Determine the Optimal Order Quantity in Multi-items&s EOQ Model with Backorder (original) (raw)
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A review on fuzzy economic order quantity model under shortage
INTERNATIONAL SCIENTIFIC AND PRACTICAL CONFERENCE “TECHNOLOGY IN AGRICULTURE, ENERGY AND ECOLOGY” (TAEE2022)
Fuzzy set theory has a remarkable progress in the field of research. It initiates many areas in both practical & theoretical studies. It is really useful for several people engaged in research and development including medical researchers, mathematician, businessman, social scientists, natural researchers etc. This field of mathematics has introduced new life into technical and scientific fields that have been undeveloped for a long period. Thousands of scholars are operating and working with fuzzy set theory and presented a lot of research papers. In this paper latest review of existing literature & numerous types of fuzzy EOQ inventory models under shortage situation. It assists to categorize how the concept of fuzzy sets theory has been applied in inventory models which motivate researchers to concentrating on new technique in study of inventory control models in fuzzy environment. In this review, we study desirable constraints of existing models in fuzzy environment under shortage of supplies. A lot of effort is attempted to deliver the latest review of existing literature of inventory and fuzzy models. The purpose of the work is to obtain a continuous and comprehensive assessment of existing literature and recognize upcoming research guidelines. This review helps other researchers to draft an outcome during the situation of short supplies. This will also help to manage inventory according to the situation & reduce the loss during shortage of supplies, this review also helps to reduce loss with proper inventory management in real-life applications and marketable products.
Fuzzy Economic Order Quantity Model with Partial Backorder
In this paper, fuzzy economic order quantity (EOQ) model for inventory system with partial backorder is proposed. The fuzzy total relevance cost of the model is calculated under function principle. The optimal EOQ is derived using median rule. Fuzzy variables are appropriate when the exact information is unavailable. In the proposed model, the optimal solution for the fuzzy EOQ model is higher than the EOQ in crisp value due to the lack of information.
Fuzzy order quantity inventory model with fuzzy shortage quantity and fuzzy promotional index
Economic Modelling, 2013
The article deals with a backorder EOQ (Economic Order Quantity) model with promotional index for fuzzy decision variables. Here, a profit function is developed where the function itself is the function of m-th power of promotional index (PI) and the order quantity, shortage quantity and the PI are the decision variables. The demand rate is operationally related to PI variables and the model has been split into two types for the multiplication and addition operation. First the crisp profit function is optimized, letting it free from fuzzy decision variable. Yager (1981) ranking index method is utilized here to have a best inventory policy for the fuzzy model. Finally, a graphical presentation of numerical illustrations and sensitivity analysis are done to justify the general model.
Fuzzy stochastic EOQ inventory model for items with imperfect quality and shortages are backlogged
This article deals with an economic order quantity (EOQ) inventory model for items with imperfect quality in fuzzy stochastic environment, wherein shortages are allowed and completely backlogged. Fuzzy stochastic environment means linguistic 'impreciseness' and statistical 'uncertainty' both appear simultaneously. Due to uncertain demand trend, imperfect production process, natural disaster etc., the demand rate or imperfect quality items in the lot size can't predict precisely or to fit the exact probability density function. In this context, we assume that demand rate as a fuzzy number and fraction of defective items as a fuzzy random variable. We formulate the model and derive the total profit which is a function of fuzzy random variable. The fuzzy random renewal reward theorem is used to find the fuzzy expected total profit per unit time. The fuzzy expected total profit function is defuzzified by using the signed distance method. The closed form solution of the model is derived and subsequently the concavity of the total profit function is proved. The solution procedure is illustrated with the help of numerical examples. Sensitivity of decision variables for change in different parameters is examined and discussed.
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.
Decision making in fuzzy reasoning to solve a backorder economic order quantity model
Rairo-operations Research, 2023
Fuzzy reasoning is the subject of fuzzy system where the fuzzy set is characterized by the randomization of the variable associated in the fuzzy set itself. It is the first-time application of fuzzy reasoning over the backorder economic order quantity (EOQ) inventory management problem. We first define the fuzzy reasoning membership function through the use of L-fuzzy number and possibility theory on fuzzy numbers. Considering the holding cost, set up cost, backordering cost and demand rate as reasoning based fuzzy number, we have constructed a dual fuzzy mathematical problem. Then this problem has been solved over the dual feasible space which is associated to the aspiration level and the fuzzy approximation constant. Numerical study reveals the superiority of the proposed method with respect to the crisp solution as well as general fuzzy solution. Sensitivity analysis and graphical illustrations have also been done to justify the novelty of this article.
Optimization of Fuzzy Inventory Models under Fuzzy Demand and Fuzzy Lead Time
Inventory model under risk that demand is uncertain is recognized. In this paper, the fuzzy demand per day and fuzzy lead time on a cycle in fuzzy inventory control system are assumed to trapezoidal distribution, trapezoidal fuzzy number by decision maker. A fuzzy inventory model under manager's preference for order quantity is presented first. This model is given by fuzzy total annual inventory cost summating of total annual holding cost and fuzzy total annual setup cost. We obtain the optimal order quantity by using both Function Principle and Graded Mean Integration Representation method for both computing and representing fuzzy total annual inventory cost. The number of orders in a year, then, is getting by the above optimal order quantity. In addition, we get the reorder point and safety stock under a unit service level by manager. Furthermore, we also introduce a fuzzy inventory model under safety stock based on fuzzy total annual safety stock cost combined by total annual...
Fuzzy Inventory Model with Shortages under Fully Backlogged Using Signed Distance Method
In this paper we have studied an inventory model for deteriorating items with shortages under fully backlogged condition. The analytical development is provided to obtain the fuzzy optimal solution, defuzzification by Signed Distance Method. In fuzzy environment, all related inventory parameters are assumed to be hexagonal fuzzy numbers (HFN). Suitable numerical examples are also discussed. Keyword-Inventory Model, Deterioration, Hexagonal Fuzzy Number (HFN), Signed Distance Method.
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.
A Fuzzy Inventory Model with Shortages Using Different Fuzzy Numbers
American Journal of Mathematics and Statistics, 2015
It is found from the literature that most of the authors have considered inventory problems without shortage in fuzzy environment and they also considered different costs as fuzzy numbers and defuzzified by using signed distance method. In our present investigation an attempt has been made to study inventory model with shortage by considering the associated costs involved as fuzzy numbers. In the present piece of work we have referred the work of Dutta and Kumar (2012). They have considered fuzzy inventory model without shortages using trapezoidal fuzzy number and for defuzzification signed distance method was used. Following their work we have extended it for purchasing inventory model with shortages using trapezoidal fuzzy number for different costs and signed distance method for defuzzification, and then for the same purchasing inventory model, the associated costs were considered as different fuzzy numbers like triangular fuzzy number, trapezoidal fuzzy number and parabolic fuzz...