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Optimal policies for inventory systems with concave ordering costs
Author(s) -
Benjaafar Saif,
Chen David,
Yu Yimin
Publication year - 2018
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.21808
Subject(s) - convexity , monotonic function , bounded function , mathematical optimization , order (exchange) , mathematics , state space , concave function , piecewise , property (philosophy) , piecewise linear function , space (punctuation) , mathematical economics , regular polygon , computer science , economics , statistics , mathematical analysis , philosophy , geometry , finance , epistemology , financial economics , operating system
In this paper we study the structure of optimal policies for periodic review inventory systems with concave ordering costs and general demand distributions. By extending the Scarf ([Scarf, H, 1959]) model to systems with piecewise linear concave ordering costs, we show that, except for a bounded region, the generalized ( s , S ) policy is optimal. We do so by ( a ) introducing the notion of c ‐convexity and ( b ) proving a conditional monotonicity property for the optimal order‐up‐to levels. We also provide conditions under which the generalized ( s , S ) policy is optimal for all regions of the state space.