Fuzzy stochastic EOQ inventory model for items with imperfect quality and shortages are backlogged (original) (raw)
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Fuzzy E.O.Q Model for Deteriorating Items, with Constant Demand, Shortages, and Fully Backlogging
The Oxford Journal of Intelligent Decision and Data Science, 2016
In this paper analyzes fuzzy inventory system for deteriorating items with constant demand. Shortages are allowed under fully backlogged here. Fixed cost, deterioration cost, shortages cost, holding cost are the cost considered in this model. In this model first time we have considered a special condition that the demand falls to zero in a time interval (0 ≤ ≤) for an unexpected condition (flood, strike, earthquake, etc.) and considered three cases. Fuzziness is applying by allowing the cost components (holding cost, deterioration, shortage cost, etc). In fuzzy environment it considered all required parameter to be triangular fuzzy numbers. Here we use nearest interval approximation method to convert a triangular fuzzy number to an interval number and we have transformed this interval number to a parametric interval-valued functional form. Several numerical examples are given to verify optimal solutions. The purpose of the model is to minimize total cost function.
Fuzzy Inventory Model for Deteriorating Items with Shortages under Fully Backlogged Condition
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.
Computers & Industrial Engineering, 2013
This paper considers inventory models for items with imperfect quality and shortage backordering in fuzzy environments by employing two types of fuzzy numbers, which are trapezoidal and triangular. Two fuzzy models are developed. In the first model the input parameters are fuzzified, while the decision variables are treated as crisp variables. In the second model, not only the input parameters but also the decision variables are fuzzified. For each fuzzy model, a method of defuzzification, namely the graded mean integration method, is employed to find the estimate of the profit function in the fuzzy sense, and then the optimal policy for the each model is determined. The optimal policy for the second model is determined by using the Kuhn-Tucker conditions after the defuzzification of the profit function. Numerical examples are provided in order to ascertain the sensitiveness in the decision variables with respect to fuzziness in the components.
International Journal of Supply Chain Management, 2018
In this paper, we develop an economic order quantity model with imperfect quality, inspection errors and sales returns, where upon the arrival of order lot, 100% screening process is performed and the items of imperfect quality are sold as a single batch at a lessen price, prior to receiving the next shipment. The screening process to remove the defective items may involve two types of errors. In this article we extend the Khan et al. (2011) model by considering demand and defective rate in fuzzy sense and also sales return in our model. The objective is to determine the optimal order lot size to maximize the total profit. We use the signed distance, a ranking method for fuzzy numbers, to find the approximate of total profit per unit time in the fuzzy sense. The impact of fuzziness of fraction of defectives and demand rate on optimal solution is showed by numerical example.
Fuzzy Inventory Model for Deteriorating Items with Time-varying Demand and Shortages
2012
Fu zzy set theory is primarily concerned with how to quantitatively deal with imp rec ision and uncertainty, and offers the decision maker another tool in addition to the classical deterministic and probabilistic mathematical tools that a re used in modeling real-world problems. The present study investigates a fuzzy economic order quantity model for deteriorating items in which demand increases with time. Shortages are allowed and fully backlogged. The demand, holding cost, unit cost, shortage cost and deterioration rate are taken as a triangular fuzzy nu mbers. Graded Mean Representation, Signed Distance and Centroid methods are used to defuzzify the total cost function and the results obtained by these methods are compared with the help of a numerical example. Sensitivity analysis is also carried out to explore the effect of changes in the values of some of the system parameters. The proposed methodology is applicable to other inventory models under uncertainty.
A fuzzy inventory model with imperfect items and backorder with allowable proportionate discount
Modelling, Measurement and Control D
This paper presents both crisp and fuzzy EOQ models for defective items present in each lot when shortages are allowed and backorder takes place. The aim of the work is to first construct an optimal order quantity for the crisp case and then to develop the corresponding fuzzy model. In contrast to the previous inventory models, an allowable proportionate discount is incorporated for the defective items present in each lot to provide a general framework to the model. The aim of the present paper is to find the optimal order size and the expected shortage level so as to obtain the optimum total profit for both the models. The necessary and sufficient conditions for the existence and uniqueness of the optimal solutions are derived and it is also shown that under certain conditions the crisp model boils down the traditional EOQ backorder formula. For the fuzzy case, triangular fuzzy numbers are used for the defective rates and for defuzzification signed distance method is used. Finally, numerical example is provided to illustrate the solution procedure and sensitivity analysis is performed on the results to analyze the effect of the variations taken place for the parameters involved in the model.
A Fuzzy Production Inventory Model for Deteriorating Items with Shortages
International Journal for Research in Applied Sciences and Biotechnology, 2021
In this paper we have developed a supply chain production inventory model for deteriorating items with shortage under Fuzzy environment. The formulae for the optimal average system cost, stock level, backlog level and production cycle time are derived when the deterioration rate is very small. In reality it is seen that we cannot define all parameters precisely due to imprecision or uncertainty in the environment. So, we have defined the inventory parameter deterioration rate as triangular fuzzy numbers. The signed distance method and graded mean integration method have been used for defuzzification. Numerical examples are taken to illustrate the procedure of finding the optimal total inventory cost, stock level and backlog level. Sensitivity analysis is carried out to demonstrate the effects of changing parameter values on the optimal solution of the system.
Multi-item imperfect production inventory model in Bi-fuzzy environments
OPSEARCH, 2016
In this paper, we propose a mathematical model for a single period multiproduct production inventory model producing stochastically imperfect items with continuous stochastic demand under budget and limited shortage constraints in Bifuzzy environment. The stochastic constraints are first converted into corresponding crisp values using expected value method. Here, we have considered the model as single period's inventory for each item and the cycle lengths for different items are constant but different. Total demand for a cycle and the rate of production of defective units is considered as stochastic. The model is formulated and the expected average profits for each product are calculated from density function of demand and percentage of imperfectness in general form and then particular expressions are obtained by using appropriate boundary conditions. Here, all the constraints are Bi-fuzzy in nature and represented by possibility constraints. The deterministic problem is then solved by using generalized reduced gradient method. The model is illustrated through numerical examples. Sensitivity analysis on profit functions due to different aspiration and confidence level is presented via graphically.
This paper presents a fuzzy continuous review inventory model for deteriorating items in a supply chain management system with price dependent demand. In reality it is seen that, the cycle time of almost every supply chain system is uncertain, so we describe it as symmetric triangular fuzzy number. Signed distance method is used to defuzzify the cost function. To illustrate the proposed model a numerical example and sensitivity analysis with respect to different associated parameters has been presented.
Journal of Uncertainty Analysis and Applications
Possibility, necessity, and credibility measures play a significant role to measure the chances of occurrence of fuzzy events. In this paper, possibility, necessity, and credibility measures of exponential fuzzy number, and its expected value has been derived. A multi-item two-warehouse deterministic inventory model for deteriorating items with stock-dependent demand has been developed. For the proposed inventory model, the different costs and other parameters are considered in exponential fuzzy nature. Solution methodology of this model using expected value has been discussed. A numerical example is considered to illustrate the multi-item two-warehouse deterministic inventory model. Finally, few sensitivity analyses are presented under different rates of deterioration to check the validity of the proposed model.