A fuzzy multi-item production model with reliability (original) (raw)
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International Journal of Mathematics in Operational Research, 2011
A multi-item EPQ model for deteriorating items is built-up with limited storage space and with flexibility and reliability of production process. Here, production rate for the items is depends on the demand and items deteriorate at constant rates. Due to high rent in market place, storage space is considered limited and imprecise in nature. Inventory related costs, storage space and other parameters are imprecise and taken as it triangular fuzzy number. We solve this inventory decision problem using Modified Geometric Programming (MGP) method. Following the theoretical treatment, we provide a numerical example to demonstrate that MGP has potential as a valuable analytical tool for researchers. At the end some sensitivity analysis with different parameters are made.
Multi-item fuzzy inventory problem with space constraint via geometric programming method
Yugoslav Journal of Operations Research, 2006
In this paper, a multi-item inventory model with space constraint is developed in both crisp and fuzzy environment. A profit maximization inventory model is proposed here to determine the optimal values of demands and order levels of a product. Selling price and unit price are assumed to be demand-dependent and holding and set-up costs sock dependent. Total profit and warehouse space are considered to be vague and imprecise. The impreciseness in the above objective and constraint goals has been expressed by fuzzy linear membership functions. The problem is then solved using modified geometric programming method. Sensitivity analysis is also presented here.
In this paper a multi item EOQ model with stock dependent demand for deteriorating items is considered in fuzzy environment. Different inventory costs and the amount of investment are represented as triangular fuzzy numbers The model has been solved by Robust ranking method, fuzzy optimization technique (FOT) and intuitionistic fuzzy optimization technique (IFOT). Nearest interval approximation method is used in FOT and IFOT. Pareto optimality test is done for fuzzy optimization and intuitionistic fuzzy optimization techniques. The methods are illustrated with a 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 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.
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 production inventory model with fuzzy coefficients using parametric geometric programming approach
International Journal of Machine Learning and Cybernetics, 2011
In general, cost constant parameters of inventory or production models are not rigid in real life rather these are imprecise in nature. In this paper we have presented imprecise cost constant parameters for an economic production quantity model. The unit production cost of this economic production quantity model is demand and reliability dependent. The imprecise parameters of the production model are considered as fuzzy in nature. The fuzzy model is solved by fuzzy parametric geometric programming technique. Finally, production model is numerically illustrated using fuzzy parametric geometric programming.
Independent Journal of Management & Production, 2019
The inventory system has been drawing more intrigue because this system deals with the decision that minimizes the total average cost or maximizes the total average profit. For any farm, the demand for any items depends upon population, selling price and frequency of advertisement etc. Most of the model, it is assumed that deterioration of any item in inventory starts from the beginning of their production. But in reality, many goods are maintaining their good quality or original condition for some time. So, price discount is availed for defective items. Our target is to calculate the total optimal cost and the optimal inventory level for this inventory model in a crisp and fuzzy environment. Here Holding cost taken as constant and no-shortages are allowed. The cost parameters are considered as Triangular Fuzzy Numbers and to defuzzify the model Signed Distance Method is applied. A numerical example of the optimal solution is given to clarify the model. The changes of different para...
Multi-Objective Inventory Model for Deteriorating Items with Shortages: A Fuzzy Programming Approach
In this paper we have formulated a multi-objective inventory model of deteriorating items, where demand is constant and shortage is allowed with limitations on capital investment, storage space and total inventory. In most of the real world situations, the objective functions of the decision makers are imprecise in nature. Hence the objective functions are imposed here in fuzzy environment. Then we have solved it using Fuzzy Additive Goal Programming and Fuzzy Non-Linear Programming. Finally the model is illustrated with numerical example. And the results by different techniques are compared.