scholarly journals Classical Fuzzy Retrial Queue with Working Vacation using Hexagonal Fuzzy Numbers

2021 ◽  
Vol 2070 (1) ◽  
pp. 012018
Author(s):  
G. Kannadasan ◽  
V. Padmavathi
Keyword(s):  
Sojourn Time ◽  
Fuzzy Numbers ◽  
Retrial Queue ◽  
Numerical Results ◽  
Working Vacation ◽  
Fuzzy Environment ◽  
Fuzzy Techniques

Abstract Using fuzzy techniques “Classical Fuzzy Retrial Queue with Working Vacation(WV) using Hexagonal Fuzzy Numbers” is discussed in this paper. We acquire model in fuzzy environment as the average orbit length, Probability(Pr) that the server busy, and Pr(the server is in a WV period), the sojourn time of a customer in the queue. Finally numerical results are presented.

INDIVIDUAL EQUILIBRIUM DYNAMIC ROUTING IN A MULTIPLE SERVER RETRIAL QUEUE

2000 ◽  
Vol 14 (1) ◽  
pp. 9-26 ◽  
Author(s):  
Anthony C. Brooms
Keyword(s):  
Nash Equilibrium ◽  
Poisson Process ◽  
Sojourn Time ◽  
Service System ◽  
Transmission Rate ◽  
Retrial Queue ◽  
Dynamic Learning ◽  
Arrival Times ◽  
The Public ◽  
Expected Sojourn Time

Customers arrive sequentially to a service system where the arrival times form a Poisson process of rate λ. The system offers a choice between a private channel and a public set of channels. The transmission rate at each of the public channels is faster than that of the private one; however, if all of the public channels are occupied, then a customer who commits itself to using one of them attempts to connect after exponential periods of time with mean μ−1. Once connection to a public channel has been made, service is completed after an exponential period of time, with mean ν−1. Each customer chooses one of the two service options, basing its decision on the number of busy channels and reapplying customers, with the aim of minimizing its own expected sojourn time. The best action for an individual customer depends on the actions taken by subsequent arriving customers. We establish the existence of a unique symmetric Nash equilibrium policy and show that its structure is characterized by a set of threshold-type strategies; we discuss the relevance of this concept in the context of a dynamic learning scenario.

scholarly journals Vendor-Buyers relationship model for deteriorating items with shortages, fuzzy trapezoidal costs and inflation

2013 ◽  
Vol 23 (1) ◽  
pp. 73-85 ◽  
Author(s):  
Chaman Singh ◽  
S.R. Singh
Keyword(s):  
Optimal Policy ◽  
Fuzzy Numbers ◽  
Deteriorating Items ◽  
Inventory Cost ◽  
Fuzzy Environment ◽  
Relationship Model ◽  
Present Worth ◽  
Total Inventory ◽  
Integrated Cost ◽  
Representation Method

In this paper, an integrated inventory model is developed from the perspective of a single vendor and multi-buyers for deteriorating items under fuzzy environment and inflation. In the development of the model, it is assumed that all costs parameters, demand and the production rates are imprecise in nature; they are represented by the trapezoidal fuzzy numbers, as these parameters are not constant and can be disturbed due to daily market changes. We use function principle as arithmetic operations to find the total inventory cost in fuzzy sense and Graded Mean - Integration Representation Method to defuzzify the fuzzy total inventory cost. Inflation is used to find the present worth of total cost. Since the optimal policy of buyers may not be the most economical for a vendor, thus to deal with this situation, integrated cost policy is used to reach the optimal policy. Finally, a numerical example is given to illustrate the model.

scholarly journals Inventory Model with Demand Dependant on Unit Cost- Input Parameters as Triangular Fuzzy Numbers

2021 ◽  
Vol 12 (2) ◽  
Author(s):  
R. Kasthuri, Et. al.
Keyword(s):  
Fuzzy Numbers ◽  
Unit Cost ◽  
Inventory Model ◽  
Average Total Cost ◽  
Triangular Fuzzy Numbers ◽  
Lot Size ◽  
Distance Method ◽  
Total Cost ◽  
Signed Distance ◽  
Fuzzy Environment

This paper considers an inventory model in which the shortages are backlogged and the demand is dependent on unit cost. An optimum value for average total cost is calculated by considering various input costs, lot size and maximum inventory under fuzzy environment. The process of defuzzification is done by using the signed distance method. Numerical example and sensitivity analysis is given for calculating both crisp and fuzzy values of the total cost.

scholarly journals Multi Objective Multi Mode Project Management Problem in Triangular Fuzzy Environment

2020 ◽  
Vol 9 (2) ◽  
pp. 1772-1781
Keyword(s):  
Project Management ◽  
Fuzzy Numbers ◽  
Critical Path ◽  
Decision Makers ◽  
Programming Approach ◽  
Management Problem ◽  
Linguistic Variables ◽  
Multi Objective ◽  
Fuzzy Environment ◽  
Multi Mode

Execution of any project with optimum duration, cost, quality and risk is very significant for project administrators in recent very competitive commercial situation. Sometimes it is not possible to have detailed earlier statistics about project criteria. In such situations, estimation of different Decision makers are considered in linguistic variables and altered into triangular fuzzy numbers as fuzzy numbers have ability to deal with vagueness. In this paper, we frame a new multi-mode multi objective critical path problem and suggest a possibilistic methodology to find critical path for a project where three decision makers’ views are considered as three modes of execution in terms of linguistic variables. We have formulated model of multiple mode in project network problem and find its solution with fuzzy programming approach with exponential membership and linear membership function. The proposed approach is useful to solve multi-mode project management problem which calculates optimal critical path according to four criteria- time, cost, risk and quality with three activities modes of execution in fuzzy environment.

A Study on Cooperative Continuous Static Games without Differentiability under Fuzzy Environment

2022 ◽  
Vol 11 (1) ◽  
pp. 0-0
Keyword(s):  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Solution Concept ◽  
Proper Understanding ◽  
Fuzzy Environment ◽  
The Stability ◽  
The Right ◽  
The Cost ◽  
Stability Sets ◽  
Fuzzy Parameters

In this study, a fuzzy cooperative continuous static game (PQFCCSG) with n players having fuzzy parameters in all of the cost functions and the right- hand-side of constraints is characterized. Their fuzzy parameters are represented by piecewise quadratic fuzzy numbers. The α-pareto optimal solution concept is specified. In addition, the stability sets of the first and second kind without differentiability are conceptualized and established. An illustrated numerical example is discussed for proper understanding and interpretation of the proposed concept.

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.

A Novel Ranking Approach to Solving Fully LR-Intuitionistic Fuzzy Transportation Problems

2018 ◽  
Vol 15 (01) ◽  
pp. 95-112 ◽  
Author(s):  
Abhishekh ◽  
A. K. Nishad
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Ranking Functions ◽  
Transportation Problems ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Fuzzy Transportation Problem

To the extent of our knowledge, there is no method in fuzzy environment to solving the fully LR-intuitionistic fuzzy transportation problems (LR-IFTPs) in which all the parameters are represented by LR-intuitionistic fuzzy numbers (LR-IFNs). In this paper, a novel ranking function is proposed to finding an optimal solution of fully LR-intuitionistic fuzzy transportation problem by using the distance minimizer of two LR-IFNs. It is shown that the proposed ranking method for LR-intuitionistic fuzzy numbers satisfies the general axioms of ranking functions. Further, we have applied ranking approach to solve an LR-intuitionistic fuzzy transportation problem in which all the parameters (supply, cost and demand) are transformed into LR-intuitionistic fuzzy numbers. The proposed method is illustrated with a numerical example to show the solution procedure and to demonstrate the efficiency of the proposed method by comparison with some existing ranking methods available in the literature.

Extending TOPSIS in fuzzy environment by using the nearest weighted interval approximation of fuzzy numbers

2014 ◽  
Vol 27 (6) ◽  
pp. 2725-2736 ◽  
Author(s):  
Mohammad Izadikhah ◽  
Abolfazl Saeidifar ◽  
Razieh Roostaee
Keyword(s):  
Fuzzy Numbers ◽  
Fuzzy Environment ◽  
Interval Approximation

scholarly journals M/M/1 Retrial Queue with Working Vacation Interruption and Feedback under N-Policy

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Li Tao ◽  
Liyuan Zhang ◽  
Shan Gao
Keyword(s):  
Retrial Queue ◽  
Stochastic Decomposition ◽  
Service Rate ◽  
Working Vacation ◽  
Stationary Probability Distribution ◽  
The Matrix ◽  
Vacation Interruption ◽  
Necessary And Sufficient ◽  
Vacation Period ◽  
Conditional Stochastic Decomposition

We consider an M/M/1 retrial queue with working vacations, vacation interruption, Bernoulli feedback, and N-policy simultaneously. During the working vacation period, customers can be served at a lower rate. Using the matrix-analytic method, we get the necessary and sufficient condition for the system to be stable. Furthermore, the stationary probability distribution and some performance measures are also derived. Moreover, we prove the conditional stochastic decomposition for the queue length in the orbit. Finally, we present some numerical examples and use the parabolic method to search the optimum value of service rate in working vacation period.

Fuzzy Reliability of an Imprecise Failure to Start of an Automobile Using Pseudo-Parabolic Fuzzy Numbers

2018 ◽  
Vol 14 (03) ◽  
pp. 323-341 ◽  
Author(s):  
F. Abbasi
Keyword(s):  
Fuzzy Systems ◽  
Fuzzy Numbers ◽  
Extension Principle ◽  
Fuzzy Arithmetic ◽  
Fuzzy Reliability ◽  
Fuzzy Environment ◽  
Distributed Components ◽  
Proposed Model ◽  
New Type ◽  
The Membership Function

In this paper, we propose the notion of pseudo-parabolic fuzzy numbers and the component failure probabilities are considered as a new type of fuzzy number as pseudo-parabolic to incorporate the uncertainties in the parameter, due to a more realistic estimate of them. Then, we analyze the reliability of fuzzy system (particularly, series and parallel system) with independent and non-identically distributed components, and using the new operations of TA [F. Abbasi et al., Journal of Intelligent and Fuzzy Systems 29 (2015) 851–861], due to the smaller results support, easier calculations and special properties than fuzzy arithmetic operations based on the extension principle (in the domain of the membership function) and the interval arithmetic (in the domain of the [Formula: see text]-cuts). We provide a more realistic fuzzy reliability analysis. Finally, an imprecise failure to start of an automobile is considered in fuzzy environment. The reliability of components of the proposed model is considered as pseudo-parabolic fuzzy numbers.

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