Weighting method for non-preemptive multi-objective mathematical programming

A study was undertaken in Bhagwanpur distributary of Vaishali Branch Canal in Gandak Canal Command Area, Bihar to optimally allocate land area under different crops (rice and maize in kharif, wheat, lentil, potato in rabi and green gram in summer) in such a manner that maximizes net return, maximizes crop production and minimizes labour requirement employing simplex linear programming method and Multi-Objective Fuzzy Linear Programming (MOFLP) method. Maximum net return, maximum agricultural production, and minimum labour required under defined constraints (including 10% affinity level of farmers to rice and wheat crops) as obtained employing Simplex method were ` 3.7 × 108, 5.06 × 107 Kg and 66,092 man-days, respectively, whereas Multi-Objective Fuzzy Linear Programming (MOFLP) method yielded compromised solution with net return, crop production and labour required as ` 2.4 × 108, 3.3 × 107Kg and 1,79,313 man-days, respectively. As the affinity level of farmers to rice and wheat crops increased from 10% to 40%, maximum net return and maximum production as obtained from simplex linear programming method and MOFLP followed a decreasing trend and minimum labour required followed an increasing trend. MOFLP may be considered as one of the best capable ways of providing a compromised solution, which can fulfill all the objectives at a time.

Chapter 11 - Parameter Space Investigation Method

In this study, an inexact fuzzy multiobjective programming (IFMOP) method is developed and applied to a case study of water pollution control planning in the Lake Erhai Basin. The IFMOP improves upon the existing multiobjective programming methods with advantages in data availability, solution algorithm, computational requirement and result interpretation. The case study project was supported by the United Nations Environment Programme (UNEP). The results indicate that desired schemes for a number of system activities in different subareas/periods were obtained. Inheriting uncertain natures of the model inputs, the majority of solutions present as inexact values which provide decision-makers with a flexible decision space. Generally, the modeling results would provide scientific bases for the formulation of policies/strategies regarding regional socio-economic development and environmental protection.

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.

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

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.

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.

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

An improved version of the augmented ε-constraint method (AUGMECON2) for finding the exact pareto set in multi-objective integer programming problems

Planning of sewer systems typically involves limitations and problems, regardless of whether traditional planning methods or optimization models are used. Such problems include non-quantifiability, fuzzy objectives, and uncertainties in decision-making variables which are commonly applied in the planning of any process. Particularly, uncertainties have prevented the inclusion of these variables in models. Consequently, the theoretical optional solution of the mathematical models is not the true optimum solution to practical problems. In this study, to solve the above problems for regional sewer system planning, multi-objective programming (MOP), nonlinear programming, mixed-integer programming, and compromise fuzzy programming were used. The objectives of this study were two-fold: (1) determination of the necessary decision-making variables or parameters, such as the optimum number of plants, piping layout, size of the plant, and extent of treatment; (2) establishment of a framework and methodology for optimal planning for designing a regional sewer system, matching demanded targets with the lowest cost, which would achieve the aim of lower space and energy requirements as well as consumption and high treatment efficiency for the purpose of meeting effluent standards. The findings of this study revealed that individual regional sewage treatment plants could be merged to form a centralized system. Land acquisition was difficult; thus, reducing the number of plants was required. Therefore, the compromise-fuzzy-based MOP method could effectively be used to build a regional sewer system plan, and the amount of in-plant establishment reached its maximized value with a minimized cost.

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.

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.

Electronic countermeasure (ECM) has become one of the most significant factors in modern warfare, in the course of combat, the electronic jamming allocation tasks need to be flexibly adjusted with the change of combat stage, which puts forward higher requirements for the modeling and solution method of this kind of problems. To solve the ECM dynamic weapon target assignment (ECM-DWTA) problem, a hybrid multi-target bi-level programming model is established. The upper level takes the sum of the electronic jamming effects in the whole combat stage as an optimization objective, and locally optimizes the ECM weapon (ECM-WP) assignment scheme in each stage. The lower level takes the importance expectation value of the target subjected to interference and combat consumption as double optimization objectives to globally optimize the ECM-WP assignment scheme. Focus on solving this complex model, a hybrid multi-objective bi-level interactive fuzzy programming algorithm (HMOBIF) is proposed, in this method, exponential membership function is used to describe the satisfaction degree of each level. When solving the multi-objective optimization problem composed of membership functions in the upper and lower levels, we use the MOEA/D algorithm to obtain the Pareto Front (PF) solution set, and then each solution in PF is evaluated and selected by the TOPSIS multi-criteria evaluation method. This local and global interactive optimization process of bi-level model is actually the process of executing observation-orientation-decision-action loop in practical combat. According to the current example, we conduct numerical simulation on the parameters in the model and obtain the parameter values suitable for the model solution. The computational experiments on different scale ECM-DWTA problems show that HMOBIF method is superior to four bi-level programming algorithms in terms of performance index, and can better solve ECM-DWTA problems.

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.