Year: 2026
Type: preprint
Abstract: We study multi-product replenishment subject to aggregate operating limits imposed pathwise in place of expectation. On-hand and in-transit inventory, warehouse capacity and an emission allowance define a safe set, and the resulting multi-product lost-sales problem is posed as a safe stochastic optimal control problem. The Hamilton--Jacobi--Bellman (HJB) equation is represented as a system of forward--backward stochastic differential equations (FBSDEs) and solved by learning the value function and its gradient, with a quadratic program derived by control barrier function (CBF) is solved at each decision epoch. Because purchase orders enter the in-transit pipeline only, the in-transit constraints have relative degree one while the on-hand constraints have relative degree two. We extend the stochastic high-relative-degree construction of (Clark, 2021) from a single barrier to four coupled aggregate constraints of mixed relative degree, and we establish its initial-condition requirement by design.
Source: arXiv (Cornell University)
Authors: Lim, Keunwoo, Bloem, Michael
Subfield: Management Information Systems
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7212275183
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