Fuzzy Multi-objective Programming Approach Research Articles

Multi-skill resource-constrained project scheduling problem considering overlapping: fuzzy multi-objective programming approach to a case study

Resource-constrained project scheduling problem (RCPSP) is a broadly researched issue in the literature. The purpose of the classic form of the problem is scheduling a set of activities considering resource and precedence constraints for minimizing the project completion time. Companies mostly deal with the issue of properly assigning multi-skilled workforces and maintaining the needed skill levels while implementing projects. In this study, a novel MILP model with three objectives is presented to tackle multi-skill RCPSP (MS-RCPSP). This study concentrates on minimizing project makespan, minimizing resource costs as well as tardiness costs, and maximizing quality under uncertainty. However, the standard MS-RCPSP is not able to consider several practical engineering requirements owing to its narrow assumptions. Therefore, key assumptions including overlap between activities, tardiness penalties of activities and the rework duration concept for activities in this model are considered. Due to the complexity of the real world, interval valued fuzzy numbers are taken into account for some of the problem’s parameters. The efficiency of the proposed mathematical framework is represented using both a real case study to construct a railway bridge with 34 activities and large-size problem instances from MMLIB (MM50 and MM100). Since this model is multi-objective, a new extended IVF-ABS approach is presented in this study. Finally, the proposed approach is compared with two methods, namely SO and ABS, from the literature.

Towards sustainable project scheduling with reducing environmental pollution of projects: fuzzy multi-objective programming approach to a case study of Eastern Iran

Towards sustainable project scheduling with reducing environmental pollution of projects: fuzzy multi-objective programming approach to a case study of Eastern Iran

A Fuzzy multi-objective programming approach to develop a green closed-loop supply chain network design problem under uncertainty: Modifications of imperialist competitive algorithm

The last decade has seen a numerous studies focusing on the closed-loop supply chain. Accordingly, the uncertainty conditions as well as the green emissions of facilities are still open issues. In this paper, a new fuzzy multi-objective programming approach is to present for a production-distribution model in order to develop a multi-product, multi-period and multi-level green closed-loop supply chain network problem, which this model is formulated as multi-objective mixed linear integer programming (MOMILP). In regards to offered fuzzy multi-objective model, three conflicting goals are exited, simultaneously. The objective functions are to minimizing the total cost, minimizing the gas emissions costs due to vehicle movements between centers, and maximizing the reliability of delivery demand due to the reliability of the suppliers. To get closer to real-world applications, the parameters of model are considered by fuzzy numbers. Another novelty of proposed model is in the solution methodology. To solve the model, this study not only uses a well-known Imperialist Competitive Algorithm (ICA) but a number of new modifications of ICA (MICA) also have been provided to address the proposed problem, which is to demonstrate the efficiency and performance of the proposed algorithm with other algorithms included: SA, ICA, ACO, GA, and PSO are compare. Finally, different analyses with a variety of problem complexity in different sizes are performed to assess the performance of algorithms as well as some sensitivity analyses on the efficiency of model are studied.

Fuzzy Multi-objective Programming Approach for Constrained Matrix Games with Payoffs of Fuzzy Rough Numbers

Imprecise constrained matrix games (such as fuzzy constrained matrix games, interval-valued constrained matrix games, and rough constrained matrix games) have attracted considerable research interest. This article is concerned with developing an effective fuzzy multi-objective programming algorithm to solve constraint matrix games with payoffs of fuzzy rough numbers (FRNs). For simplicity, we refer to this problem as fuzzy rough constrained matrix games. To the best of our knowledge, there are no previous studies that solve the fuzzy rough constrained matrix games. In the proposed algorithm, it is proven that a constrained matrix game with fuzzy rough payoffs has a fuzzy rough-type game value. Moreover, this article constructs four multi-objective linear programming problems. These problems are used to obtain the lower and upper bounds of the fuzzy rough game value and the corresponding optimal strategies of each player in any fuzzy rough constrained matrix games. Finally, a real example of the market share game problem demonstrates the effectiveness and reasonableness of the proposed algorithm. Additionally, the results of the numerical example are compared with the GAMS software results. The significant contribution of this article is that it deals with constraint matrix games using two types of uncertainties, and, thus, the process of decision-making is more flexible.

An integrated chance-constrained stochastic model for efficient and sustainable supplier selection and order allocation

Effective allocation of scarce resources across supply chain environments is an emerging issue, as enterprises face shortfalls in raw materials, human labour, budgetary resources, equipment, energy and capacity. We consider these related objectives in designing efficient and sustainable supply networks using a multi-objective mixed-integer non-linear programming (MINLP) model for efficient and sustainable supplier selection and order allocation with stochastic demand. Our approach considers sustainability dimensions including economic, environmental and social responsibility, but also seeks to design the most efficient supply network given constraints of the supply market. Enterprise efficiency is assessed using a bi-objective data envelopment analysis (DEA) whose inputs include raw materials, current expenses and labour force capacity. The resulting model is non-convex because of the presence of bilinear terms in DEA-related constraints, so we introduce a multi-stage solution procedure that first uses piecewise McCormick envelopes (PCM) to linearise the bilinear terms. Next, we introduce a set of valid inequalities in order to improve solution time of the problem whose dimension significantly increases after being linearised. We then exploit chance constrained programming approaches to deal with stochastic demand. Finally, a single aggregated objective function is derived using a fuzzy multi-objective programming approach. A manufacturing case study demonstrates the validity of the proposed approach, and its effectiveness in designing a supply network that addresses the ‘triple bottom line’ of people, profit and planet that comprises many sustainability initiatives in an efficient manner.

Fuzzy criteria programming approach for optimising the TBL performance of closed loop supply chain network design problem

Immense concern for sustainability and increasing stakeholders’ involvement has sparked tremendous interest towards designing optimal supply chain networks with significant economic, environmental, and social influence. Central to the idea, this study aims to design a closed loop supply chain (CLSC) network for an Indian laptop manufacturer. The network configuration, which involves a manufacturer, suppliers, third party logistics providers (forward and reverse), retailers, customers and a non-government organisation (NGO), is modelled as a mixed integer linear programming problem with fuzzy goals of minimising environmental impact and maximising net profit and social impact, subject to fuzzy demand and capacity constraints. Profit is generated from the sale of primary and secondary laptops, earned tax credits, and revenue sharing with reverse logistics providers. The environmental implications are investigated by measuring the carbon emitted due to activities of manufacturing, assembling, dismantling, fabrication, and transportation. The social dimension is quantified in terms of the number of jobs created, training hours, community service hours, and donations to NGO. The novelty of the model rests on its quantification of the three triple bottom line (TBL) indicators and on its use of AHP–TOPSIS for modelling the multi-criteria perspectives of the stakeholders. Numerical weights for the triple lines of sustainability are utilized. Further, a fuzzy multi-objective programming approach that integrates fuzzy set theory with goal programming techniques is utilised to yield properly efficient solutions to the multi-objective problem and to provide a trade-off set for conflicting objectives. The significance of the CLSC model is empirically established as a decision support tool for improving the TBL performance of a particular Indian laptop manufacturer. Practical and theoretical implications are derived from the result analysis, and a generalised quantitative closed-loop model can be effectively adapted by other electronic manufacturers to increase their competitiveness, profitability, and to improve their TBL.

A fuzzy multi-objective programming approach for determination of resilient supply portfolio under supply failure risks

The main contribution of this paper is to develop a new decision tool that interprets strategies for determination of resilient supply portfolio under supply failure risks. The strategic decisions include the allocation of emergency capacities to be pre-positioned at backup suppliers, the output of which can be increased in the event of mitigating a shortage caused by another supplier's failure. The model contains three objective functions – minimising the total cost, minimising the net rejected items and minimising the net late deliveries – while satisfying capacity and minimum order quantity requirement constraints. A weighted additive fuzzy multi-objective model is proposed to simultaneously consider the imprecision of information and the relative importance of objectives for determining the allocation of order quantity and emergency capacity to each supplier. The application of the proposed model is illustrated using an example case of global supply chains with different supplier characteristics.

Fuzzy Multi-Objective Capacitated Transportation Problem with Mixed Constraints

In this article a capacitated transportation problem is considered which is formulated as a multi objective capacitated transportation problem with mixed constraints. To determine the optimum compromise solution of multi objective capacitated transportation problem (MOCTP) with mixed constraints a Fuzzy multi objective programming approach has been applied in which we use three different forms of membership functions viz. linear, exponential and hyperbolic. A numerical illustration has been provided to illustrate the solution procedure.

Fuzzy R&D portfolio selection of interdependent projects

Global competition of markets has forced firms to invest in targeted R&D projects so that resources can be focused on successful outcomes. A number of options are encountered to select the most appropriate projects in an R&D project portfolio selection problem. The selection is complicated by many factors, such as uncertainty, interdependences between projects, risk and long lead time, that are difficult to measure. Our main concern is how to deal with the uncertainty and interdependences in project portfolio selection when evaluating or estimating future cash flows. This paper presents a fuzzy multi-objective programming approach to facilitate decision making in the selection of R&D projects. Here, we present a fuzzy tri-objective R&D portfolio selection problem which maximizes the outcome and minimizes the cost and risk involved in the problem under the constraints on resources, budget, interdependences, outcome, projects occurring only once, and discuss how our methodology can be used to make decision support tools for optimal R&D project selection in a corporate environment. A case study is provided to illustrate the proposed method where the solution is done by genetic algorithm (GA) as well as by multiple objective genetic algorithm (MOGA).

A genetic algorithm-based fuzzy multi-objective programming approach for environmental water allocation

A fuzzy multiobjective-programming model was presented to determine appropriate environmental flow allocation in urban rivers. An integrated nonlinear fuzzy membership function, that represents a broader implication in fuzzy decision-making, was regarded as the general objective and genetic algorithm became an essential tool in search for the global optimal solution. A case study of optimal allocation for environmental water requirements in the Liming River Basin, Daqing, demonstrates the capability of the fuzzy multiobjective model based on fuzzy decision theories to work suitably in water environmental management in a river basin.

Impact of mitigating CO2 emissions on Taiwan’s economy: a fuzzy multiobjective programming approach

A computationally fuzzy multiobjective programming (MOP) approach with a Leontief interindustry model is used to investigate the trade-offs between per capita gross domestic product, national employment, and per capita CO2 emissions in Taiwan. To achieve the objectives of our investigation, the relevant literature is first reviewed, followed by construction of a fuzzy MOP coupled with an input-output model to evaluate the economic impact of the reduction of CO2 emissions on Taiwan’s economy as a whole. Empirical data have been collected, and various strategies for mitigating industrial CO2 emissions are simulated. Based on these simulations, policy recommendations are also proposed.

A fuzzy multi-objective programming approach for optimal management of the reservoir watershed

This paper applies a fuzzy multi-objective programming model for the evaluation of sustainable management strategies of optimal land development in the reservoir watershed. The environmental goals lie in the conservation of reservoir water quality and the economic goals focus on the rewards from various uses of land within the watershed. Carrying capacity of the land and assimilative capacity of the reservoir are two major limitations encountered in systems analysis. In particular, it demonstrates how imprecise information in such a system can be quantified by specific membership functions in a fuzzy multi-objective analytical framework. It shows that the fuzzy outputs associated with different weight distribution sin decision analysis can successfully reflect system complexity and generate more realistic management policies. A case study of the planning for land use programs in the Tweng-Wen reservoir watershed in Taiwan was demonstrated.

A grey fuzzy multiobjective programming approach for the optimal planning of a reservoir watershed. Part A: Theoretical development

The conflict among environmental and economic goals is a constant problem that always bothers the decision makers in regional planning. Besides, the uncertainties regarding the fuzzy goals in decision making and the impreciseness of parameter values in a system always create additional difficulties in management planning and analysis. This paper develops a new approach, a grey fuzzy multiobjective linear programming (GFMOLP) method, for the evaluation of sustainable management strategies for systems analysis. In particular, it demonstrates how uncertain messages of the planning objectives can be quantified by specific membership functions and combined through the use of grey numbers in a multiobjective analytical framework. It is verified that such an approach can successfully reflect system complexity and generate more flexible and robust management policies.

A grey fuzzy multiobjective programming approach for the optimal planning of a reservoir watershed. Part B: Application

The conflict between environmental protection of reservoir water quality and economic development by different uses of land within a watershed is a problem that constantly bothers the public officials in regional planning. Besides, the uncertainties regarding to the fuzzy goals in decision making and the impreciseness of parameter values always create additional difficulties in systems analysis. This paper applies the grey fuzzy multiobjective linear programming (GFMOLP) method for the evaluation of sustainable management strategies for optimal land development in a reservoir watershed. In particular, it demonstrates how uncertain messages in water resources management systems can be quantified by specific fuzzy membership functions and grey numbers in a multiobjective analytical framework. A case study of the planning for land-use programs in the Tweng-Wen reservoir watershed in Taiwan was prepared for the purpose of demonstration.