Synthesis and Generalization of Structural Results in Inventory Management: A Generalized Convexity Property

Mathematics of Operations Research, Forthcoming

Columbia Business School Research Paper No. 18-13

35 Pages Posted: 9 Jan 2018 Last revised: 3 Apr 2019

See all articles by Awi Federgruen

Awi Federgruen

Columbia Business School - Decision Risk and Operations

Zhe Liu

Columbia University - Columbia Business School

Lijian Lu

Columbia University - Columbia Business School

Date Written: August 1, 2018

Abstract

We address a general periodic review inventory control model with the simultaneous presence of the following complications: (a) bilateral inventory adjustment options, via procurement orders and salvage sales or returns to the supplier; (b) fixed costs associated with procurement orders and downward inventory adjustments (via salvage sales or returns); and (c) capacity limits associated with upward or downward inventory adjustments. We characterize the optimal adjustment strategy, both for finite and infinite horizon periodic review models, by showing that in each period the inventory position line is to be partitioned into (maximally) five regions.

Our results are obtained by identifying a novel generalized convexity property for the value functions, which we refer to as (C1K1,C2K2)-convexity. To our knowledge, we recover most existing structural results for models with exogenous demands as special cases of a unified analysis.

Keywords: inventory management, convexity, capacity constraint, bilateral adjustment, fixed cost, infinite horizon

Suggested Citation

Federgruen, Awi and Liu, Zhe and Lu, Lijian, Synthesis and Generalization of Structural Results in Inventory Management: A Generalized Convexity Property (August 1, 2018). Mathematics of Operations Research, Forthcoming; Columbia Business School Research Paper No. 18-13. Available at SSRN: https://ssrn.com/abstract=3096735 or http://dx.doi.org/10.2139/ssrn.3096735

Awi Federgruen

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

Zhe Liu (Contact Author)

Columbia University - Columbia Business School ( email )

3022 Broadway
New York, NY 10027
United States

Lijian Lu

Columbia University - Columbia Business School ( email )

3022 Broadway
New York, NY 10027
United States

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