Fuzzy inventory model with quadratic demand, linear time dependent holding cost, constant deterioration rate and shortages (original) (raw)
Related papers
This paper develops a production inventory model for deteriorating items under fuzzy environment. Since holding cost, setup cost, deterioration cost, deterioration rate, production rate, demand etc. are uncertain in nature; these are carried by pentagonal fuzzy numbers. Graded Mean Integration Representation (GMIR) method is used to defuzzify the total cost function. Numerical example is given to explore the theoretical results and made the comprehensive. Sensitivity analysis with different parameters on the optimal solution is carried to illustrate the effectiveness and behavior of the model.
Journal of Ultra Scientist of Physical Sciences Section A, 2017
This paper develops a production inventory model for deteriorating items under fuzzy environment. Since holding cost, setup cost, deterioration cost, deterioration rate, production rate, demand etc. are uncertain in nature; these are carried by pentagonal fuzzy numbers. Graded Mean Integration Representation (GMIR) method is used to defuzzify the total cost function. Numerical example is given to explore the theoretical results and made the comprehensive. Sensitivity analysis with different parameters on the optimal solution is carried to illustrate the effectiveness and behavior of 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.
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.
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.
Fuzzy inventory model with exponential demand and time-varying deterioration
2016
This paper investigates with the development of a fuzzy inventory model with time-varying demand, deterioration and salvage. The deterioration rate, demand, holding cost, unit cost and salvage value are taken as trapezoidal fuzzy numbers. Both graded mean integration and signed distance method are used to defuzzify the total cost function. Numerical examples are given to validate the proposed mathematical model which has been developed for determining the optimal order quantity, optimal cycle time and optimal total inventory cost. Sensitivity analysis is also carried out to explore the effect of changes in the optimal solution with respect to change in various parameters. AMS subject classification:
Fuzzy Inventory Model without Shortage Using Trapezoidal Fuzzy Number with Sensitivity Analysis
In the present paper, an inventory model without shortages has been considered in a fuzzy environment. Our goal is to determine the optimal total cost and the optimal order quantity for the proposed inventory model. The Trapezoidal fuzzy numbers have been introduced in order to achieve this goal. The computation of economic order quantity (EOQ) is carried out through defuzzification process by using signed distance method. The signed distance method is more applicable than the other methods of defuzzification. To illustrate the results of the proposed model, we have given two model examples and presented the computational results. Sensitivity for this model is also studied, which shows a linear relation between demand, EOQ, and total cost. The advantage of the proposed approach is that it is simple, gives a better result in relatively less computational work.
Logforum, 2019
Background: In this paper we developed a fuzzy two-warehouse (one is OW, the own warehouse and other is RW, the rented warehouse) inventory model of deteriorating items with price dependent demand rate and allowed shortages under partially backlogged conditions. Since the capacity of any warehouse is limited, the supplier has to rent a warehouse for keeping the excess units over the fixed capacity W of the own warehouse in practice. The rented warehouse owed higher holding cost than the own warehouse. In this paper we considered holding cost, deterioration rate, shortages cost and lost sales as triangular fuzzy numbers. Methods: Graded Mean Integration Representation is used to defuzzify the total cost function. The result obtained by this method is compared with crisp model with the help of a numerical example. Sensitivity analysis is accomplished to changing one parameter at a time and keeping others at their archetypal. Results and conclusions: It has been proved that graded mean integration representation method gives more accurate result as compare to crisp model.
International journal of engineering applied science and technology, 2020
An inventory model for a single deteriorating item under fuzzy environment has been presented in this paper. Here demand rate is considered to be constant for some time period, post which the same is a linear function of time. This situation is common during the time of a new product launch in the market. As the product becomes popular, its demand increases with time although it remains constant during the initial days. Cycle time is considered to be constant in most of the models. However, practically it has been observed that it is difficult to pro-actively predict the cycle time. Because of this problem, cycle time has been considered as uncertain and has been further described as Symmetric Triangular Fuzzy number. The Signed Distance method has been used for defuzzification of the total cost function. For illustration of the process for finding the total optimal cost and the cycle time, numerical examples have been considered. The effects of changing parameter values on the optimal solution of the system have been demonstrated through Sensitivity Analysis.
Operations Research and Applications : An International Journal, 2023
The present paper deals with the development of a fuzzy inventory model of deteriorating itemsunder power demand rate and inventory level dependent holding cost function. The deteriorationrate, demand rate, holding cost and unit cost are considered as trapezoidal fuzzy numbers. Both the crisp model and fuzzy model are developed in this paper. The graded mean integration method(GM) and signed distance method(SD) are used to defuzzify the total cost of the present model. Both the models are illustrated by suitable numerical examples and a sensitivity analysis for the optimal solution towards changes in the system parameters are discussed. Lastly a graphical presentation is furnished to compare the total costs under the above two mentioned methods in the fuzzy model.