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Fuzzy inventory with backorder for fuzzy total demand based on interval-valued fuzzy set. (English) Zbl 0978.90009

Summary: It is difficult to determine the fixed total demand \(r_0\) in an inventory problem with backorder in a whole plan period. We will fuzzify it as \(R=\lceil\text{near} r_0\rceil\). In this article, we will classify \(R\) into three kinds: (1) fuzzy total demand with triangular fuzzy number (Section 2), (2) fuzzy total demand with interval-valued fuzzy set based on two triangular fuzzy numbers (Section 3), (3) fuzzy total demand with interval-valued fuzzy set based on two trapezoidal fuzzy numbers (Section 4). We will find the corresponding order quantities and the shortage inventories, respectively.

MSC:

90B05 Inventory, storage, reservoirs
03E72 Theory of fuzzy sets, etc.
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References:

[1] Chang, S.-C.; Yao, J.-S.; Lee, H.-M., Economic reorder point for fuzzy backorder quantity, Europan journal operational research, 109, 183-202, (1998) · Zbl 0951.90003
[2] Gorzalczany, M.B., A method of inference in approximate resoning,based on interval-valued fuzzy sets, Fuzzy sets and systems, 21, 1-17, (1987) · Zbl 0635.68103
[3] H. Lee, J.-S. Yao, Economic order quantity in fuzzy sense for inventory without backorder model. Fuzzy Sets and Systems (to appear) · Zbl 0947.90005
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[5] Yao, J.-S.; Lee, H.-M., Fuzzy inventory with backorder for fuzzy order quantity, Information science, 93, 283-319, (1996) · Zbl 0884.90077
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