The bottom line: when a retailer has milliseconds to decide which warehouse should ship an order, a full-blown stochastic optimization model is often too slow to run live, so researchers are training machine learning models to approximate what that model would have decided. A new paper from a Georgia Tech-affiliated research team calls these approximators "optimization proxies" and applies them to sequential order fulfillment, a problem every e-commerce and omnichannel retailer wrestles with daily.
Order fulfillment sounds simple — send the order to whichever warehouse has the item — but at scale it is a sequential decision problem under uncertainty. Every order that arrives now competes with orders that haven't arrived yet for the same limited inventory, and today's assignment shapes what options remain tomorrow. That makes it a natural fit for stochastic programming, a branch of optimization that explicitly models unknown future demand as a set of probable scenarios rather than pretending the future is known.
The textbook formulation for this kind of problem is a multistage stochastic program. In its general form, a planner chooses a decision $x_t$ at each stage $t$ to minimize expected cost across an uncertain future, something like $$\min_{x_1,\dots,x_T} \; \mathbb{E}_{\xi}\left[\sum_{t=1}^{T} c_t(x_t, \xi_t)\right] \quad \text{s.t. } x_t \in \mathcal{X}_t(x_{1:t-1}, \xi_{1:t}),$$ where $\xi_t$ represents the random demand or context revealed at stage $t$ and $\mathcal{X}_t$ captures inventory, capacity, and fulfillment feasibility constraints carried forward from earlier decisions. In plain terms: pick today's shipping assignments so that, averaged over all the ways future demand could unfold, total cost is as low as possible, while never promising more inventory than a warehouse actually has.
Solving that expectation exactly means evaluating or sampling many demand scenarios and re-solving a large mixed-integer or linear program every time a new order context arrives — computationally out of reach for the sub-second response times that live fulfillment systems need. The paper's proposed fix is to train a proxy model, typically a neural network, on a large set of pre-solved instances of the stochastic program, so that at run time the proxy maps the current context directly to a near-optimal fulfillment decision without solving anything from scratch. This is the same basic idea behind learning-to-optimize and end-to-end learning approaches that have gained traction in the optimization research community over the past several years: shift the computational burden from inference time to training time.
What distinguishes this work is the sequential, contextual structure of the problem. A proxy trained on a single-shot stochastic program can't simply be reused stage after stage, because each stage's optimal decision depends on the state left behind by the last one, and that state depends on inventory levels, order patterns, and warehouse capacities that shift over time. The authors design their learning architecture and training procedure specifically to respect this sequential dependency, so the proxy's decisions at stage $t$ remain consistent with the constraints inherited from stages $1$ through $t-1$, rather than optimizing each stage in isolation and hoping the pieces fit together.
For a retail operations leader, the practical payoff is speed without abandoning the rigor of stochastic optimization. A proxy that can be evaluated in milliseconds lets a fulfillment engine make an inventory-aware, uncertainty-aware assignment for every order the moment it arrives, rather than falling back on a simpler greedy rule because the exact optimization model can't keep up with order volume. That matters most during peak demand periods — holiday shopping, flash sales — precisely when the gap between a naive rule and a genuinely optimized assignment is most costly in wasted inventory, split shipments, and missed service levels.
The tradeoff, as with any learned approximation, is that a proxy is only as good as the training distribution it has seen and the fidelity with which it reproduces the underlying optimization model's behavior on new instances. This is an emerging research area, and the specific numerical performance of the proxy against the exact stochastic program on the order fulfillment application is a core empirical contribution of the paper; practitioners considering the approach should treat published speed-versus-quality tradeoffs as instance-specific rather than universal until validated on their own data.
The broader signal here is about where machine learning is heading inside classical operations research: not replacing solvers, but sitting alongside them as a fast approximation layer for the subset of decisions that must be made in real time. As stochastic programming techniques mature and computing environments push more decisions to the edge — point-of-sale systems, warehouse robotics, real-time routing — optimization proxies of this kind are likely to become a standard tool for translating solver-quality decisions into millisecond-scale operations.
Sources: Ye, Tong, Guan, Basciftci, Van Hentenryck, 'Learning Optimization Proxies for Sequential Contextual Stochastic Programs: An Order Fulfillment Application', arXiv:2606.25362
