Development of a fuzzy economic order quantity model for imperfect quality items using the learning effect on fuzzy parameters (original) (raw)
Related papers
2017
Background: This model presents a significant model for analyzing the effect of deteriorating items and promotional effort in fuzzy optimal instantaneous replenishment model for finite planning horizon. Accounting for holding cost per unit per unit time and ordering cost per order have traditionally been the case of modeling inventory systems in fuzzy environment. These imprecise parameters defined on a bounded interval on the axis of real numbers and the physical characteristics of stocked items dictate the nature of inventory policies implemented to manage and control in the production system. Methods: This model postulates the promotional effort cost to frame total inventory cost. Thus a modified fuzzy EOQ (FEOQ) model with promotional effort factor is introduced, it assumes that a percentage of the on-hand inventory is wasted due to deterioration and considered as an enhancement to EOQ model to determine the optimal promotional effort and the replenishment quantity so that the n...
Fuzzy Economic Order Quantity (FEOQ) Model with Units Lost Due to Deterioration
Statistics, Optimization & Information Computing, 2014
This model investigates the instantaneous fuzzy economic order quantity model by allocating the percentage of units lost due to deterioration in an on-hand inventory by framing variable ordering cost. The objective is to maximize the fuzzy net profit so as to determine the order quantity, the cycle length and number of units lost due to deterioration in fuzzy decision space. For any given number of replenishment cycles the existence of a unique optimal replenishment schedule are proved and mathematical model is developed to find some important characteristics for the concavity of the fuzzy net profit function. Numerical examples are provided to illustrate the results of proposed model which benefit the retailer and this policy is important, especially for wasting of deteriorating items. Finally, sensitivity analyses of the fuzzy optimal solution with respect to the major parameters are also studied.
A fuzzy imperfect quality inventory model with proportionate discount under learning effect
International Journal of Intelligent Enterprise, 2017
The present article establishes both crisp and fuzzy economic order quantity (EOQ) models with proportionate discount for items with imperfect quality under learning effect in a finite time horizon. The objective of the crisp model is to determine the optimal order lot size to maximise the total profit where the demand rate is constant and the defective items follow a learning curve. Then, we discussed on two different cases of fuzzy inventory models. Case-1: Defective rate follows a learning curve and the demand rate assumed to be a triangular fuzzy number. Case-2: Defective rate, fixed ordering cost and holding cost follow the learning curve and the demand rate taken to be a triangular fuzzy number. The objective of the fuzzy models is to estimate the maximum total profit per unit time in fuzzy sense and then to derive formula of the optimal lot size for each case and the corresponding total profit functions are defuzzified by using signed distance method. Numerical examples are provided to demonstrate the developed models. Sensitivity analysis is conducted both for crisp and fuzzy models to examine the effect of number of shipments on the order quantity and total profits under various conditions.
A Replenishment Policy for Items with Finite Production Rate and Fuzzy Deterioration Rate
OPSEARCH, 2001
In order 10 solve the economic production quantity (EPQ) inventory model, we always consider the deterioration rate as a constant quantity. But in the real situation, the deterioration rate will have little disturbances from the actual constant value. Therefore, we have developed an EPQ inventory model with fuzzy deterioration rate and finite production rate. The effect in the loss in production quantity due to faulty/aged machine have also been considered. The methodology for obtaining the optimum value of fuzzy total cost is also derived and the solution procedure is explained with one numerical example. To study the effect of changes in the system parameters on the decision variables, a sensitivity analysis is carried out by one numerical example.
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.
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.
International Journal For Multidisciplinary Research
This research paper deals with an inventory replenishment model for both deteriorating and ameliorating items under linear trend in demand over a fixed time horizon. This paper aimed to develop the model with shortages which are partially backlogged. The model is developed under the fuzzy environment. Optimal technique is used to solve the model considering Signed Distance Method (SD). The ordering cost, purchase cost, holding cost, deteriorating cost, ameliorating cost, shortage cost and opportunity cost are all considered as fuzzy cost parameters. Finally the fuzzy model is illustrated with the help of a numerical example and a sensitivity of the optimal solution towards the changes in the values of all fuzzy cost parameters is also furnished, and a concluding remark is given expressing the model development and also future research works in consequence of the present.
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: