) model with defective products that can be repaired. In this model, we consider a fuzzy opportunity cost, trapezoidal fuzzy costs and quantities into the traditional production inventory model. We use Function Principle and Graded Mean Integration Representation Method to find optimal economic production quantity of the fuzzy production inventory model.

An inventory model with backorders with fuzzy parameters and decision variables

International Journal of Approximate Reasoning, 2010

The paper considers an inventory model with backorders in a fuzzy situation by employing two types of fuzzy numbers, which are trapezoidal and triangular. A full-fuzzy model is developed where the input parameters and the decision variables are fuzzified. The optimal policy for the developed model is determined using the Kuhn-Tucker conditions after the defuzzification of the cost function with the graded mean integration (GMI) method. Numerical examples and a sensitivity analysis study are provided to highlight the differences between crisp and the fuzzy cases.

A note on fuzzy inventory model with storage space and budget constraints

Applied Mathematical Modelling, 2009

In 1997, Roy and Maiti developed a fuzzy EOQ model with fuzzy budget and storage capacity constraints where demand is influenced by the unit price and the setup cost varies with the quantity purchased [T.K. Roy, M. Maiti, A fuzzy EOQ model with demand-dependent unit cost under limited storage capacity, Eur. J. Oper. Res. 99 ]. However, their procedure has some questionable points and their numerical examples contain rather peculiar results. The purpose of this paper is threefold. First, for the same inventory model with fuzzy constraints, based on the max-min operator, we proposed an improved solution procedure. Second, we review the solution procedure by Roy and Maiti that is based on Kuhn-Tucker approach to point out their questionable results. Third, we compare Roy and Maiti's approach with ours to explain why our approach can solve the problem and theirs cannot. Numerical examples provided by them also support our findings.