Multi Objective Multi Mode Project Management Problem in Triangular Fuzzy Environment

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.

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Possibilistic Distribution for Selection of Critical Path in Multi Objective Multi-Mode Problem with Trapezoidal Fuzzy Number

International Journal of Recent Technology and Engineering - 2 ◽

10.35940/ijrte.d4372.118419 ◽

2019 ◽

Vol 8 (4) ◽

pp. 10833-10842

Keyword(s):

Fuzzy Numbers ◽

Critical Path ◽

Fuzzy Programming ◽

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. In this paper 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

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Extended TOPSIS Method for Supplier Selection under Picture Hesitant Fuzzy Environment Using Linguistic Variables

Journal of Mathematics ◽

10.1155/2021/6652586 ◽

2021 ◽

Vol 2021 ◽

pp. 1-28

Author(s):

Rabia Ambrin ◽

Muhammad Ibrar ◽

Manuel De La Sen ◽

Ihsan Rabbi ◽

Asghar Khan

Keyword(s):

Fuzzy Numbers ◽

Fuzzy Topsis ◽

Vital Role ◽

Decision Makers ◽

Linguistic Variables ◽

Comparison Analysis ◽

Topsis Method ◽

Practical Applications ◽

Fuzzy Environment ◽

Intuitionistic Fuzzy Topsis

The main purpose of this planned manuscript is to establish an algorithm for the solution of multiattribute decision-making (MADM) issues, where the experts utilizing linguistic variables provide the information about attributes in the form of picture hesitant fuzzy numbers. So, for the solution of these kinds of issues, we develop the TOPSIS algorithm under picture hesitant fuzzy environment using linguistic variables, which plays a vital role in practical applications, notably MADM issues, where the decision information is arranged by the decision-makers (DMs) in the form of picture hesitant fuzzy numbers. Finally, a sample example is given as an application and appropriateness of the planned method. At the end, we conduct comparison analysis of the planned method with picture fuzzy TOPSIS method and intuitionistic fuzzy TOPSIS method.

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Goal programming approach for solving multi-objective fractional transportation problem with fuzzy parameters

RAIRO - Operations Research ◽

10.1051/ro/2019005 ◽

2019 ◽

Vol 53 (1) ◽

pp. 157-178 ◽

Cited By ~ 2

Author(s):

Paraman Anukokila ◽

Bheeman Radhakrishnan ◽

Antony Anju

Keyword(s):

Goal Programming ◽

Transportation Problem ◽

Fuzzy Numbers ◽

Decision Makers ◽

Programming Approach ◽

Multi Objective ◽

Proposed Model ◽

Fuzzy Goal ◽

Fuzzy Parameters ◽

Interval Valued

In this paper, authors studied a goal programming approach for solving multi-objective fractional transportation problem by representing the parameters (γ, δ) in terms of interval valued fuzzy numbers. Fuzzy goal programming problem with multiple objectives is difficult for the decision makers to determine the goal valued of each objective precisely. The proposed model presents a special type of non-linear (hyperbolic) membership functions to solve multi-objective fractional transportation problem with fuzzy parameters. To illustrate the proposed method numerical examples are solved.

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Multi-objective Optimization Algorithms with the Island Metaheuristic for Effective Project Management Problem Solving

Organizacija ◽

10.1515/orga-2017-0027 ◽

2017 ◽

Vol 50 (4) ◽

pp. 364-373 ◽

Cited By ~ 3

Author(s):

Christina Brester ◽

Ivan Ryzhikov ◽

Eugene Semenkin

Keyword(s):

Decision Making ◽

Project Management ◽

Optimization Problem ◽

Decision Makers ◽

Management Problem ◽

Multi Objective Optimization ◽

Financial Investment ◽

Financial Responsibility ◽

Multi Objective ◽

Decision Making Problem

Abstract Background and Purpose: In every organization, project management raises many different decision-making problems, a large proportion of which can be efficiently solved using specific decision-making support systems. Yet such kinds of problems are always a challenge since there is no time-efficient or computationally efficient algorithm to solve them as a result of their complexity. In this study, we consider the problem of optimal financial investment. In our solution, we take into account the following organizational resource and project characteristics: profits, costs and risks. Design/Methodology/Approach: The decision-making problem is reduced to a multi-criteria 0-1 knapsack problem. This implies that we need to find a non-dominated set of alternative solutions, which are a trade-off between maximizing incomes and minimizing risks. At the same time, alternatives must satisfy constraints. This leads to a constrained two-criterion optimization problem in the Boolean space. To cope with the peculiarities and high complexity of the problem, evolution-based algorithms with an island meta-heuristic are applied as an alternative to conventional techniques. Results: The problem in hand was reduced to a two-criterion unconstrained extreme problem and solved with different evolution-based multi-objective optimization heuristics. Next, we applied a proposed meta-heuristic combining the particular algorithms and causing their interaction in a cooperative and collaborative way. The obtained results showed that the island heuristic outperformed the original ones based on the values of a specific metric, thus showing the representativeness of Pareto front approximations. Having more representative approximations, decision-makers have more alternative project portfolios corresponding to different risk and profit estimations. Since these criteria are conflicting, when choosing an alternative with an estimated high profit, decision-makers follow a strategy with an estimated high risk and vice versa. Conclusion: In the present paper, the project portfolio decision-making problem was reduced to a 0-1 knapsack constrained multi-objective optimization problem. The algorithm investigation confirms that the use of the island meta-heuristic significantly improves the performance of genetic algorithms, thereby providing an efficient tool for Financial Responsibility Centres Management.

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The LR-Type Fuzzy Multi-Objective Vendor Selection Problem in Supply Chain Management

Mathematics ◽

10.3390/math8091621 ◽

2020 ◽

Vol 8 (9) ◽

pp. 1621

Author(s):

Irfan Ali ◽

Armin Fügenschuh ◽

Srikant Gupta ◽

Umar Muhammad Modibbo

Keyword(s):

Supply Chain ◽

Supply Chain Management ◽

Real Life ◽

Selection Problem ◽

Programming Approach ◽

Vendor Selection ◽

Chain Management ◽

Multi Objective ◽

Fuzzy Environment ◽

Proposed Model

Vendor selection is an established problem in supply chain management. It is regarded as a strategic resource by manufacturers, which must be managed efficiently. Any inappropriate selection of the vendors may lead to severe issues in the supply chain network. Hence, the desire to develop a model that minimizes the combination of transportation, deliveries, and ordering costs under uncertainty situation. In this paper, a multi-objective vendor selection problem under fuzzy environment is solved using a fuzzy goal programming approach. The vendor selection problem was modeled as a multi-objective problem, including three primary objectives of minimizing the transportation cost; the late deliveries; and the net ordering cost subject to constraints related to aggregate demand; vendor capacity; budget allocation; purchasing value; vendors’ quota; and quantity rejected. The proposed model input parameters are considered to be LR fuzzy numbers. The effectiveness of the model is illustrated with simulated data using R statistical package based on a real-life case study which was analyzed using LINGO 16.0 optimization software. The decision on the vendor’s quota allocation and selection under different degree of vagueness in the information was provided. The proposed model can address realistic vendor selection problem in the fuzzy environment and can serve as a useful tool for multi-criteria decision-making in supply chain management.

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Significance of multi-objective optimization in logistics problem for multi-product supply chain network under the intuitionistic fuzzy environment

Complex & Intelligent Systems ◽

10.1007/s40747-021-00326-9 ◽

2021 ◽

Author(s):

Srikant Gupta ◽

Ahteshamul Haq ◽

Irfan Ali ◽

Biswajit Sarkar

Keyword(s):

Decision Making ◽

Supply Chain ◽

Real Life ◽

Decision Makers ◽

Supply Chain Network ◽

Multi Objective ◽

Intuitionistic Fuzzy ◽

Fuzzy Environment ◽

Hierarchical Decision

AbstractDetermining the methods for fulfilling the continuously increasing customer expectations and maintaining competitiveness in the market while limiting controllable expenses is challenging. Our study thus identifies inefficiencies in the supply chain network (SCN). The initial goal is to obtain the best allocation order for products from various sources with different destinations in an optimal manner. This study considers two types of decision-makers (DMs) operating at two separate groups of SCN, that is, a bi-level decision-making process. The first-level DM moves first and determines the amounts of the quantity transported to distributors, and the second-level DM then rationally chooses their amounts. First-level decision-makers (FLDMs) aimed at minimizing the total costs of transportation, while second-level decision-makers (SLDM) attempt to simultaneously minimize the total delivery time of the SCN and balance the allocation order between various sources and destinations. This investigation implements fuzzy goal programming (FGP) to solve the multi-objective of SCN in an intuitionistic fuzzy environment. The FGP concept was used to define the fuzzy goals, build linear and nonlinear membership functions, and achieve the compromise solution. A real-life case study was used to illustrate the proposed work. The obtained result shows the optimal quantities transported from the various sources to the various destinations that could enable managers to detect the optimum quantity of the product when hierarchical decision-making involving two levels. A case study then illustrates the application of the proposed work.

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Application of multi-objective optimization based on genetic algorithm for sustainable strategic supplier selection under fuzzy environment

Journal of Industrial Engineering and Management ◽

10.3926/jiem.2078 ◽

2017 ◽

Vol 10 (2) ◽

pp. 188 ◽

Cited By ~ 5

Author(s):

Muhammad Hashim ◽

Muhammad Nazam ◽

Liming Yao ◽

Sajjad Ahmad Baig ◽

Muhammad Abrar ◽

...

Keyword(s):

Genetic Algorithm ◽

Supply Chain ◽

Supplier Selection ◽

Decision Makers ◽

Quality Level ◽

Multi Objective Optimization ◽

Multi Objective ◽

Fuzzy Environment ◽

Proposed Model ◽

Textile Sector

Purpose: The incorporation of environmental objective into the conventional supplier selection practices is crucial for corporations seeking to promote green supply chain management (GSCM). Challenges and risks associated with green supplier selection have been broadly recognized by procurement and supplier management professionals. This paper aims to solve a Tetra “S” (SSSS) problem based on a fuzzy multi-objective optimization with genetic algorithm in a holistic supply chain environment. In this empirical study, a mathematical model with fuzzy coefficients is considered for sustainable strategic supplier selection (SSSS) problem and a corresponding model is developed to tackle this problem.Design/methodology/approach: Sustainable strategic supplier selection (SSSS) decisions are typically multi-objectives in nature and it is an important part of green production and supply chain management for many firms. The proposed uncertain model is transferred into deterministic model by applying the expected value mesurement (EVM) and genetic algorithm with weighted sum approach for solving the multi-objective problem. This research focus on a multi-objective optimization model for minimizing lean cost, maximizing sustainable service and greener product quality level. Finally, a mathematical case of textile sector is presented to exemplify the effectiveness of the proposed model with a sensitivity analysis.Findings: This study makes a certain contribution by introducing the Tetra ‘S’ concept in both the theoretical and practical research related to multi-objective optimization as well as in the study of sustainable strategic supplier selection (SSSS) under uncertain environment. Our results suggest that decision makers tend to select strategic supplier first then enhance the sustainability.Research limitations/implications: Although the fuzzy expected value model (EVM) with fuzzy coefficients constructed in present research should be helpful for solving real world problems. A detailed comparative analysis by using other algorithms is necessary for solving similar problems of agriculture, pharmaceutical, chemicals and services sectors in future.Practical implications: It can help the decision makers for ordering to different supplier for managing supply chain performance in efficient and effective manner. From the procurement and engineering perspectives, minimizing cost, sustaining the quality level and meeting production time line is the main consideration for selecting the supplier. Empirically, this can facilitate engineers to reduce production costs and at the same time improve the product quality.Originality/value: In this paper, we developed a novel multi-objective programming model based on genetic algorithm to select sustainable strategic supplier (SSSS) under fuzzy environment. The algorithm was tested and applied to solve a real case of textile sector in Pakistan. The experimental results and comparative sensitivity analysis illustrate the effectiveness of our proposed model.

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On characterizing solution for multi-objective fractional two-stage solid transportation problem under fuzzy environment

Journal of Intelligent Systems ◽

10.1515/jisys-2020-0095 ◽

2021 ◽

Vol 30 (1) ◽

pp. 620-635

Author(s):

Hamiden Abd El-Wahed Khalifa ◽

Pavan Kumar ◽

Majed. G. Alharbi

Keyword(s):

Membership Function ◽

Transportation Problem ◽

Programming Approach ◽

Solid Transportation Problem ◽

Two Stage ◽

Multi Objective ◽

Fuzzy Environment ◽

The Stability ◽

Fuzzy Cost ◽

Necessary And Sufficient

Abstract This article attempts to study cost minimizing multi-objective fractional solid transportation problem with fuzzy cost coefficients c ˜ i j k r {\tilde{c}}_{ijk}^{r} , fuzzy supply quantities a ˜ i {\tilde{a}}_{i} , fuzzy demands b ˜ j {\tilde{b}}_{j} , and/or fuzzy conveyances e ˜ k {\tilde{e}}_{k} . The fuzzy efficient concept is introduced in which the crisp efficient solution is extended. A necessary and sufficient condition for the solution is established. Fuzzy geometric programming approach is applied to solve the crisp problem by defining membership function so as to obtain the optimal compromise solution of a multi-objective two-stage problem. A linear membership function for the objective function is defined. The stability set of the first kind is defined and determined. A numerical example is given for illustration and to check the validity of the proposed approach.

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Multi-attributive border approximation area comparison (MABAC) method based on normal q-rung orthopair fuzzy environment

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-201526 ◽

2021 ◽

pp. 1-27

Author(s):

Peide Liu ◽

Qian Pan ◽

Hongxue Xu

Keyword(s):

Membership Function ◽

Fuzzy Numbers ◽

Strong Stability ◽

Decision Makers ◽

Uncertain Information ◽

Intuitionistic Fuzzy Number ◽

Attribute Weights ◽

Fuzzy Environment ◽

Operational Laws ◽

Evaluation Information

The normal intuitionistic fuzzy number (NIFN), which membership function and non-membership function are expressed by normal fuzzy numbers (NFNs), can better describe the normal distribution phenomenon in the real world, but it cannot deal with the situation where the sum of membership function and non-membership function is greater than 1. In order to make up for this defect, based on the idea of q-rung orthopair fuzzy numbers (q-ROFNs), we put forward the concept of normal q-rung orthopair fuzzy numbers (q-RONFNs), and its remarkable characteristic is that the sum of the qth power of membership function and the qth power of non-membership function is less than or equal to 1, so it can increase the width of expressing uncertain information for decision makers (DMs). In this paper, firstly, we give the basic definition and operational laws of q-RONFNs, propose two related operators to aggregate evaluation information from DMs, and develop an extended indifference threshold-based attribute ratio analysis (ITARA) method to calculate attribute weights. Then considering the multi-attributive border approximation area comparison (MABAC) method has strong stability, we combine MABAC with q-RONFNs, put forward the q-RONFNs-MABAC method, and give the concrete decision steps. Finally, we apply the q-RONFNs-MABAC method to solve two examples, and prove the effectiveness and practicability of our proposed method through comparative analysis.

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Multi-Criteria Decision-Making for Airport Operation Performance Using Triangular Fuzzy Numbers

Scientific Inquiry and Review ◽

10.32350/sir.33.01 ◽

2019 ◽

Vol 3 (3) ◽

pp. 01-15

Author(s):

Adeel Ahmad ◽

Sana Akram ◽

Muhammad Farhan Tabassum ◽

Alia Kausar ◽

Nousheen Ilyas

Keyword(s):

Decision Making ◽

Fuzzy Numbers ◽

Decision Makers ◽

Multi Criteria Decision Making ◽

Triangular Fuzzy Numbers ◽

Operation Performance ◽

Linguistic Form ◽

Fuzzy Environment ◽

Simple Additive Weighting

This paper advocates Multi-Criteria Decision-Making (MCDM) which evaluates the operation performance of airports using Fuzzy Simple Additive Weighting (FSAW) method. Assigned weights by decision- makers were in a linguistic form. These linguistic forms were converted into triangular fuzzy numbers. We chose three airports designated as A1, A2 and A3 and examined by four decision makers D1, D2, D3 and D4 under a fuzzy environment for performance against the chosen criteria. FSAW method gives similar decision results which shows that this method is effective, relevant and reliable for this kind of MCDM.

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