Optimal policies for inventory systems with concave ordering costs | Zendy

Benjaafar Saif | Zendy; Chen David | Zendy; Yu Yimin | Zendy

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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.

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