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Fuzzy production inventory for fuzzy product quantity with triangular fuzzy number. (English) Zbl 0947.90003
Summary: In this paper we consider the fundamental production inventory problem such that the product quantity is a triangular fuzzy number \(\widetilde Q=(q_1,q_0,q_2)\), where \(q_1=q_0-\Delta_1\), \(q_2=q_0+\Delta_2\). Suppose \(q_*\) denotes the crisp economic product quantity in the classical production inventory model and we assume \(0<q_1<q_*<q_0<q_2\) or \(0<q_1<q_0 <q_* <q_2\). According to two relations of \(q_*\) and \(q_1,q_0,q_2\) \((q_1<q_0<q_2)\) we find the membership function \(\mu_{F(\widetilde Q)}(y)\) of the fuzzy cost function \(F(\widetilde Q)\) and their centroid, then obtain the economic product quantity \(q^{**}\) in the fuzzy sense.

MSC:
90B05 Inventory, storage, reservoirs
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
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[1] Buchanan, J.L.; Twrner, P.R., Numerical methods and analysis, (1992), McGraw-Hill New York
[2] S.-C. Chang, J.-S. Yao, H.-M. Lee, Economic reorder point for fuzzy backorder quantity, European J. Oper. Res., to appear. · Zbl 0951.90003
[3] Kaufmann, A.; Gupta, M.M., Introduction to fuzzy arithmetic theory and application, (1992), van Norstrand Reinhold New York
[4] H.-M. Lee, J.-S. Yao, Economic order quantity in fuzzy sense for inventory without backorder model, Fuzzy Sets and Systems, to appear. · Zbl 0947.90005
[5] Mathews, J.H., Numerical methods for computer science, engineering and mathematics, (1992), Prentice-Hall International London · Zbl 0753.65002
[6] Yao, J.-S.; Lee, H.-M., Fuzzy inventory with backorder for fuzzy order quantity, Inform. sci., 93, 283-319, (1996) · Zbl 0884.90077
[7] J.-S. Yao, H.-M. Lee, Fuzzy inventory with or without backorder for fuzzy order quantity with trapezoid fuzzy number, Fuzzy Sets and Systems, to appear. · Zbl 0959.90002
[8] Zimmermann, H.J., Fuzzy set theory and its applications, (1991), Kluwer Academic Dordrecht · Zbl 0719.04002
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