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.

scholarly journals Optimization of Inventory Model-Cost Parameters, Inventory and Lot Size as Fuzzy Numbers

2020 ◽  
Vol 10 (1) ◽  
pp. 365-368
Keyword(s):  
Fuzzy Numbers ◽  
Analytic Solution ◽  
Unit Cost ◽  
Optimal Solution ◽  
Inventory Model ◽  
Lot Size ◽  
Fuzzy Environment ◽  
Demand Rate ◽  
Cost Parameters ◽  
Fuzzy Parameters

In general, the demand rate and the unit cost of the items remains constant inspite of lot size in inventory models. But in reality, the demand rate and the unit cost of the items are connected together. In this research, demand dependent unit cost inventory model is considered where different cost parameters, maximum inventory and the lot size of the model are taken under fuzzy environment. First an analytic solution of the crisp model is obtained by the method of calculus where the inventory parameters are exact and deterministic. Later, the problem is developed with fuzzy parameters where inaccuracy has been introduced through triangular membership function.Then the defuzzification of the model is done by using the method of Graded mean integration. An optimal solution is obtained using Karush Kuhn-Tucker conditions approach. An illustrative model is done and an analysis of total cost for different measures of possibility are performed and tabulated.

scholarly journals Goal programming approach for solving heptagonal fuzzy transportation problem under budgetry constraint

2020 ◽  
Vol 30 (1) ◽  
Author(s):  
Hamiden Abd El-Wahed Khalifa
Keyword(s):  
Goal Programming ◽  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Optimal Solution ◽  
Programming Approach ◽  
Solution Approach ◽  
Fuzzy Transportation Problem ◽  
The Stability ◽  
The Cost

Transportation problem (TP) is a special type of linear programming problem (LPP) where the objective is to minimize the cost of distributing a product from several sources (or origins) to some destinations. This paper addresses a transportation problem in which the costs, supplies, and demands are represented as heptagonal fuzzy numbers. After converting the problem into the corresponding crisp TP using the ranking method, a goal programming (GP) approach is applied for obtaining the optimal solution. The advantage of GP for the decision-maker is easy to explain and implement in real life transportation. The stability set of the first kind corresponding to the optimal solution is determined. A numerical example is given to highlight the solution approach.

scholarly journals Managing cost uncertainties in transportation and assignment problems

1998 ◽  
Vol 2 (1) ◽  
pp. 65-104 ◽  
Author(s):  
V. Adlakha ◽  
H. Arsham
Keyword(s):  
Time Lag ◽  
Real Life ◽  
Optimal Solution ◽  
Global Market ◽  
Solution Algorithm ◽  
Assignment Problems ◽  
The Stability ◽  
Order Assignment ◽  
Cost Parameters ◽  
The Cost

In a fast changing global market, a manager is concerned with cost uncertainties of the cost matrix in transportation problems (TP) and assignment problems (AP).A time lag between the development and application of the model could cause cost parameters to assume different values when an optimal assignment is implemented. The manager might wish to determine the responsiveness of the current optimal solution to such uncertainties. A desirable tool is to construct a perturbation set (PS) of cost coeffcients which ensures the stability of an optimal solution under such uncertainties.The widely-used methods of solving the TP and AP are the stepping-stone (SS) method and the Hungarian method, respectively. Both methods fail to provide direct information to construct the needed PS. An added difficulty is that these problems might be highly pivotal degenerate. Therefore, the sensitivity results obtained via the available linear programming (LP) software might be misleading.We propose a unified pivotal solution algorithm for both TP and AP. The algorithm is free of pivotal degeneracy, which may cause cycling, and does not require any extra variables such as slack, surplus, or artificial variables used in dual and primal simplex. The algorithm permits higher-order assignment problems and side-constraints. Computational results comparing the proposed algorithm to the closely-related pivotal solution algorithm, the simplex, via the widely-used pack-age Lindo, are provided. The proposed algorithm has the advantage of being computationally practical, being easy to understand, and providing useful information for managers. The results empower the manager to assess and monitor various types of cost uncertainties encountered in real-life situations. Some illustrative numerical examples are also presented.

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.

scholarly journals A fuzzy multi-objective linear programming with interval-typed triangular fuzzy numbers

2019 ◽  
Vol 17 (1) ◽  
pp. 607-626 ◽  
Author(s):  
Chunquan Li
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Optimal Solution ◽  
Objective Functions ◽  
Triangular Fuzzy Numbers ◽  
Matlab Toolbox ◽  
Multi Objective ◽  
Cut Set ◽  
The Stability

Abstract A multi-objective linear programming problem (ITF-MOLP) is presented in this paper, in which coefficients of both the objective functions and constraints are interval-typed triangular fuzzy numbers. An algorithm of the ITF-MOLP is provided by introducing the cut set of interval-typed triangular fuzzy numbers and the dominance possibility criterion. In particular, for a given level, the ITF-MOLP is converted to the maximization of the sum of membership degrees of each objective in ITF-MOLP, whose membership degrees are established based on the deviation from optimal solutions of individual objectives, and the constraints are transformed to normal inequalities by utilizing the dominance possibility criterion when compared with two interval-typed triangular fuzzy numbers. Then the equivalent linear programming model is obtained which could be solved by Matlab toolbox. Finally several examples are provided to illuminate the proposed method by comparing with the existing methods and sensitive analysis demonstrates the stability of the optimal solution.

scholarly journals The multisourcing model of safe supply chain management

2020 ◽  
Vol 1 (4) ◽  
pp. 19-26
Author(s):  
Lesia Kostiuchenko ◽  
Keyword(s):  
Rapid Change ◽  
Optimal Solution ◽  
Multiple Sources ◽  
Internal Resources ◽  
Supply Channel ◽  
Current Context ◽  
The Right ◽  
Supply Costs ◽  
The Cost ◽  
A Company

The logistics outsourcing concept is to address the feasibility of using its own capabilities and sources of supply to perform certain logistics functions that the company can entrust to an external partner. However, in the current context of rapid change, it is important to make a quick and efficient decision on sources of supply: regardless of the sourcing model of the company. That is, what is the usual supply strategy for the company. Security (reliability and stability) of supplies is at the first place. Therefore, a quick decision on the optimal source of supply is the optimal solution. More precisely is the optimal combination of the use of internal resources of the company and the resources of external suppliers. Multisourcing is a type of outsourcing used by many companies in conditions of frequent changes. Unlike traditional outsourcing, the multisourcing model involves the use of several different vendors for the same product at different times. The decision depends on the level of security. For example, with multiple sources, a company can choose the best supplier for a particular task. By outsourcing certain operations, a company can perform critical tasks on its own. These actions can achieve optimization of operating costs. However, when deciding on multisourcing, it is important to assess the risks. It is important to estimate the cost of supply according to different options. You should compare the results of calculations and compare with the risks. These actions can ensure security of supply. So, the proposed economic and mathematical model is able to help to make the right decision of the rational choice of supply channel from several alternatives and, as a consequence, to achieve the following main goals: improving the quality of supply management; reduction of the logistics cycle; reduction of supply costs; increase the reliability of supply

scholarly journals Group Replacement Strategy under Fuzzy Methods

2019 ◽  
Vol 9 (1S5) ◽  
pp. 250-254
Keyword(s):  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Active Role ◽  
Replacement Policy ◽  
Replacement Strategy ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Methods ◽  
Fuzzy Environment

Intuitionistic Fuzzy Numbers play an active role in finding an optimal solution for replacement problems under vague and uncertain situations. This paper gives a group replacement policy under fuzzy environment. Here all the costs and the number of units are taken as Triangular Intuitionistic Fuzzy Numbers (TIFNs). An example is used for illustration of the policy

scholarly journals Stability of Solutions for Parametric Inverse Nonlinear Cost Transportation Problem

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2027
Author(s):  
Abd Allah A. Mousa ◽  
Yousria Abo-Elnaga
Keyword(s):  
Nonlinear Programming ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Solution Stability ◽  
Tuning Parameters ◽  
Input Parameters ◽  
Feasible Alternative ◽  
The Stability ◽  
The Cost

This paper investigates the solution for an inverse of a parametric nonlinear transportation problem, in which, for a certain values of the parameters, the cost of the unit transportation in the basic problem are adapted as little as possible so that the specific feasible alternative become an optimal solution. In addition, a solution stability set of these parameters was investigated to keep the new optimal solution (feasible one) is unchanged. The idea of this study based on using a tuning parameters λ∈Rm in the function of the objective and input parameters υ∈Rl in the set of constraint. The inverse parametric nonlinear cost transportation problem P(λ,υ), where the tuning parameters λ∈Rm in the objective function are tuned (adapted) as less as possible so that the specific feasible solution x∘ has been became the optimal ones for a certain values of υ∈Rl, then, a solution stability set of the parameters was investigated to keep the new optimal solution x∘ unchanged. The proposed method consists of three phases. Firstly, based on the optimality conditions, the parameter λ∈Rm are tuned as less as possible so that the initial feasible solution x∘ has been became new optimal solution. Secondly, using input parameters υ∈Rl resulting problem is reformulated in parametric form P(υ). Finally, based on the stability notions, the availability domain of the input parameters was detected to keep its optimal solution unchanged. Finally, to clarify the effectiveness of the proposed algorithm not only for the inverse transportation problems but also, for the nonlinear programming problems; numerical examples treating the inverse nonlinear programming problem and the inverse transportation problem of minimizing the nonlinear cost functions are presented.

Picture fuzzy MABAC method based on prospect theory for multiple attribute group decision making and its application to suppliers selection

2022 ◽  
pp. 1-11
Author(s):  
Zhiwei Jiang ◽  
Guiwu Wei ◽  
Yanfeng Guo
Keyword(s):  
Prospect Theory ◽  
Manufacturing Industry ◽  
Fuzzy Numbers ◽  
Purchasing Management ◽  
Fuzzy Environment ◽  
Multiple Attribute ◽  
Todim Method ◽  
Picture Fuzzy Sets ◽  
The Cost

In the garment manufacturing industry, purchasing management is an important link. The materials of making clothes often need high cost. In addition, customers put forward a request in the quality of clothes. Thus, choosing an optimal supplier is an essential part of job. Reaching cooperation with an optimal supplier not only can help garment manufacturer improve the quality of clothes but also is benefit to reduce the cost of producing. Most importantly, it can improve the competitiveness of manufacture enterprises. So, it is important for managers to find an optimal supplier and make a cooperation with it. In this paper, we analysis an issue about choosing an optimal supplier during four different suppliers. With analyzing this problem, we can introduce an extended method under picture fuzzy environment to evaluate and choose an optimal supplier. In this article, we describe some basic knowledges about picture fuzzy sets (PFSs) and picture fuzzy numbers (PFNs). Then, we introduce the extension of MABAC method which is on the basis of prospect theory (PT) with picture fuzzy numbers (PF-PT-MABAC) and utilize the PF-PT-MABAC model to evaluate different suppliers to choose an optimal supplier. Finally, we compare the result of PF-PT-MABAC with the result of traditional MABAC, PFWG operators and traditional TODIM method to test the efficiency of PF-PT-MABAC model.

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