Modified S-curve Membership Function Research Articles

A fuzzy compromise programming model based on the modified S-curve membership functions for supplier selection

Among various decision techniques, multi-objective programming model is a proper approach to solve the supplier selection problem. Notice that the multi-objective programming problem often consists of conflicting goals that cannot be achieved simultaneously, we present an approach to obtain the marginal evaluation of each objective and to aggregate these marginal evaluations into the global evaluation. Moreover, due to the limited historical data of prospective suppliers and most companies are reluctant to share proprietary information. Therefore, the decision makers often rely on vague information in their supplier selections. S-curve membership function is more flexible and robust than linear membership function when describing the vagueness. Thus, the compromise satisfactory level of multiple goals in the supplier selection problem can be represented by the modified S-curve membership function. Based on the global evaluation obtained, we can formulate a fuzzy compromise programming model based on the modified S-curve membership function. Lastly, a numerical example is given to demonstrate the efficiency of our method by comparing it with the weighted max–min method and the weighted additive method.

Cost-effectiveness analysis of the mobile phone manufacturing sector by using a novel fuzzy multi-objective programming model

This work presents a novel fuzzy multi-objective programming (FMOP) model with a modified S-curve membership function capable of solving integrated multi-component, multi-supplier, and multi-time-period production planning problems by using fuzzy objectives for the mobile phone manufacturing sector. The proposed model attempts to minimize total manufacturing, total inventory holding and total penalty costs simultaneously in relation to manufacturer/supplier capacity and warehouse space. Additionally, the proposed model provides a systematic means of facilitating the fuzzy decision-making process, enabling decision makers to interactively adjust the search direction during the solution procedure in order to obtain the preferred satisfactory solution of a decision maker (DM). Moreover, adequacy of the proposed model is demonstrated, based on an implementation design involving several scenarios of manufacturing production system for mobile phones. Analytical results provide a valuable reference for decision managers attempting to more thoroughly understand the systematic analysis and potential of cost-effective production planning.

PENENTUAN JUMLAH PRODUKSI MENGGUNAKAN MODEL FUZZY MULTI OBJECTIVE LINEAR PROGRAMMING PADA INDUSTRI PANGAN (Studi Kasus Pada Industri Roti PT NIC)

Production Planning and Inventory Control (PPIC) activities in the food industry requires a reliable decision model to support the effectiveness and efficiency of PPIC function. Master Production Scheduling / MPS is one of the PPIC decision model that aims to get the number of items that must be produced by the company to meet consumer demand based on its production capacity. This research had been done in the food industry with a case study on PT NIC bread industry, using Fuzzy Multi Objective Linear Programming Model as a decision model to determine the amount of production.This model is an optimization model that was developed by utilizing the modified S-curve membership function for Fuzzy Linear Programming problems with the aim of minimizing costs and maximizing production utilization. This model is reliable enough to improve the functioning of PPIC in the food industry.

IMPROVED TABU SEARCH RECURSIVE FUZZY METHOD FOR CRUDE OIL INDUSTRY

The minimization of the profit function with respect to the decision variables is very important for the decision makers in the oil field industry. In this paper, a novel approach of the improved tabu search algorithm has been employed to solve a large scale problem in the crude oil refinery industry. This problem involves 44 variables, 36 constraints, and four decision variables which represent four types of crude oil types. The decision variables have been modeled in the form of fuzzy linear programming problem. The vagueness factor in the decision variables is captured by the nonlinear modified S-curve membership function. A recursive improved tabu search has been used to solve this fuzzy optimization problem. Tremendously improved results are obtained for the optimal profit function and optimal solution for four crude oil. The accuracy of constraints satisfaction and the quality of the solutions are achieved successfully.

Application of Multi Objective Fuzzy Linear Programming in Supply Production Planning Problem

The objective of this paper is to establish the usefulness of modified s-curve membership function in a limited supply production planning problem with continuous variables. In this respect, fuzzy parameters of linear programming are modeled by non-linear membership functions such as s-curve function. This paper begins with an introduction and construction of the modified s-curve membership function. A numerical real life example of supply production planning problem is then presented. The computational results show the usefulness of the modified s-curve membership function with fuzzy linear programming technique in optimising individual objective functions, compared to non-fuzzy linear programming approach. Futhermore, the optimal solution helps to conclude that by incorporating fuzziness in a linear programming model through the objective function and constraints, a better level of satisfactory solution will be provided in respect to vagueness, compared to non-fuzzy linear programming.

Transportation planning with modified S-curve membership functions using an interactive fuzzy multi-objective approach

In this paper, we consider the transportation planning decision (TPD) problem with fuzzy goals, available supply and forecast demand. An interactive method is designed for solving the multi-objective TPD problem where the fuzzy data are represented by modified S-curve membership functions. The proposed method attempts to simultaneously minimize the total production and transportation costs and the total delivery time with reference to budget constraints and available supply, machine capacities at each source, as well as forecast demand and warehouse space constraints at each destination. An interactive fuzzy approach is applied to solve the multi-objective TPD problem and to find a preferred compromise solution. Finally, the performance of S-curve membership functions that represent uncertainty goals and constraints in TPD problems with linear membership functions in an industrial case is compared.

FUZZY TECHNIQUE FOR OPTIMIZATION OF OBJECTIVE FUNCTION WITH UNCERTAIN RESOURCE VARIABLES AND TECHNOLOGICAL COEFFICIENTS

In this paper, a new fuzzy optimization based on methodology utilizing a modified s-curve membership function has been applied to an industrial production problem in an oil company. The major contribution of this paper is the optimization of a profit function with respect to uncertain resource variables and technological coefficients. Three cases have been thoroughly studied in this paper. Comparative results have been successfully obtained for these three cases. This piece of information will be very important for the decision makers in implementing their decisions in a vague environment. It will be shown that there are many advantages of using the modified s-curve membership to optimize the profit function used by the decision maker; in particular strategic and flexible decisions are facilitated.

FUZZY LINEAR PROGRAMMING FOR SUPPLY CHAIN PLANNING UNDER UNCERTAINTY

A new fuzzy mathematical programming model for supply chain planning under supply, process and demand uncertainty is proposed in this paper. A tactical supply chain planning problem has been formulated as a fuzzy mixed integer linear programming model where data are ill-known and modeled by fuzzy numbers with modified s-curve membership functions. The fuzzy model provides alternative decision plans to the decision maker (DM) for different degrees of satisfaction. Finally, the proposed model is tested by using data from a real automobile supply chain.

Vendor selection problem by using an interactive fuzzy multi-objective approach with modified S-curve membership functions

In this paper, the vendor selection (VS) problem with fuzzy goals is considered. An interactive method is developed for solving multi-objective VS problems where fuzzy data are represented by using S-curve membership functions. The proposed method attempts simultaneously to minimize the total order costs, the number of rejected items and the number of late delivered items with reference to several constraints such as meeting buyers’ demand, vendors’ capacity, vendors’ quota flexibility, vendors’ allocated budget, etc. An interactive solution methodology is proposed to solve the multi-objective VS problem and to find a preferred compromise solution. Moreover, the performance of S-curve membership functions that represent uncertainty goals and constraints in VS problems with linear membership functions in an industrial case is compared.

Fuzzy decision making of profit function in production planning using S-curve membership function

Any modern industrial manufacturing unit inevitably faces problems of vagueness in various aspects such as raw material availability, human resource availability, processing capability and constraints and limitations imposed by marketing department. Such a complex problem of vagueness and uncertainty can be handled by the theory of fuzzy linear programming. In this paper, a new fuzzy linear programming based methodology using a modified S-curve membership function is used to solve fuzzy mix product selection problem in Industrial Engineering. Profits and satisfactory level have been computed using fuzzy programming approach. Since there are several decisions to be taken, a performance measure has been defined to identify the decision for high level of profit with high degree of satisfaction.

Fuzzy Production Planning and its Application to Decision Making

This paper presents new methods for solving a production-planning problem. First the modified s-curve membership function as a methodology is constructed. Then fuzzy production planning problems with vagueness parameters alpha and fuzzy objective coefficients, fuzzy technical coefficients and fuzzy resource variables are outlined. The objective of this paper is to find a satisfactory solution for optimal profit in which vagueness is playing major factor in selecting the solution. Finally a practical application of decision-making in production planning is illustrated.

Fuzzy optimization of units products in mix-product selection problem using fuzzy linear programming approach

In this paper, the modified S-curve membership function methodology is used in a real life industrial problem of mix product selection. This problem occurs in the production planning management where by a decision maker plays important role in making decision in an uncertain environment. As analysts, we try to find a good enough solution for the decision maker to make a final decision. An industrial application of fuzzy linear programming (FLP) through the S-curve membership function has been investigated using a set of real life data collected from a Chocolate Manufacturing Company. The problem of fuzzy product mix selection has been defined. The objective of this paper is to find an optimal units of products with higher level of satisfaction with vagueness as a key factor. Since there are several decisions that were to be taken, a table for optimal units of products respect to vagueness and degree of satisfaction has been defined to identify the solution with higher level of units of products and with a higher degree of satisfaction. The fuzzy outcome shows that higher units of products need not lead to higher degree of satisfaction. The findings of this work indicates that the optimal decision is depend on vagueness factor in the fuzzy system of mix product selection problem. Further more the high level of units of products obtained when the vagueness is low.

SOLVING FUZZY LINEAR PROGRAMMING PROBLEMS WITH MODIFIED S-CURVE MEMBERSHIP FUNCTION

In this paper, we concentrate on two kinds of fuzzy linear programming problems: linear programming problems with only fuzzy resource variables and linear programming problems in which both the resource variables and the technological coefficients are fuzzy numbers. We consider here only the case of fuzzy numbers with modified s-curve membership functions. We propose here the modified s-curve membership function as a methodology for fuzzy linear programming and use it for solving these problems. We also compare the new proposed method with non-fuzzy linear programming optimization method. Finally, we provide real life application examples in production planning and their numerical solutions.

FUZZY OPTIMIZATION OF COST FUNCTION IN PRODUCT MIX SELECTION PROBLEM

The modern trend in industrial application problem deserves modeling of all relevant vague or fuzzy information involved in a real decision making problem. In this paper the usefulness of the proposed S-curve membership function is established using a real life industrial production planning of a chocolate manufacturing unit. The unit produces 8 products using 8 raw materials; mixed in various proportions by 9 different processes under 29 constraints. A solution to this problem establishes the usefulness of the suggested membership function for decision making in industrial production planning. The objective of this paper is to find the optimal cost to produce 8 products using modified S-curve membership function as a methodology. The fuzzy linear programming approach is used to solved this problem. The optimal cost function is obtained respect to two major factors of degree of satisfaction and vagueness.

INDUSTRIAL PRODUCTION PLANNING USING INTERACTIVE FUZZY LINEAR PROGRAMMING

Any modern industrial manufacturing unit inevitably faces problems of vagueness in various aspects such as raw material availability, human resource availability, processing capability and constraints and limitations imposed by marketing department. Such a complex problem of vagueness and uncertainty can be handled by the theory of fuzzy linear programming. In this paper, a new fuzzy linear programming based methodology using a modified S-curve membership function is used to solve fuzzy mix product selection problem in Industrial Engineering. Profits and satisfactory level have been computed using fuzzy linear programming approach. Since there are several decisions to be taken, a performance measure has been defined to identify the decision for high level of profit with high degree of satisfaction.