Abstract
This paper applies fuzzy criterion decision processes to inventory systems with several types of partial backorders, such as (i) the unfulfilled demand is completely backordered, (ii) the unfulfilled demand is completely lost, (iii) a fixed fraction of unfulfilled demand is backordered, and (iv) a stochastic portion of unfulfilled demand is backordered. We will formulate different dynamic fuzzy criterion models and show that the optimal inventory control for all these cases is characterized by a bounded critical number policy.
Similar content being viewed by others
References
B.T. Doshi, F.A. van der Duyn Schouten and A.J.J. Talman, A production-inventory control model with a mixture of back-orders and lost-sales, Management Science 24(1978)1078-1086.
A.O. Esogbue and R.E. Bellman, Fuzzy dynamic programming and its extensions, Fuzzy Sets and Decision Analysis, TIMS/Studies in the Management Science, Vol. 20, 1984, pp. 147-167.
A.O. Esogbue, M. Theologidu and K. Guo, On the application of fuzzy sets theory to the optimal flood control problem arising in water resources systems, Fuzzy Sets and Systems 48(1992)155-172, 1992.
J. Kacprzyk J. and A.O. Esogbue, Fuzzy dynamic programming: Main developments and applications, Fuzzy Sets and Systems 81(1996)31-45.
D.H. Kim and K.S. Park, (Q, r) inventory model with mixture of lost sales and time-weighted backorders, Journal of the Operational Research Society 36(1985)231-238.
B. Liu, Studies in inventory processes and reservoir operations, Ph.D. Dissertation, Institute of Systems Science, Chinese Academy of Sciences, 1992.
B. Liu and T. Odanaka, Dynamic fuzzy criterion model for reservoir operations and a case study, to appear in: Computers and Mathematics with Applications.
B. Liu and A.O. Esogbue, Fuzzy criterion set and fuzzy criterion dynamic programming, Journal of Mathematical Analysis and Applications 199(1996)293-311.
B. Liu and A.O. Esogbue, Fuzzy criterion dynamic programming for open inventory networks, Technical Report, Tsinghua University, 1996.
K. Moinzadeh, Operating characteristics of the (S — 1, S) inventory system with partial backorders and constant resupply times, Management Science 35(1989)472-477.
D.C. Montgomery, M.S. Bazarra and A.K. Keswani, Inventory models with a mixture of backorders and lost sales, Nav. Res. Legist. Q. 20(1973)255-263.
K.S. Park, Inventory model with partial backorders, International Journal of Systems Science 13 (1982)1313-1317.
Rights and permissions
About this article
Cite this article
Liu, B. Fuzzy criterion models for inventory systems with partial backorders. Annals of Operations Research 87, 117–126 (1999). https://doi.org/10.1023/A:1018912431271
Issue Date:
DOI: https://doi.org/10.1023/A:1018912431271