Multi-Objective Fuzzy Linear Programming for Land Allocation under Different Crops in Bhagwanpur Distributary

In this paper, we discusses the problem that involving the conflict fuzzy multi-objective in transportation planning which is one of special case in multi-objective linear programming. To find the simultaneously optimal solution of the problem, we use the Interactive Fuzzy Multi-Objective Linear Programming (IFMOLP) method. This method can reduce the fuzzy multi-objective linear programming problem into deterministic single objective linear programming which can be solved using simplex method. Beside that , with IFMOLP method, decision maker (DM) can establish interactively the goal from the objective function to produce the pareto optimal solution so that.

A multiobjective linear programming (MOLP) problem with fuzzy parameters in the constraints and objective functions in considered. Assuming fuzzy aspiration levels for the particular objectives and involving the comparison of fuzzy numbers, the problem is transformed into a multiobjective linear fractional program. For its solution an interactive method involving a linear programming procedure is proposed. This method has been developed for an application to long-term development planning of a water supply system. It has been first described in Slowinski (1986) and in this paper it is outlined and shown in the context of an updated review of recent proposals for multiobjective fuzzy linear programming.

Multi-criteria decision making method is used in such cases having multiple targets. Multi-objective linear programming problems, which deal with uncertain measurements for both objectives and constraints, are solved by fuzzy multi-objective linear programming methods. Analytic hierarchy process (AHP), one of the multi-criteria decision-making methods based on weighting of objectives, is designed to solve complex problems. In this study, multiple criteria decision making problems and decision makers’ opinions on these problems as well as their solution processes are discussed. Firstly, a fuzzy multi objective linear programming problem is solved using the approaches of Zimmerman and Hybrid. In the literature, these methods are applied using triangular fuzzy numbers based on decision makers’ opinions only in cases where the objective function is minimization. In this study, as an alternative to the triangular fuzzy numbers, trapezoidal fuzzy numbers are defined, and both minimization and maximization of objective functions are examined. Finally, a solution algorithm for a fuzzy multi-objective linear programming problem is proposed under some given conditions. The algorithm is applied to a sample problem that involves modeling of a congress organizing which aims to place attendees to accommodations under specific objectives and constraints. In the evaluation phase of the algorithm, targets are weighted by using triangular and trapezoidal fuzzy numbers. At the end, the results of the proposed algorithm are compared with the results of other methods in the literature.

The purpose of this paper is to develop a new two-stage method for fuzzy multi-objective linear program and apply to engineering project portfolio selection. In the fuzzy multi-objective linear program, all the objective coefficients, technological coefficients and resources are trapezoidal fuzzy numbers (TrFNs). An order relationship for TrFNs is introduced by using the interval expectation of TrFNs. In the first stage, the fuzzy multi-objective linear program with TrFNs is transformed into an interval multi-objective linear program according to the order relationship of TrFNs. Combining the ranking order relation between intervals with the satisfactory crisp equivalent forms of interval inequality relations, the interval multi-objective linear program is further transformed into a crisp multi-objective linear program. In the second stage, the positive and negative ideal solutions are calculated as well as the closeness degrees from the positive ideal solution to all objectives on the basis of the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution). Then, using the closeness degrees, we convert the crisp multi-objective linear program into mono-objective program to solve. The proposed method is not only mathematically rigorous, but also can adequately consider the acceptance degree of decision maker that the fuzzy constraints may be violated. The other possible cases of the fuzzy multi-objective linear program are also discussed. The proposed method is illustrated by means of a project portfolio selection problem.

Study on multi-objective linear fractional programming problem involving pentagonal intuitionistic fuzzy number

The difficulty in solving either multi-objective linear programming (MOLP) problems or fuzzy multi-objective linear programming (FMOLP) problems is the trade-off among objectives. To deal with this difficulty, we proposed a new algorithm for solving FMOLP problems by using zero-sum game. First, FMOLP problem given is converted to a crisp MOLP problem by using ranking function, and then a payoff matrix is constructed to find the weights of each objective function of the MOLP problem. After that, each weight is multiplied with the corresponding objective function, a single-objective LP problem is obtained and thus, FMOLP problem is solved. The proposed algorithm is illustrated by numerical examples for the FMLOP problems having fuzzy constraints or not.

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

Strange: An interactive method for multi-objective linear programming under uncertainty

In this paper, the optimal load curtailment (OLC) problem is formulated as a multi‐objective optimization framework, which objectives include maximizing the security margin and minimizing the cost incurred for load curtailment. A new and comprehensive multi‐objective fuzzy linear programming (MFLP) method is developed to solve this presented OLC model. Using the MFLP method, objectives and constrains of the OLC model are fuzzied and their enforcements are maximized. The MFLP model can deal with the uncertainties that exist in certain variables and overcome the limitations of minor constraint violations in normal LP model. The effectiveness of the developed method is tested on the modified IEEE 30 bus system and the IEEE 118 bus system. Copyright © 2009 John Wiley & Sons, Ltd.

Due to severe competition among business organizations, the selection of supplier becomes more important for business success. However, supplier selection problems are complex and unstructured since it involves a large number of criteria and some of the criteria cannot be assessed accurately. Also, supplier’s performance fluctuations and unknown information always exist in the real-world decisions. Moreover, the criteria may be qualitative or quantitative in nature as well as supplier evaluation involves a group of experts with diverse opinions. To handle such uncertain and vague information of suppliers, use of fuzzy sets is an appropriate option. Hence, for making a realistic decision, this research proposes a two-phase method to select the suitable suppliers and allocate appropriate orders to them. In first phase of the study, the ranking of supplier is performed by using fuzzy MULTIMOORA method with regard to the important criteria. Then, multi-objective linear programming (MOLP) method in fuzzy environment is proposed to allocate orders to the preferred suppliers in the second phase. The model is developed in multi-product environment by satisfying demand, lead time and capacity constraints. We used expected value method to transform the fuzzy multi objective problem into a crisp single objective problem. Appropriate orders are assigned to the preferred suppliers by considering the closeness coefficient to the fuzzy MOLP model. At last, a case study is performed in an Indian manufacturing organization to illustrate the proposed model.

To develop a drone disaster response system, this paper aims at the relationship between drone fleet, medical kit, and ISO container to meet the needs of medical kits. Restrictions. Finally, the optimal combination of drone rescue was selected by TOPSIS method.

Supply chain network design is one of the most important issues in designing supply chains because of its effect on performance and efficiency of the logistics network. Customer service improvements and environmental requirements have forced most companies to take into account the reverse flows in designing their supply chain networks. This paper employs an interactive fuzzy multi-objective linear programming (IFMOLP) method to solve fuzzy bi-objective reverse logistics network design problems. This method attempts to minimize the total cost and total delivery time of the system simultaneously. The presented method provides decision makers with an interactive framework that facilitates the process of decision making in a fuzzy environment. Moreover, this framework enables the decision makers to interactively change fuzzy data in order to reach the most satisfactory solutions. A genetic-based heuristic algorithm is presented to solve the model for larger cases. A case study in a bread-producing factory is presented to show the feasibility of the proposed approach.

This study discussed fuzzy multi-objective linear programming (FMOLP) and its application. This research was conducted in Rumah Batik Mentari Jambi, which produces five batik motifs typical of the Jambi. In this research, the tolerance for additional raw material capacity is included in the model. This research aims to find out the number of tolerances needed, the maximum number of batik needed to be produced, and the minimum production time so that the producer can earn the maximum profit. The decision variables in FMOLP are the number of pieces of batik measuring in 2m2, which means the decision variables must be an integer. Therefore, after obtaining the optimal solution from FMOLP, then proceed with the branch and bound method to obtain the integer solution. The result of this research is that the addition of raw materials needed to earn optimal solutions is as much as 50% of the tolerance assumed in the model. Thus, owner can earn the optimal profit of Rp. 5,675,800.00/week by producing as many as 67 pieces of batik with the design of angso duo, 18 pieces with the design of gentala, and 50 pieces with the design of batang hari, and the minimum production time is 270 hours/week.

We attempt to find solutions to the fully fuzzified linear program where all the parameters and variables are fuzzy numbers. We first change the problem of maximizing a fuzzy number, the value of the objective function, into a multiobjective fuzzy linear programming problem. We prove that fuzzy flexible programming can be used to explore the whole undominated set to the multiobjective fuzzy linear program. An evolutionary algorithm is designed to solve the fuzzy flexible program. The program was applied to two applications with good solutions.

On computational methods for solutions of multiobjective linear production programming games