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Journal of Information Science and Engineering, Vol. 21 No. 4, pp. 673-694 (July 2005)

Fuzzy Inventory with Backorder Defuzzification by Signed Distance Method

Jershan Chiang, Jing-Shing Yao+ and Huey-Ming Lee*
Department of Applied Mathematics
*Department of Information Management
Chinese Culture University
Taipei, 111 Taiwan
+Department of Mathematics
National Taiwan University
Taipei, 106 Taiwan

In this paper, we consider fuzzy inventory with backorder. First, we fuzzify the storing cost a, backorder cost b, cost of placing an order c, total demand r, order quantity q, and shortage quantity s as the triangular fuzzy numbers in the total cost. From these, we can obtain the fuzzy total cost. Using the signed distance method to defuzzify, we get the estimate of the total cost in the fuzzy sense. Two special cases of the optimal solutions on fuzzifying the storage quantity and order quantity as triangular fuzzy numbers will be treated numerically by the Nedler-Mead algorithm.

Keywords: fuzzy inventory, fuzzy sets, fuzzy total cost, signed distance, extension principle

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Received November 17, 2003; revised July 19 & October 18, 2004; accepted November 11, 2004.
Communicated by Pau-Choo Chung.