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Multiitem fuzzy inventory problem with space constraint via geometric programming method
 Yugoslav Journal of Operation Research
"... Abstract: In this paper, a multiitem inventory model with space constraint is developed in both crisp and fuzzy environment. A profit maximization inventory model is proposed here to determine the optimal values of demands and order levels of a product. Selling price and unit price are assumed to b ..."
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Abstract: In this paper, a multiitem inventory model with space constraint is developed in both crisp and fuzzy environment. A profit maximization inventory model is proposed here to determine the optimal values of demands and order levels of a product. Selling price and unit price are assumed to be demanddependent and holding and setup costs sock dependent. Total profit and warehouse space are considered to be vague and imprecise. The impreciseness in the above objective and constraint goals has been expressed by fuzzy linear membership functions. The problem is then solved using modified geometric programming method. Sensitivity analysis is also presented here.
leadtime and dynamic demand
, 2003
"... Normally, the realworld inventory control problems are imprecisely defined and human interventions are often required to solve these decisionmaking problems. In this paper, a realistic inventory model with imprecise demand, leadtime and inventory costs have been formulated and an inventory policy ..."
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Normally, the realworld inventory control problems are imprecisely defined and human interventions are often required to solve these decisionmaking problems. In this paper, a realistic inventory model with imprecise demand, leadtime and inventory costs have been formulated and an inventory policy is proposed to minimize the cost using man–machine interaction. Here, demand increases with time at a decreasing rate. The imprecise parameters of leadtime, inventory costs and demand are expressed through linear/nonlinear membership functions. These are represented by different types of membership functions, linear or quadratic, depending upon the prevailing supply condition and marketing environment. The imprecise parameters are first transformed into corresponding interval numbers and then following the interval mathematics, the objective function for average cost is changed into respective multiobjective functions. These functions are minimized and solved for a Paretooptimum solution by interactive fuzzy decisionmaking procedure. This process leads to man–machine interaction for optimum and appropriate decision acceptable to the decision makerÕs firm. The model is illustrated numerically and the results are presented in tabular forms.
Solution of a Probabilistic Inventory Model with Chance Constraints: A General Fuzzy Programming and Intuitionistic Fuzzy Optimization Approach
"... Abstract: This paper considers a probabilistic inventory model with uniform leadtime demand and fuzzy cost components under probabilistic and imprecise constraints. Firstly we solve the model by general fuzzy nonlinear programming technique. Then intuitionistic fuzzy optimization technique is appli ..."
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Abstract: This paper considers a probabilistic inventory model with uniform leadtime demand and fuzzy cost components under probabilistic and imprecise constraints. Firstly we solve the model by general fuzzy nonlinear programming technique. Then intuitionistic fuzzy optimization technique is applied and finally, regarding the optimization of the objective function a comparative study is presented among fuzzy optimization technique, general fuzzy nonlinear programming technique and intuitionistic fuzzy optimization technique. All the results and comparative discussions are illustrated numerically.
Maximum Likelihood Estimation: A Single and Multiobjective Entropy Optimization Approach
"... Abstract: In this paper we first considered a maximum likelihood estimation of trip distribution problem and next use primaldual geometric programming method the said trip distribution problem converted into an entropy maximization trip distribution problem. Here the generalized cost function is as ..."
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Abstract: In this paper we first considered a maximum likelihood estimation of trip distribution problem and next use primaldual geometric programming method the said trip distribution problem converted into an entropy maximization trip distribution problem. Here the generalized cost function is assumed in different form, and then the said formulation is equivalent to single or multiobjective entropy maximization trip distribution problem. We use fuzzy mathematical programming method to show this equivalent problem formulation. The present article we use the concept of multiobjective trip distribution problem.
Fuzzy Transportation Linear Programming Models based on LR Fuzzy Numbers
"... Transportation models play an important role in logistics and supply chain management for reducing cost and improving service. In this paper two new fuzzy transportation linear programming models are developed: one with equality constraints and other with inequality constraints using LR fuzzy numbe ..."
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Transportation models play an important role in logistics and supply chain management for reducing cost and improving service. In this paper two new fuzzy transportation linear programming models are developed: one with equality constraints and other with inequality constraints using LR fuzzy numbers. The membership functions of LR fuzzy numbers of fuzzy transportation cost are consider being linear and exponential. This paper develops a procedure to derive the fuzzy objective value of the fuzzy transportation problem, in that the cost coefficients and the supply and demand are LR fuzzy numbers. The two models are illustrated with an example. The optimal fuzzy transportation cost for the two models slightly varies when linear membership functions are equal and the optimal fuzzy transportation cost is same in case of different membership functions i.e., either linear or exponential membership functions defined on LR fuzzy numbers. Most of the fuzzy transportation problems reviewed in literature have the negative optimal fuzzy transportation cost but in our proposed method we obtain positive optimal fuzzy transportation cost in all most all cases. Keywords Fuzzy transportation problem; Yager’s ranking index; LR fuzzy numbers; linear programming. 1.
Modeling of a Continuous Review Supply Chain in an Uncertain Environment
"... Although supply chain (SC) has gained increasing attention in the last two decades and numerous SC problems have been identified and solved, there is a lack of systematic approach to solve SC problems in an uncertain environment. Since past data are not always available or reliable due to market du ..."
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Although supply chain (SC) has gained increasing attention in the last two decades and numerous SC problems have been identified and solved, there is a lack of systematic approach to solve SC problems in an uncertain environment. Since past data are not always available or reliable due to market durbulance, the sources of uncertainty (e.g. lead time, demand rate, inventory costs and backorder costs) are modeled by fuzzy numbers rather than by probabilistic distributions. In this paper, a realistic supply chain model with imprecise demand, leadtime and inventory costs have been formulated and an optimal policy is proposed to minimize the cost using manmachine interaction. Here we consider a twolevel supply chain with single warehouse at the upper echelon and many retailers at the lowerechelon. The unsatisfied customer demands at the retailers are partially backordered using the control parameter b. The replenishment policy at all installations is continuous review policy. The imprecise parameters of leadtime, inventory costs and demand are expressed through linear/nonlinear membership functions. These are represented by different types of membership functions, linear or quadratic, depending upon the prevailing supply condition and marketing environment. The imprecise parameters are transformed into corresponding interval numbers and then following the interval analysis, the objective function for average cost is changed into respective multiobjective functions. These functions are minimized and solved for a Paretooptimum solution by interactive fuzzy decisionmaking procedure. This process leads to manmachine interaction for optimum and appropriate decision acceptable to the decision makers firm. The model is illustrated numerically and the results are presented in tabular forms.
© Impact Journals ON INTUITIONISTIC FUZZY INVENTORY MODELS WITHOUT ALLOWING STORAGE CONSTRAINT
"... This paper deals with the problem of determining the economic order quantity (EOQ), as a function of the setup cost and the holding cost in the interval sense. Practically vagueness caused by the variation in fixing these costs is inevitable. Intuitionistic fuzzy inventory model with instantaneous r ..."
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This paper deals with the problem of determining the economic order quantity (EOQ), as a function of the setup cost and the holding cost in the interval sense. Practically vagueness caused by the variation in fixing these costs is inevitable. Intuitionistic fuzzy inventory model with instantaneous replenishment and no shortages is analyzed to compute the economic order quantity and the total annual cost by assigning fuzzy quantity and intuitionistic fuzzy quantity instead of real quantity to these costs. Parametric programming technique is applied and the results are compared numerically both in fuzzy optimization and intuitionistic fuzzy optimization techniques. Necessary graphical presentations are also given besides numerical illustrations.
MultiObjective Structural Design Optimization using Fuzzy Optimization Programming based on TNorm
"... In this paper we propose an approach to solve multiobjective structural design problem using basic tnorm based fuzzy optimization programming technique. Here a planer truss structural model in fuzzy environment has been developed. In this structural model formulation, the objective functions are t ..."
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In this paper we propose an approach to solve multiobjective structural design problem using basic tnorm based fuzzy optimization programming technique. Here a planer truss structural model in fuzzy environment has been developed. In this structural model formulation, the objective functions are the weight of the truss and the vertical deflection of loaded joint; the design variables are the crosssections of the truss members; the constraints are the stresses in members. A classical truss optimization example is presented here in to demonstrate the efficiency of our propose optimization approach. The test problem includes a threebar planar truss subjected to a single load condition. This approximation approach is used to solve this multiobjective structural optimization model. The model is illustrated with numerical examples.