Fuzzy Programming Technique Research Articles

Compromise mixed allocation using fuzzy programming approach

In stratified random sampling, Ahsan et al. [Mixed allocation in stratified sampling. Aligarh J Stat. 2005;25:87–97] introduced the concept of ‘Mixed allocation’ for fixed cost by minimizing the variance of the stratified sample mean which was based on the work of Clark and Steel [Optimum allocation of sample to strata and stages with simple additional constraints. Statistician. 2000;49(2):197–207] for two-stage univariate sampling design. The present manuscript studies the problem of obtaining a ‘compromise mixed allocation’ in multivariate stratified sampling using Fuzzy Programming Technique. To exhibit the application of the defined approach, a numerical illustration is considered and solved using Lingo 13.0. In order to demonstrate the superiority of proposed approach, the obtained results have been compared with four other existing approaches.

Tolerance Approach to Sensitivity Analysis in Multiobjective Transportation Problem

This paper represents ordinary sensitivity analysis and tolerance approach to sensitivity analysis in supply and demand values of the multiobjective transportation problem. Our proposed approach allows simultaneous and independent changes in the supply and demand values. The aim of this paper is to find the ranges for each supply and demand value within which the changes can occur without affecting the current basis of the best compromise solution. We have used the best compromise solution obtained using fuzzy programming technique for the postoptimality analysis of the multiobjective transportation problem. The approach is illustrated by a numerical example.

Multi-item multi-objective fixed charged solid transportation problem with type-2 fuzzy variables

A multi-item multi-objective fixed charged solid transportation problema with guidelines e.g. unit transportation penalty, amounts, requirements, and conveyances as type-2 triangular fuzzy variables with conditions on few items and conveyances is formulated here. A chance constrained programming model applying generalized credibility measure for the objective function as well as the constraints is formed with the critical value based reductions of corresponding type-2 fuzzy guidelines for this particular problem. The model is then converted into the equivalent crisp deterministic form. The optimal compromise solutions are obtained by fuzzy programming technique. An example is contributed to highlight the model and is then solved by applying Generalized Reduced Gradient (GRG) technique (applying LINGO 16). The sensitivity analysis of the model is also given to illustrate the model.

Multi objective fuzzy inventory model with deterioration, price and time dependent demand and time dependent holding cost

In this paper, we have formulated an inventory model with time dependent holding cost, selling price as well as time dependent demand. Multi-item inventory model has been considered under limitation on storage space. Due to uncertainty all the require cost parameters are taken as generalized trapezoidal fuzzy number. Our proposed multi-objective inventory model has been solved by using fuzzy programming techniques which are FNLP, FAGP, WFNLP and WFAGP methods. A numerical example is provided to demonstrate the application of the model. Finally to illustrate the model and sensitivity analysis and graphical representation have been shown.

A Soft-Path Solution to Risk Reduction by Modeling Medical Waste Disposal Center Location-Allocation Optimization.

The risk of medical waste pollution and huge demand of daily medical waste disposal pose great difficulties to medical waste management. Establishing medical waste disposal centers (MWDCs) is considered one of the ways to reduce the environmental and public risk of medical waste pollution. However, how to serve the medical waste disposal demand in optimal MWDCs' locations is a key challenge due to the complexity of the whole system and relationships among stakeholders. This article develops a soft-path solution for reducing risks as well as mitigating the related costs by optimizing the MWDC location-allocation problem. A risk mitigation-oriented bilevel equilibrium optimization model is developed for modeling the Stackelberg game behavior between the local government and the medical institutions. The objectives of the local government are minimizing the total risk of loss, the subsidy costs, and the investment cost of building the MWDCs, while minimizing the disposal and transportation costs are the objectives at the medical institution level. Fuzzy random variables are introduced by combining insufficient historical data with expert knowledge via consulting surveys to describe the coexisting uncertainties in the data. To solve the model, a hybrid approach combined with the interactive fuzzy programming technique and an Entropy-Boltzmann selection-based genetic algorithm are designed and tested. The Chengdu Medical Waste Disposal Centers Planning Project is used as a practical application. The results show that it is possible to achieve a balanced market with higher economic efficiency and significantly reduced risk through an appropriate principle of interactive actions between the bilevel stakeholders.

Multi-item a supply chain production inventory model of time dependent production rate and demand rate under space constraint in fuzzy environment

In this paper, we have developed an integrated production inventory model for two echelon supply chain consisting of one vendor and one retailer. Production rate and demand rate of retailer and customer are time dependent. Idle time cost of the vendor has been considered. Multi-item inventory has been considered. In integrated inventory model average cost has been calculated under limitation on stroge space. Two echelon supply chain fuzzy inventory model has been solved by various techniques like as Fuzzy programming technique with hyperbolic membership functions (FPTHMF), Fuzzy non-linear programming technique (FNLP) and Fuzzy additive goal programming technique (FAGP), weighted Fuzzy non-linear programming technique (WFNLP) and weighted Fuzzy additive goal programming technique (WFAGP). A numerical example is illustrated to test the model. Finally to make the model more realistic, sensitivity analysis has been shown.

Application of fuzzy programming techniques to solve solid transportation problem with additional constraints

An innovative, real-life solid transportation problem is explained in a non-linear form. As in real life, the total transportation cost depends on the procurement process or type of the items and the distance of transportation. Besides, an impurity constraint is considered here. The proposed model is formed with fuzzy imprecise nature. Such an interesting model is optimised through two different fuzzy programming techniques and fractional programming methods, using LINGO-14.0 tools followed by the generalized gradient method. Finally, the model is discussed concerning these two different methods.

Multi-Objective Two Echelon Supply Chain Inventory Model with Lot Size and Customer Demand Dependent Purchase Cost and Production Rate Dependent Production Cost

This paper develops an integrated production inventory model for a two echelon supply chain consisting of one manufacturer and one retailer. Purchase cost for the manufacturer is dependent on inventory lot size, production cost of the manufacturer is dependent on production rate. Purchase cost of the retailer is dependent on demand rate of the customer. Idle time cost has been considered. Multi-item has been considered in this supply chain inventory model. Average cost in integrated inventory model has been calculated per unit time. The formulated problem has been solved by various techniques like as Fuzzy programming technique with hyperbolic membership functions (FPTHMF), Fuzzy non-linear programming technique (FNLP) and Fuzzy additive goal programming technique (FAGP), weighted Fuzzy non-linear programming technique (WFNLP) and weighted Fuzzy additive goal programming technique (WFAGP). A numerical example is provided to justify the proposed model. Finally graphical illustrations are considered and its sensitivity analysis is provided to test feasibility of the model.

An interval type-2 fuzzy stochastic approach for regional-scale electric power system under parameter uncertainty

ABSTRACTIn this study, an interval type-2 fuzzy stochastic linear programming method (IT2FSLP) is developed to support regional-scale electric power system (REM) planning. The IT2FSLP-REM model is based on an integration of interval type-2 fuzzy sets boundary programming and stochastic linear programming techniques enable it to have robust abilities to the deal with uncertainties expressed as type-2 fuzzy intervals and probabilistic distributions within a general optimization framework. Moreover, it can reflect dynamic decisions for energy supply and energy conversion processes, as well as provide capacity expansion options with multiple periods. The developed model is applied to a case of planning regional-scale energy and environmental systems to demonstrate its applicability. Based on a two-step solution algorithm, reasonable solutions have been obtained, which reflect tradeoffs among economic cost, environmental requirements, and energy-supply security. Thus, the lower and upper solutions of IT2FSLP-REM would then help energy authorities adjust or justify allocation patterns of regional energy resources and services.

Maximizing profit and responsiveness of a closed-loop supply chain in presence of product exchange offer

Designing an effective collection process is strategically important due to its impact on product-recovery, profit and responsiveness of overall closed-loop supply chain (CLSC). In this paper, we propose a product-recovery framework which models consumers’ willingness to accept a product exchange offer (PEO) as non-linear function of discount amount offered to them on returning used product and utility they obtain on receiving the new product. The proposed recovery framework is then integrated with a multi-objective optimization model, which takes into account the responsiveness of both forward and reverse supply chain, in order to maximize profit and responsiveness of the overall CLSC. The optimization model is solved using a modified interactive fuzzy goal programming technique, which allows the decision makers to adjust lower and/or upper bound of the objective functions during the interactive decision making process. The developed optimization model determines optimal value of discount, optimal return and remanufacturing quantity of used products, and optimal manufacturing quantity of fresh-new products. The analysis suggests a trade-off between amount of discount offered to consumers on returning used products and perceived quality of the new product while accepting the PEO.

Solution of fuzzy multi criteria project management problem by Fuzzy programming technique with possibilistic approach

Objective: This study contains a linear and exponential membership function based fuzzy programming technique with possibilistic approach and its application to find the critical path in project network. Methods: It contains four criteria; cost, quality, time and risk of the project activities for project management. For finding the solution of this multi-criteria project management problem in fuzzy programming technique for better decision by Decision Maker (DM) alpha level set concept is utilized. We have provided numerical illustration to demonstrate working of the proposed methodology. Findings: To analyse the performance of the proposed approach, we have compared it with closely related fuzzy group multi-criteria decision making related Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method for the critical path selection. Application: Further, a case study from manufacturing engineering industry is also presented to justify the applicability and potentials of proposed methodology in a better way. Degree of satisfaction is calculated for different values of alpha levels to validate the applicability of this new approach. Keywords: α-level, Critical Path, Fuzzy Programming, Project Management, Possibilistic Approach

Stochastic Inventory Model with Income and Price Dependent Demand

A multi-item cost minimising stochastic inventory model is developed in stochastic environment. Demand is considered to be function of income level of consumer and price of commodity. Budget, income and price are assumed to be random and their randomness is expressed by normal distribution. Deterioration rate is modelled using Weibull distribution. Stochastic inventory model is converted into equivalent crisp inventory model by using stochastic nonlinear programming (SNLP) technique. Crisp problem is solved by fuzzy nonlinear programming (FNLP) technique and intuitionistic fuzzy optimisation (IFO) technique. Sensitivity analysis of the optimum solution with respect to feasible changes in average and variance of income level and price is discussed and conclusions are noted.

Solution of fuzzy multi objective generalised assignment problem

In this paper, multi objective generalised assignment problem (MOGAP) with fuzzy parameters has been solved using three different approaches. Here, we consider three objective functions which are to be minimised. In the first approach, weighted sum method has been used and the problem is converted into a single objective one and then solved by extremum difference method (EDM) to get the optimal assignment. In the second one, modified fuzzy programming technique (MFPT) has been used for the same problem. Application of linear and exponential membership functions give comparative results with the goal that the better alternative can be obtained. The third one describes multi objective genetic algorithm (MOGA) to find the solution surface and the Pareto optimal front including the optimal assignment. The methods are demonstrated by a suitable numerical example.

A carbon emission optimization model with reduction method of type-2 zigzag uncertain variable

The main investigation of the paper is to propose a reduction method of type-2 zigzag uncertain variables. We have also proposed an innovative, dynamic solid transportation problem (STP) considering maximization of profit and minimization of emission. The model has been presented to show an awareness among the drivers or managers of firms to emit less amount of carbon particles. The transportation parameters of the model have been taken as type-2 zigzag uncertain variables. The proposed expected value-based reduction method has been used to convert the transportation parameters into deterministic form. A real-life study has been presented here to show the use of the proposed reduction method and proposed STP. LINGO 13.0 optimization software has been used to solve the multi-objective STP using fuzzy satisficing method and intuitionistic fuzzy programming technique. The transportation parameters of the model are also presented in type-2 triangular fuzzy variables to show a comparison with the type-2 zigzag uncertain variable. A sensitivity analysis is presented with respect to different credibility levels of profit, emission, source, demand and conveyance.

Longitudinal cooperative robust optimization model for sustainable supply chain management

This paper considers the trade-offs of two-tier supply chain enterprises in an uncertain environment, and can be formulated into a two-tiered multi-programming formula. The model we proposed considers green building alternatives’ cost, duration and carbon emissions uncertainties simultaneously, making it more realistic comparing to models in previous literature. In this model, the interval number and expected value based on Me are adopted to handle the uncertain coefficients contained in the objective function and constraints, then a stochastic-based robust optimization method is developed to get a solution that can resist the uncertain environment. To solve the complex and non-linear bi-level multi-follower model, an interactive fuzzy programming technique combined an effective multi-objective algorithm, NSGA-II, is designed as the solution method. Finally, an applicant for a contractor of Urban Construction Group and its sub-contractors is given as an illustration that demonstrates the practicality and efficiency of the proposed model. The sensitivity analysis towards the change of important parameters is also provided.

A gamma type-2 defuzzification method for solving a solid transportation problem considering carbon emission

This paper intends to develop a multi-objective solid transportation problem considering carbon emission, where the parameters are of gamma type-2 fuzzy in nature. This paper proposed the defuzzification process for gamma type-2 fuzzy variable using critical value (CV ) and nearest interval approximation method. A chance constraint programming problem is generated using the CV based reduction method to convert the fuzzy problem to its equivalent crisp form. Applying the $\alpha $ -cut based interval approximation method, a deterministic problem is developed. Some real life data are used to minimize the cost and carbon emission. LINGO standard optimization solver has been used to solve the multi-objective problem using weighted sum method and intuitionistic fuzzy programming technique. The Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) algorithm are implemented to generate efficient optimal solution by converting the multi-objective problem to a single objective problem using penalty cost for carbon emission. After solving the problem, analysis on some particular cases has been presented. The sensitivity analysis has been shown to different credibility levels of cost, emission, source, demand, conveyance to find total cost, emission and transported amount in each level. A comparison study on the performance of three algorithms (LINGO, GA and PSO) is presented. At the end, some graphs have been plotted which shows the effect of emission with different emission parameters.

Multiperiod Fuzzy Portfolio Selection Optimization Model Based on Possibility Theory

Using the central value operator and the semi-dispersion measure of fuzzy number, this paper proposes the definitions of the lower and upper semi-variances. A general multiperiod fuzzy portfolio optimization model with return demand on the portfolio at each period is proposed with the objectives of maximizing both terminal wealth and the cumulative diversification degree of portfolios over the whole investment horizon, and minimizing terminal risk. A fuzzy multiobjective nonlinear programming technique is applied to convert the proposed model into a single-objective model. A genetic algorithm (GA) is given to solve it. Besides, a numerical example is given to illustrate the application of the proposed model and the effectiveness of the designed algorithm.

Multi item two-warehouse fuzzy inventory model

In this paper multi-item fuzzy profit maximisation inventory model with ramp type demand under imprecise space, budget constraints and imprecise holding cost with two storage facilities are presented. There are two warehouses, one is situated at market place called as own warehouse (OW) and another is little away from market place called as rented warehouse (RW). The sale is conducted from OW and the sold items are replaced continuously by the items at RW. Here shortages are not allowed. The fuzzy model has been solved by using fuzzy nonlinear programming technique and illustrated numerically.

Solution of Fuzzy Multi-Objective Fractional Linear Programming Problem Using Fuzzy Programming Technique based on Exponential Membership Function

Solution of Fuzzy Multi-Objective Fractional Linear Programming Problem Using Fuzzy Programming Technique based on Exponential Membership Function

Fuzzy E.O.Q model with constant demand and shortages: A fuzzy signomial geometric programming (FSGP) approach

In this paper, a fuzzy economic order quantity (E.O.Q) model with shortages under fully backlogging and constant demand is formulated and solved. Here the model is solved by fuzzy signomial geometric programming (FSGP) technique. Fuzzy signomial geometric programming (FSGP) technique provides a powerful technique for solving many non-linear problems. Here we have proposed a new idea that is fuzzy modified signomial geometric programming (FMSGP) and some necessary theorems have been derived. Finally, these are illustrated by some numerical examples and applications.