Preservation of Additive Convexity and Its Applications in Stochastic Optimization Problems

Operations Research Forthcoming

34 Pages Posted: 8 Aug 2018 Last revised: 8 Mar 2021

See all articles by Xiting Gong

Xiting Gong

The Chinese University of Hong Kong

Tong Wang

Shanghai Jiao Tong University

Date Written: June 16, 2020

Abstract

In this paper, we establish two preservation results of additive convexity for a class of optimal transformation problems and a class of optimal disposal problems. For both classes of problems, there are multiple resources and our results show that if these resources have different priorities to be transformed/disposed under the optimal policy, then the additive convexity and bounded monotonicity of the objective function are preserved to the value function after optimization. A key observation is that an optimal transformation problem with prioritized optimal decisions is equivalent to a serial inventory problem with zero lead times. We demonstrate the applications of our results to several stochastic optimization problems in operations management.

Keywords: dynamic programming, additive convexity, serial inventory systems, remanufacturing systems, inventory rationing, expediting, disposal, capacity management

Suggested Citation

Gong, Xiting and Wang, Tong, Preservation of Additive Convexity and Its Applications in Stochastic Optimization Problems (June 16, 2020). Operations Research Forthcoming, Available at SSRN: https://ssrn.com/abstract=3217007 or http://dx.doi.org/10.2139/ssrn.3217007

Xiting Gong

The Chinese University of Hong Kong ( email )

Room 906, 9/F, Cheng Yu Tung Building
12 Chak Cheung Street, Shatin, N.T.
Hong Kong
China

HOME PAGE: http://www.bschool.cuhk.edu.hk/staff/gong-xiting/

Tong Wang (Contact Author)

Shanghai Jiao Tong University ( email )

No.535 Fahuazhen Road
Shanghai Jiao Tong University
Shanghai, Shanghai 200052
China

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