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Fuzzy Inventory Model for Deteriorating Items with Shortages under Fully Backlogged Condition
"... Abstract — In this paper, a fuzzy inventory model for deteriorating items with shortages under fully backlogged condition is formulated and solved. Deterioration rate and demand are assumed to be constant. Shortages are allowed and assumed to be fully backlogged. Fuzziness is introduced by allowing ..."
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Abstract — In this paper, a fuzzy inventory model for deteriorating items with shortages under fully backlogged condition is formulated and solved. Deterioration rate and demand are assumed to be constant. Shortages are allowed and assumed to be fully backlogged. Fuzziness is introduced by allowing the cost components (holding cost, shortage cost, etc.), demand rate and the deterioration. In fuzzy environment, all related inventory parameters are assumed to be trapezoidal fuzzy numbers. The purpose of this paper is to minimize the total cost function in fuzzy environment. A numerical example is given in order to show the applicability of the proposed model. The convexity of the cost function is shown graphically. Sensitivity analysis is also carried out to detect the most sensitive parameters of the system. From sensitivity analysis, we show that the total cost function is extremely influenced by the holding cost, demand rate and the shortage cost. Keywords—Inventory model, Trapezoidal fuzzy number, Fuzzy demand, Fuzzy deterioration.
FUZZY ECONOMIC PRODUCTION QUANTITY MODEL FOR ITEMS WITH IMPERFECT QUALITY
, 2006
"... Abstract. In the real world, vague phenomenon is quite common in the production/inventory models. In order to process the vagueness, a production/inventory model that can be more closely related to the real vagueness and can take account of the vague factors that contribute to production costs, is r ..."
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Abstract. In the real world, vague phenomenon is quite common in the production/inventory models. In order to process the vagueness, a production/inventory model that can be more closely related to the real vagueness and can take account of the vague factors that contribute to production costs, is required. The model must be extended or altered to fit in with the fuzzy situation. Since items with imperfect quality, during production or inventory procedure, are unavoidable, we also consider this situation. In order to treat the case in the vague environment, we propose a Fuzzy Economic Production Quantity (FEPQ) model with imperfect products that can be sold at a discount price. In this model, costs and quantities are expressed as trapezoidal fuzzy numbers. Moreover, we use Function Principle to manipulate arithmetical operations, Graded Mean Integration Representation method to defuzzify, and KuhnTucker conditions to find the optimal economic production quantity of the fuzzy production inventory model. Finally, an application of an electronics industry example gives a satisfactory result.
Fuzzy Flexibility and Product Variety in LotSizing
"... In terms of flexibility and product variety in lotsizing systems of crisp cases, the average demand of per unit of time (mj), the relative duration of setup (qj), and the unit cost of production (cj) are considered. Instead of using the usual method that the mj, qj, and cj in the total cost functio ..."
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In terms of flexibility and product variety in lotsizing systems of crisp cases, the average demand of per unit of time (mj), the relative duration of setup (qj), and the unit cost of production (cj) are considered. Instead of using the usual method that the mj, qj, and cj in the total cost function are respectively fuzzified by the triangular fuzzy numbers to derive fuzzy total cost, in this paper, we construct three different intervals to include mj, qj, and cj, respectively, and then consider the fuzzification of the system from these three different intervals directly. And finally the fuzzy total cost is obtained. By applying respectively the signed distance and centroid method for defuzzification, two different total cost functions are obtained, and thus the respective optimal solutions are computed.
Optimization of Fuzzy Inventory Models under kpreference
, 2002
"... Inventory is any stored resource that is used to satisfy a current or a future need. In this paper, two fuzzy inventory models with fuzzy parameters for crisp order quantity, or for fuzzy order quantity under decision maker’s preference are introduced. We propose the fuzzy total annual inventory cos ..."
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Inventory is any stored resource that is used to satisfy a current or a future need. In this paper, two fuzzy inventory models with fuzzy parameters for crisp order quantity, or for fuzzy order quantity under decision maker’s preference are introduced. We propose the fuzzy total annual inventory costs based on the fuzzy arithmetical operations under Function Principle. The final purpose is to find the optimal order quantities of our proposed models under the preference of manager by using Graded kpreference Integration Representation method for defuzzifing the fuzzy total annual inventory cost, and by using Extension of the Lagrangean method for solving inequality constrain problem. Furthermore, we find the optimal order quantity or the optimal fuzzy order quantity of our proposed models are the real numbers. In addition, when the k = 0.5 and all fuzzy parameters are the crisp real numbers, our optimal solutions can be specified to meet classical production inventory models.
Fuzzy Inventory Model for Deteriorating Items with Time Dependent Demand and
"... In this paper we developed a fuzzy inventory model for deteriorating items with time dependent demand rate. Shortages are allowed and completely backlogged. The backlogging rate of unsatisfied demand is assumed to be a decreasing exponential function of waiting time. The demand rate, deterioration ..."
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In this paper we developed a fuzzy inventory model for deteriorating items with time dependent demand rate. Shortages are allowed and completely backlogged. The backlogging rate of unsatisfied demand is assumed to be a decreasing exponential function of waiting time. The demand rate, deterioration rate and backlogging rate are assumed as a triangular fuzzy numbers. The purpose of our study is to defuzzify the total profit function by signed distance method and centroid method. Further a numerical example is also given to demonstrate the developed crisp and fuzzy models. A sensitivity analysis is also given to show the effect of change of the parameters.
A Fuzzy Inventory System with Deteriorating Items under Supplier Credits Linked to Ordering Quantity
"... The inventory problem associated with trade credit is a popular topic in which interest income and interest payments are important issues. Most studies related to trade credit assume that the interest rate is both fixed and predetermined. However, in the real market, many factors such as financial ..."
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The inventory problem associated with trade credit is a popular topic in which interest income and interest payments are important issues. Most studies related to trade credit assume that the interest rate is both fixed and predetermined. However, in the real market, many factors such as financial policy, monetary policy and inflation, may affect the interest rate. Moreover, within the environment of merchandise storage, some distinctive factors arise which ultimately affect the quality of products such as temperature, humidity, and storage equipment. Thus, the rate of interest charges, the rate of interest earned, and the deterioration rate in a real inventory problem may be fuzzy. In this paper, we deal with these three imprecise parameters in inventory modeling by utilizing the fuzzy set theory. We develop the fuzzy inventory model based on Chang et al.’s [1] model by fuzzifying the rate of interest charges, the rate of interest earned, and the deterioration rate into the triangular fuzzy number. Subsequently, we discuss how to determine the optimal ordering policy so that the total relevant inventory cost, in the fuzzy sense, is minimal. Furthermore, we show that Chang et al.’s [1] model (the crisp model) is a special case of our model (the fuzzy model). Finally, numerical examples are provided to illustrate these results.
A note on optimal ordering policy for deteriorating items with uncertain maximum lifetime
, 2016
"... As in case of deteriorating items, expiration plays a major role in management of inventory. In addition, maximum lifetime is not available certainly for items like food stuffs, packaged food, electronic items, etc. To incorporate uncertainty, a Fuzzy Economic Ordering Policy is formulated to minim ..."
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As in case of deteriorating items, expiration plays a major role in management of inventory. In addition, maximum lifetime is not available certainly for items like food stuffs, packaged food, electronic items, etc. To incorporate uncertainty, a Fuzzy Economic Ordering Policy is formulated to minimize total cost of an inventory system. We consider triangular fuzzy maximum lifetime and triangular fuzzy costs under crisp ordering policy, in order to extent traditional optimal ordering policy to the fuzzy environment. We use function principle as arithmetic operations of Fuzzy Total Inventory Cost (FTIC), and Graded Mean Integration Representation is used to defuzzify the FTIC. Formulation is illustrated through numerical example. Sensitivity is carried out with respect to different parameters.
Fuzzy production planning models for an unreliable production system with fuzzy production rate and stochastic/fuzzy demand rate
, 2011
"... In this article, we consider a singleunit unreliable production system which produces a single item. During a production run, the production process may shift from the incontrol state to the outofcontrol state at any random time when it produces some defective items. The defective item producti ..."
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In this article, we consider a singleunit unreliable production system which produces a single item. During a production run, the production process may shift from the incontrol state to the outofcontrol state at any random time when it produces some defective items. The defective item production rate is assumed to be imprecise and is characterized by a trapezoidal fuzzy number. The production rate is proportional to the demand rate where the proportionality constant is taken to be a fuzzy number. Two production planning models are developed on the basis of fuzzy and stochastic demand patterns. The expected cost per unit time in the fuzzy sense is derived in each model and defuzzified by using the graded mean integration representation method. Numerical examples are provided to illustrate the optimal results of the proposed fuzzy models.
Fuzzy economic production in inventory model without shortage
, 2015
"... Abstract In this paper, an inventory model without shortage has been considered in fuzzy environment, using the new hexagonal fuzzy numbers. Our goal is to determine the fuzzy production quantity and fuzzy minimum total cost for the proposed inventory model. The storage cost, production cost and to ..."
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Abstract In this paper, an inventory model without shortage has been considered in fuzzy environment, using the new hexagonal fuzzy numbers. Our goal is to determine the fuzzy production quantity and fuzzy minimum total cost for the proposed inventory model. The storage cost, production cost and total demand quantity are taken as in terms of hexagonal fuzzy numbers. New arithmetic operations are defined and applied in sensitivity analysis. A relevant numerical example is also included, to justify the notion.