A fuzzy multi-item production model with reliability and flexibility under limited storage capacity with deterioration via geometric programming (original) (raw)
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A fuzzy multi-item production model with reliability
Abstract: 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. Keywords: storage space; triangular fuzzy number; MGP; modified geometric programming; flexibility; reliability.
Multi-item fuzzy inventory problem with space constraint via geometric programming method
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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.
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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.
Fuzzy Inventory Model for Deteriorating Items with Time-varying Demand and Shortages
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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.
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.
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.
This paper presents a mathematical framework to obtain a production model for perishable items with a learning effect in production cost. The study considers different demand rates at different. This model is along with the concept of two warehouses, where one is its own warehouse (OW) and the other is a rented warehouse (RW). The demand rate for RW is strictly increasing function of time which is exponential, and selling price of inventory in own warehouse in such a way that the producer gets the benefit and can build the according to his profit, also production rate is dependent on demand. Hethe re concept of shortage is also considered. In this model, we analyzed the changes in the total cost by taking item price and production time as a decision variable. The optimal solution has presented with the use of the centroid method with q-fuzzy number. A numerical examples and sensitivity analyses of some parameters are provided to examine the impact on the optimal total cost of the system.