Fuzzy Non-linear Programming Technique Research Articles

A Fuzzy Multi Objective Inventory Model with Production Cost and Set-up-Cost Dependent on Population

AbstractIn this paper, I have developed a multi item production inventory model for the non-deteriorating items with constant demand rate under the limitation on set up cost. The production price and set-up price are the most vital problem within the inventory system of the marketplace in international. Here the production cost is dependent on the demand as well as populations. Set up cost is dependent on the average inventory level. Holding cost is the most challenging issue in the business world. In order to reduce the holding cost, the holding cost function has been considered as on the number of peoples. Due to uncertainty all the cost parameters are taken as the generalized triangular fuzzy number. Multi objective fuzzy inventory model has been solved by various techniques like Fuzzy programming technique with hyperbolic membership function, Fuzzy non-linear programming technique and Fuzzy additive goal programming technique. Numerical example is given to illustrate the inventory model. Sensitivity analysis and the graphical representations have been shown to illustrate the reality of the inventory model.

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.

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.

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.

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.

Optimality test in fuzzy inventory model for restricted budget and space: Move forward to a non-linear programming approach

In this paper, the concept of fuzzy Non-Linear Programming Technique is applied to solve an economic order quantity (EOQ) model for restricted budget and space. Since various types of uncertainties and imprecision are inherent in real inventory problems, they are classically modeled using the approaches from the probability theory. However, there are uncertainties that cannot be appropriately treated by the usual probabilistic models. The questions are how to define inventory optimization tasks in such environment and how to interpret the optimal solutions. This paper allow the modification of the Single item EOQ model in presence of fuzzy decision making process where demand is related to the unit price, and the setup cost varies with the quantity produced/Purchased. The modification of objective function, budget, and storage area in the presence of imprecisely estimated parameters are considered. The model is developed by employing different approaches over an infinite planning horizon. It incorporates all the concepts of a fuzzy arithmetic approach and comparative analysis with other non linear models. Investigation of the properties of an optimal solution allows developing an algorithm whose validity is illustrated by an example problem, and two and three dimensional diagrams are represented to this application through MATL(R2009a) software. Sensitivity analysis of the optimal solution is studied with respect to the changes of different parameter values for obtaining managerial insights of the decision problem.

Solution of single and multi-objective fixed reorder quantity system by general fuzzy programming technique

This paper considers a multi item single period inventory problem with floor space constraint where the demand of the items follows probability distributions. Two different stochastic models are discussed where the demand follows Uniform distribution and Exponential distribution respectively. Firstly the fixed reorder quantity system with backorder and secondly fixed reorder quantity system with lost sales are discussed. Then consideration is adopted as a multi objective stochastic inventory model where average annual cost of the first item as well as the same of the second item are minimized simultaneously and is also formulated in fuzzy environment introducing fuzziness in the objectives. In this paper the concept of General Fuzzy Non-linear Programming Technique is applied to solve a multi objective single period stochastic inventory problem with floor space constraint. The solution is illustrated by numerical example and the results of different models are compared.

Multi-Objective Fuzzy Inventory Model For Deteriorating Items With Shortages Over A Finite Time Horizon

We consider here the inventory problems with infinite rate of replenishment in crisp and fuzzy environments over a finite time horizon for deteriorating multi-items taking time dependent demand and allowing shortages and equal replenishment cycles. Here, the objectives of maximizing the profit and minimizing the replenishment cost are imprecise in nature. Total shortage cost is assumed to be limited but vague and imprecise in non-stochastic sense. The impreciseness in the above objectives’ and constraint’ goals have been expressed by fuzzy linear Membership Functions (MFs). Under these assumptions, a Decision Maker (DM) is confronted with four possibilities depending upon the nature of the first and last cycles and he/she has to choose the best one for maximum profit-ratio (i.e. the ratio of total profit to total cost). Hence, both crisp and fuzzy models with different shortage criteria are developed and solved by the weighted fuzzy non-linear programming (WFNLP) and goal attainment methods (GAM). Fuzzy models have also been solved by an integrated goal attainment and fuzzy non-linear programming technique (GAFNLP). Models are illustrated with numerical examples and the results are compared.

The fuzzy weighted additive rule

Abstract The weighted additive rule is completely characterized in terms of a set of axioms and an aggregate regret function as an aggregation operator for fuzzy sets of type 1. Optimization techniques are used to assess weights for criteria based upon the opinions of experts. By means of a fuzzy non-linear programming technique, the method is extended to the case of linguistic evaluations and judgments which can be modeled as fuzzy sets of type 2.