Decision making in fuzzy reasoning to solve a backorder economic order quantity model (original) (raw)

Decision of a Fuzzy Inventory with Fuzzy Backorder Model Under Cloudy Fuzzy Demand Rate

International Journal of Applied and Computational Mathematics, 2016

This paper deals with the classical backorder economic order quantity inventory model under cloudy fuzzy environment. The traditional concepts on fuzziness of the fuzzy parameters remains the same in all the time, but in practice, due to the human experience and precision the fuzziness began to remove from the system over time. However, we take the crisp model first, then fuzzifying the model to get a decision under the cloudy fuzzy (extension of dense fuzzy) demand rate followed by its practical application. A new defuzzification method has been utilized for ranking the fuzzy numbers. Finally, comparative analysis between the crisp, general fuzzy as well as cloudy fuzzy solutions are done extensively. The graphical illustrations and numerical examples are studied to justify the usefulness of the new approach in the model itself.

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.

An inventory model with backorders with fuzzy parameters and decision variables

International Journal of Approximate Reasoning, 2010

The paper considers an inventory model with backorders in a fuzzy situation by employing two types of fuzzy numbers, which are trapezoidal and triangular. A full-fuzzy model is developed where the input parameters and the decision variables are fuzzified. The optimal policy for the developed model is determined using the Kuhn-Tucker conditions after the defuzzification of the cost function with the graded mean integration (GMI) method. Numerical examples and a sensitivity analysis study are provided to highlight the differences between crisp and the fuzzy cases.

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.

An integrated production-inventory model with backorder and lot for lot policy in fuzzy sense

International Journal of Mathematics in Operational Research, 2015

In this paper, an inventory model for two-stage supply chain is investigated in the fuzzy sense. A supply chain with single vendor and single buyer is considered. We assume that shortage as a backorder is allowed for the buyer and the vendor makes the production set up every time the buyer places an order and supplies on a lot for lot basis. The decision variables are fuzzy order quantity and fuzzy shortage quantity which are expressed as triangular fuzzy numbers. After developing the mathematical model for the joint total relevant cost in fuzzy sense, its membership function is calculated and then defuzzified with the centroid method. The proposed model is solved and the amount of joint total relevant cost function in fuzzy sense is compared with the crisp one.

Fuzzy Optimal Production and Shortage Quantity for Fuzzy Production Inventory With Backorder

Abstract: This study aims at presenting fuzzy optimal production Q∗∗ and shortage quantity b∗∗ for fuzzy production inventory with backorder when setup, holding, and shortage costs are fuzzy. For this purpose, two different fuzzy models, one of which includes crisp production and crisp shortage quantity, and the other of which involves those that are fuzzy, have been presented by making use of trapezoidal fuzzy numbers. For each model, fuzzy total cost FTC has been attained via function principle. In order to defuzzfy the FTC, graded mean integration method has been used, and as to solve inequality constrain problems, Extension of the Lagrangean method has been applied.

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.

A METHOD FOR SOLVING FUZZY INVENTORY WITH SHORTAGE UNDER THE SPACE AND INVESTMENT CONSTRAINTS

This paper discusses an Economic Order Quantity (EOQ) model with shortage under the space, investment constraints, where the setup cost, the holding cost, price per unit, the shortage cost, demand, storage area and the investment amount are considered as triangular fuzzy numbers. The fuzzy parameters in the constraints are then transformed into crisp using Robust’s ranking technique. The fuzzy parameters in the objective function are then transformed into corresponding interval numbers. Minimization of the interval objective function (obtained by using interval parameters) has been transformed into a classical multi-objective EOQ problem. The order relation that represents the decision maker’s preference among the interval objective function has been defined by the right limit, left limit, and center which is the half –width of an interval. This concept is used to minimize the interval objective function. The problem has been solved by fuzzy programming technique. Finally, the proposed method is illustrated with a numerical example.

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.

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...