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157. Inventory Planning with Supply Yield Uncertainty: On the Optimality of Linear Inflation Rules

Invited abstract in session TB-39: Stochastic Models in Logistics, stream Stochastic Modelling.

Tuesday, 10:30-12:00
Room: 35 (building: 306)

Authors (first author is the speaker)

1. Jan Van Mieghem
Kellogg School of Management, Northwestern University
2. Riccardo Mogre
Business School, Durham University

Abstract

We study inventory planning under demand and supply yield uncertainty. We present new optimality conditions and explicit solutions for the associated single-period ``newsvendor'' model. In general, the stochastic-optimal order policy is non-linear in the starting inventory level $x$. The literature has proposed Linear Inflation Rules (LIR) that inflate the classic order-up-to policy. We prove that LIR are only stochastically optimal in the degenerate setting where either demand or (not and) supply yield is uncertain.

Given the good performance of LIR we investigate their optimality under two robust formulations and provide bounds.
We prove that LIR are robustly optimal when only the support of the demand and supply yield distributions are known. Yet we also provide the optimal distribution-free policy when the first two moments of those distributions are known, which again is non-linear. Both models provide novel, explicit order rules that may be useful for dynamic inventory control.

Keywords

Status: accepted

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