Fuzzy Programming

""Origin–destination (O–D) matrix estimation methods based on traffic counts have been largely discussed and investigated. The most used methods are based on Generalised Least Square estimators (GLS) that use as input data a starting O–D matrix and a set of traffic counts. In addition to traffic counts, the analysts could know other general information about travel demand or link flows, based on their experience, or spot data, but few works deal with the matter of including effectively these sources of information.

This paper proposes a Fuzzy-GLS estimation method that allows to improve the estimation performances of classic GLS estimator by including, in addition to traffic counts, uncertain information about starting O–D demand (i.e. outdated estimates, spot data, expert knowledge, etc.). The methods explicitly take into account the relevant level of uncertainty by taking as much advantage as possible from the few vague available data. The method is developed using fuzzy sets theory and fuzzy programming that seems to be a convenient theoretical framework to represent uncertainty in the available data. A solution algorithm for the proposed problem is also presented. The method has been tested by numerical applications and then compared to the classical GLS method under different sets of constraints to the problem.""

In this paper, the optimization problems with fuzzy coefficients in unconstrained and constrained cases are
discussed. We have proposed a method for these problems using concept of alpha -cuts for fuzzy numbers, and by
considering a partial ordering on the set of all fuzz y numbers. Base on our proposed method, solving an optimization
problem with fuzzy coefficients converts to solve a crisp multi -objective optimization problem.

A multi-objective multi-item solid transportation problem with fuzzy coefficients for the objectives and constraints, is modeled and then solved by two different methods. A defuzz-ification method based on fuzzy linear programming is applied for fuzzy supplies, demands and conveyance capacities, including the condition that both total supply and conveyance capacity must not fall below the total demand. First, expected values of the fuzzy objective functions are considered to derive crisp values. Another method based on the concept of ''minimum of fuzzy number'' is applied for the objective functions that yields fuzzy values instead of particular crisp values for the fuzzy objectives. Fuzzy programming technique and global criterion method are applied to derive optimal compromise solutions of multi-objectives. A numerical example is solved using above mentioned methods and corresponding results are compared.

Abstract. Enterprises and industrial centers need current decision for making products in fast changing market. Uncertainty and yield defined goals make decision making more difficult. In this situation fuzzy logic is used for coping surrounding environment. This paper deals with a fuzzy linear programming model for a problem of food industry. The different types of achievement function such as compensatory and weighted compensatory form associated with equal importance of objectives and non-importance of objectives both have been discussed.

Mixed-model production is the practice of assembling different and distinct models in a line without changeovers with responding to sudden demand changes for a variety of models. In this paper, we specify sequence of models to minimize conveyer stoppages. We assume that our lines are fixed and we cannot change the balance of the lines. When the condition of lines like setup cost and demand of each model change, it is important to specify the sequence for minimizing the conveyer stoppages without balancing the line again because the main lines are fixed. We consider three objective functions simultaneously: minimizing the variation in the actual and required production capacity of the line and minimizing the objectives which increase the chance of conveyer stoppage, including: (a) minimizing the total setup time, (b) minimizing the total production variation cost, and (c) minimizing the total utility work cost. Because of conflicting objectives, we propose the fuzzy goal programming-based approach to solve the model. Finally, we present an estimator for nearness of conveyer stoppages and study about affecting of sub-lines and changing the conveyer velocity in a station for reducing stoppages.

The paper concerns fuzzy logic programming. As an example, we show that is not restrictive to confine ourselves to fuzzy Herbrand interpretations in giving a semantics for fuzzy programs. Also, we show that the resulting apparatus gives a unifying theoretical framework for fuzzy control.

Multi-criteria or multi-objective decision-making is becoming increasingly popular as a decision support tool for natural resource management.Stakeholders as well as the planners can be involved in the decision making process, using this approach. This article deals with the use of multi-criteria (multi-objective) technique in solving some complex problems related to water resource management. Five objectives were considered in the study.

The purpose of this paper is to propose a procedure for solving multilevel programming problems in a large hierarchical decentralized organization through linear fuzzy goal programming approach. Here, the tolerance membership functions for the fuzzily described objectives of all levels as well as the control vectors of the higher level decision makers are defined by determining individual optimal solution of each of the level decision makers. Since the objectives are potentially conflicting in nature, a possible relaxation of the higher level decision is considered for avoiding decision deadlock. Then fuzzy goal programming approach is used for achieving highest degree of each of the membership goals by minimizing negative deviational variables. Sensitivity analysis with variation of tolerance values on decision vectors is performed to present how the solution is sensitive to the change of tolerance values. The efficiency of our concept is ascertained by comparing results with other fuzzy programming approaches.

The purpose of this paper is to propose a procedure for solving multilevel programming problems in a large hierarchical decentralized organization through linear fuzzy goal programming approach. Here, the tolerance membership functions for the fuzzily described objectives of all levels as well as the control vectors of the higher level decision makers are defined by determining individual optimal solution of each of the level decision makers. Since the objectives are potentially conflicting in nature, a possible relaxation of the higher level decision is considered for avoiding decision deadlock. Then fuzzy goal programming approach is used for achieving highest degree of each of the membership goals by minimizing negative deviational variables. Sensitivity analysis with variation of tolerance values on decision vectors is performed to present how the solution is sensitive to the change of tolerance values. The efficiency of our concept is ascertained by comparing results with other fuzzy programming approaches.

Material procurement planning (MPP) deals with the problem that purchasing the right quantity of material from the right supplier at the right time, a purchaser can reduce the material procurement costs via a reasonable MPP model. In order to handle the MPP problem in a fuzzy environment, this paper presents a new class of two-stage fuzzy MPP models, in which the material demand, the spot market material unit price and the spot market material supply quantity are assumed to be fuzzy variables with known possibility distributions. In addition, the procurement decisions are divided into two groups. Some procurement decisions, called first-stage decisions, must be taken before knowing the the particular values taken by the fuzzy variables; while some other decisions, called second-stage decisions, can be taken after the realizations of the fuzzy variables are known. The objective of the proposed fuzzy MPP model is to minimize the expected material procurement costs over the two stages. On other hand, since the fuzzy material demand, the fuzzy spot market material unit price and the fuzzy spot market material supply quantity are usually continuous fuzzy variables with infinite supports, the proposed MPP model belongs to an infinite-dimensional optimization problem whose objective function cannot be computed exactly. To avoid this difficulty, we suggest an approximation approach (AA) to evaluating the objective function, and turn the original MPP model into an approximating finite-dimensional one. To show the credibility of the AA, the convergence about the objective function of the approximating MPP model to that of the original MPP one is discussed. Since the exact analytical expression for the objective function in the approximating fuzzy MPP model is unavailable, and the approximating MPP model is a mixed-integer program that is neither linear nor convex, the traditional optimization algorithms cannot be used to solve it. Therefore, we design an AA-based particle swarm optimization to solve the approximating two-stage fuzzy MPP model. Finally, we apply the two-stage MPP model to an actual fuel procurement problem, and demonstrate the effectiveness of the designed algorithm via numerical experiments.

This paper considers a fuzzy programming approach for a multi-objective single machine scheduling problem when processing times of jobs are normal random variables. The probabilistic problem is converted into an equivalent deterministic programming problem. Then the fuzzy programming technique has been applied to obtain a compromise solution. A numerical example demonstrates the feasibility of applying the proposed model to single machine scheduling problem.

A supply chain is a complex system in which operational and strategic decisions have to be made. From a global point of view, the analysis of a supply chain focuses on three distinct stages: supplying of raw materials, manufacturing process and distribution of products. In this work, the manufacturing and distribution stages of the supply chain are studied jointly. We

Abstract The paper addresses the optimal design of the last branch of the supply chain, ie, the Distribution Network (DN). We extend a deterministic optimization model previously proposed by the authors, using fuzzy numbers and fuzzy logic to take into account uncertainty in the DN model and in the DN design. Hence, a procedure employing digraph modeling and fuzzy mixed integer linear programming is presented to select the optimal DN configuration. To show the method effectiveness, the optimization model is applied to a ...