Fuzzy Inventory Model for Deteriorating Items with Shortages under Fully Backlogged Condition
D. Dutta1, Pavan Kumar2
1D. Dutta, Department of Mathematics, National Institute of Technology, Warangal, India.
2Pavan Kumar, Department of Mathematics, National Institute of Technology, Warangal, India.
Manuscript received on April 05, 2013. | Revised Manuscript received on April 27, 2013. | Manuscript published on May 05, 2013. | PP: 393-398 | Volume-3, Issue-2, May 2013. | Retrieval Number: B1580053213l/2013©BEIESP
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© The Authors. Published By: Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: 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.
Keywords: Inventory model, Trapezoidal fuzzy number, Fuzzy demand, Fuzzy deterioration.