A comprehensive study of a backlogging EOQ model with nonlinear heptagonal dense fuzzy environment

2020 ◽  
Vol 54 (1) ◽  
pp. 267-286 ◽  
Author(s):  
Suman Maity ◽  
Avishek Chakraborty ◽  
Sujit Kumar De ◽  
Sankar Prasad Mondal ◽  
Shariful Alam
Keyword(s):  
Sensitivity Analysis ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Centroid Method ◽  
Numerical Examples ◽  
Eoq Model ◽  
Fuzzy Environment ◽  
Non Linear ◽  
Demand Rate ◽  
Comprehensive Study

This paper deals with an adaptation of an application of nonlinear heptagonal dense fuzzy number. The concept of linear and as well as non-linear for both symmetric and asymmetric heptagonal dense fuzzy number is introduced here. We develop a new ranking method for non-linear heptagonal dense fuzzy number also. Considering a backorder inventory model with non-linear heptagonal dense fuzzy demand rate we have utilized a modified centroid method for defuzzification. For decision maker’s aspects, numerical examples, comparative study with other dense fuzzy numbers and a sensitivity analysis show the superiority of the nonlinear heptagonal dense fuzzy number. Finally, graphical illustrations are made to justify the model followed by a conclusion.

scholarly journals A Study On Reliability Using Pendant, Hexant, Octant Fuzzy Numbers

2021 ◽  
Author(s):  
P. Jini Varghese ◽  
G. Michael Rosario
Keyword(s):  
Fuzzy Number ◽  
Comparative Research ◽  
Fuzzy Numbers ◽  
Integration Method ◽  
Centroid Method ◽  
Distance Method ◽  
Numerical Examples ◽  
Signed Distance ◽  
Mathematical Operations

The weaving machine’s reliability is assessed using newly introduced fuzzy numbers. The fuzzy numbers introduced in this study give a better method to improve the reliability than other techniques. Pendant Fuzzy Number, Hexant Fuzzy Number, and Octant Fuzzy Number are all introduced in this present study. Pendant Fuzzy Number, Hexant Fuzzy Number, and Octant Fuzzy Number,α-cuts are defined, as well as their mathematical operations. The numerical examples are utilised to conduct a comparative research of reliability using various Fuzzy Numbers, and their defuzzification is accomplished using various ways such as Signed Distance method, Graded Mean Integration Method and Centroid Method. The purpose of this study is to discover the most reliable value for a weaving machine.

A Fuzzy EOQ Model for Deteriorating Items With Allowable Shortage and Inspection Under the Trade Credit

2018 ◽  
pp. 233-249
Author(s):  
Chandra K. Jaggi ◽  
Bimal Kumar Mishra ◽  
T. C. Panda
Keyword(s):  
Trade Credit ◽  
Method Comparison ◽  
Deteriorating Items ◽  
Order Quantity ◽  
Centroid Method ◽  
Deterioration Rate ◽  
Eoq Model ◽  
Permissible Delay In Payment ◽  
Demand Rate ◽  
Fuzzy Cost

This chapter develops an economic order quantity model for deteriorating items with initial inspection, allowable shortage under the condition of permissible delay in payment by fuzzify the demand rate, deterioration rate and inspection parameter of non-defective parameter based on as triangular fuzzy numbers to fit the real word. The total fuzzy cost function has been defuzzified using signed distance and centroid method. Comparison between these two methods has also been discussed. The validity of the model has been established with the help of a hypothetical numerical example.

Solution of Basic Inventory Model in Fuzzy and Interval Environments

2017 ◽  
pp. 65-95
Author(s):  
Sankar Prasad Mondal
Keyword(s):  
Differential Equation ◽  
Fuzzy Number ◽  
Interval Number ◽  
Inventory Model ◽  
Time Dependent ◽  
Equation Approach ◽  
Numerical Examples ◽  
Fuzzy Environment

In this present paper a basic inventory model is solved in different imprecise environments. Four different cases are discussed: 1) Crisp inventory model, that is, the quantity at present and demand is crisp number; 2) Inventory model in fuzzy environment, that is, the quantity and demand both are fuzzy number; 3) Inventory model in interval environment, that is, the quantity and demand both are interval number and lastly; 4) Inventory model in time dependent fuzzy environment, that is, quantity and demand are both time dependent fuzzy number. Different numerical examples are used to illustrate the model as well as to compute the efficiency of imprecise differential equation approach to solve the model.

Fuzzification of EOQ Model Under the Condition of Permissible Delay in Payments

2012 ◽  
Vol 3 (2) ◽  
pp. 1-19 ◽  
Author(s):  
Chandra K. Jaggi ◽  
Anuj Sharma ◽  
Reena Jain
Keyword(s):  
Fuzzy Numbers ◽  
Delay Period ◽  
Order Quantity ◽  
Distance Method ◽  
Permissible Delay In Payments ◽  
Signed Distance ◽  
Eoq Model ◽  
Fuzzy Environment ◽  
Delay In Payments ◽  
The Cost

This paper formulates an economic order quantity inventory model under the condition of permissible delay in payments in fuzzy environment. All the parameters of the model, excluding permissible delay period and cycle length, are taken to be trapezoidal Fuzzy numbers. The arithmetic operations are defined under the function principle. The cost function has been defuzzified using signed distance method and thereby solved to obtain the optimal replenishment period. The numerical example is presented to show the validity of the model followed by sensitivity analysis.

scholarly journals A Study of an EOQ Model under Lock Fuzzy Environment

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 75 ◽  
Author(s):  
Suman Maity ◽  
Sujit Kumar De ◽  
Sankar Prasad Mondal
Keyword(s):  
Inventory Management ◽  
Numerical Study ◽  
Management Problem ◽  
Final State ◽  
Eoq Model ◽  
Fuzzy Environment ◽  
Demand Rate ◽  
Computer Based ◽  
The Cost ◽  
Cost Vector

The present article was developed for the economic order quantity (EOQ) inventory model under daytime, non-random, uncertain demand. In any inventory management problem, several parameters are involved that are basically flexible in nature with the progress of time. This model can be split into three different sub-models, assuming the demand rate and the cost vector associated with the model are non-randomly uncertain (i.e., fuzzy), and these may include some of the retained learning experiences of the decision-maker (DM). However, the DM has the option of revising his/her decision through the application of the appropriate key vector of the fuzzy locks in their final state. The basic novelty of the present model is that it includes a computer-based decision‐making process involving flowchart algorithms that are able to identify and update the key vectors automatically. The numerical study indicates that when all parameters are assumed to be fuzzy, the double keys of the fuzzy lock provide a more accurate optimum than other methods. Sensitivity analysis and graphical illustrations are made for better justification of the model.

A MODIFICATION OF THE INDEX OF LIOU AND WANG FOR RANKING FUZZY NUMBER

2007 ◽  
Vol 15 (04) ◽  
pp. 411-424 ◽  
Author(s):  
M. SOCORRO GARCIA ◽  
M. TERESA LAMATA
Keyword(s):  
Satisfactory Result ◽  
Coefficient Of Variation ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Mean Value ◽  
Weighted Mean ◽  
Numerical Examples ◽  
Centroid Point ◽  
Ranking Fuzzy Number ◽  
Index Of Optimism

Different methods have been proposed for ranking fuzzy numbers. These include methods based on distances, centroid point, coefficient of variation, and weighted mean value. However, there is still no method that can always give a satisfactory result to every situation; some are counterintuitive and not discriminating. This paper presents an approach for ranking fuzzy numbers with integral value that is an extension of the index of Liou and Wang. This method, that is independent of the type of membership function used, can rank more than two fuzzy numbers simultaneously. This ranking method use an index of optimism to reflect the decision maker's optimistic attitude, but rather it also contains an index of modality that represents the neutrality of the decision maker. The approach is illustrated with numerical examples.

scholarly journals The Economic Order Quantity in a Fuzzy Environment for a Periodic Inventory Model with Variable Demand

2022 ◽  
pp. 102-107
Author(s):  
K. Kalaiarasi ◽  
MARY HENRIETTA H ◽  
M. Sumathi ◽  
A. Stanley Raj
Keyword(s):  
Sensitivity Analysis ◽  
Numerical Analysis ◽  
Fuzzy Numbers ◽  
Economic Order Quantity ◽  
Economic Order ◽  
Order Quantity ◽  
Critical Part ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment

The technique of limiting expenditure plays a critical part in an organization's ability to govern the smooth operation of its management system. The economic order quantity (EOQ) is calculated by solving a nonlinear problem, and the best solution is investigated in a fuzzy and intuitionistic fuzzy environment. The overall cost is made up of several factors, such as demand, holding, and ordering costs. The demand and stock-out characteristics were both fuzzified using fuzzy and intuitionistic fuzzy numbers. The numerical analysis shows the comparison between the two fuzzy numbers through sensitivity analysis.

Deteriorating Inventory Model under Permissible Delay in Payments and Fuzzy Environment

2016 ◽  
pp. 77-99 ◽  
Author(s):  
Nita H. Shah ◽  
Sarla Pareek ◽  
Isha Sangal
Keyword(s):  
Solution Procedure ◽  
Inventory Model ◽  
Variable Cost ◽  
Selling Price ◽  
Gravity Method ◽  
Deterioration Rate ◽  
Eoq Model ◽  
Fuzzy Environment ◽  
Demand Rate ◽  
Delay In Payments

This paper deals with the problem of determining the EOQ model for deteriorating items in the fuzzy sense where delay in payments is permissible. The demand rate, ordering cost, selling price per item and deterioration rate are taken as fuzzy numbers. The total variable cost in fuzzy sense is de-fuzzified using the centre of gravity method. The solution procedure has been explained with the help of numerical example.

A study of an EOQ model with public-screened discounted items under cloudy fuzzy demand rate

2021 ◽  
pp. 1-12
Author(s):  
Suman Maity ◽  
Sujit Kumar De ◽  
Madhumangal Pal ◽  
Sankar Prasad Mondal
Keyword(s):  
Uncertain Demand ◽  
Order Quantity ◽  
Eoq Model ◽  
Fuzzy Environment ◽  
Proposed Model ◽  
Imperfect Items ◽  
Demand Rate ◽  
Computer Based ◽  
Fuzzy Degree ◽  
Graphical Illustration

This article deals with an economic order quantity inventory model of imperfect items under non-random uncertain demand. Here we consider the customers screen the imperfect items during the selling period. After a certain period of time, the imperfect items are sold at a discounted price. We split the model into three cases, assuming that the demand rate increases, decreases, and is constant in the discount period. Firstly, we solve the crisp model, and then the model is converted into a fuzzy environment. Here we consider the dense fuzzy, parabolic fuzzy, degree of fuzziness and cloudy fuzzy for a comparative study. The basic novelty of this paper is that a computer-based algorithm and flow chart have been given for the solution of the proposed model. Finally, sensitivity analysis and graphical illustration have been given to check the validity of the model.

Fuzzy Number Approximation

1998 ◽  
Vol 06 (01) ◽  
pp. 69-78 ◽  
Author(s):  
Mariano Jiménez ◽  
Juan Antonio Rivas
Keyword(s):  
Initial Data ◽  
Economic Model ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Number ◽  
Membership Functions ◽  
Simple Method ◽  
Non Linear

As the number of parameters involved in an economic model is often uncertain, we propose that it be estimated using fuzzy numbers. Since we move in an environment of uncertainty, it is logical to leave room for deviation in estimating membership functions. We should recall that when soft max-min operators are used, the resulting deviation is never greater than the variation introduced in estimating the initial data. Often, the result of our calculations is not a triangular fuzzy number. In this paper we study the value of approximating the resulting non-linear fuzzy number using a triangular fuzzy number having the same support and kernel. Finally, we present a simple method for weighing this approximation.

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