Decision Intelligence for E-commerce: How Retailers Optimise Pricing, Demand Forecasting, Inventory, Promotions & Personalization

Executive summary

Retail e-commerce now absorbs roughly one in six retail dollars worldwide, and the operating leverage is concentrated at the top of the distribution: a small number of platform-scale retailers run end-to-end decision-intelligence systems that touch every economically significant lever, while most small and medium-sized (SMB) sellers continue to rely on spreadsheets, marketplace dashboards, and rule-based heuristics [44, 41, 45, 38]. This report is a deep technical survey of the methods used by the leading operators, the variants that matter, and the architectural and operational choices that determine whether those methods translate into margin in practice.

Our central claim is simple. The pain points reported by SMB sellers—pricing pressure, inventory mismatch, rising acquisition cost, returns, lack of analytics tools—are not, in 2026, primarily a research problem. The methods needed to address them are documented in textbooks [32, 42, 40], in canonical journal articles [17, 39, 9, 16, 11, 29], and in widely adopted open-source software (Stan, PyMC, GluonTS, EconML, CausalML, LightGBM, Transformers). The bottleneck has shifted from algorithmic novelty to integration: connectors, feature stores, optimization, experimentation, off-policy evaluation, and a human-in-the-loop UI assembled into a single workflow that a merchandiser will actually use.

The bottleneck for most sellers is no longer algorithmic novelty. It is the integration of data, models, and optimization into a single workflow.

1. The state of e-commerce, and where margin is being made and lost

Three structural forces have reshaped seller economics over the past five years. First, online penetration is high but uneven: U.S. e-commerce penetration was 15.4% of total retail in Q4 2023 [44], above 27% in China and roughly 26% in the United Kingdom [41]. Within categories, penetration ranges from below 5% in food and beverage to above 50% in consumer electronics and apparel. The marketplace structure—where a small number of platforms intermediate between many buyers and many sellers—has become the dominant organizational form, increasing price comparability and shortening the half-life of any given price advantage.

Second, returns and last-mile fulfillment have re-priced the unit economics. Industry estimates place online return rates at 25–40% in apparel [38], and free-shipping thresholds plus carrier surcharges have compressed the gap between gross and contribution margin. The seller's problem is no longer ‘maximize revenue subject to inventory'; it is ‘maximize contribution after returns, ad cost, and platform fees, subject to working-capital and service-level constraints.' This reframing matters mathematically because the relevant objective function changes: profit per unit becomes price minus cost minus expected return cost minus expected ad cost minus expected platform fee, and the optimization variables that determine each term differ.

Third, paid-media customer-acquisition cost has risen faster than basket size. Median cost-per-click on Meta and Google search has risen by an estimated 60–110% since 2020 [38, 27], while average order value has grown roughly with inflation. The competitive equilibrium has shifted toward sellers who can extract more revenue per customer—through pricing, recommendation, and retention—rather than acquire more customers at constant value. These three forces explain why the levers we focus on (pricing, inventory, promotion, personalization) are precisely the ones with the highest residual marginal value at scale, and why they are the levers that platform-scale retailers have invested most heavily in automating.

2. Quantifying the SMB seller's pain

Figure 1 summarizes the operational pain points reported by SMB sellers in 2023–24, synthesized from the Jungle Scout State of the Amazon Seller survey (n = 2,164) [45], the Shopify Commerce Trends 2024 report [38], and the McKinsey State of Small and Medium-Sized Businesses survey [28].

Three patterns dominate. After a seller has chosen what to sell, the binding constraints are commercial—price, promotion, inventory, ad cost—not supply. Roughly one in three sellers volunteers lack of analytics tools as a constraint, an unusually high rate for an unprompted answer, indicating a strong revealed preference for tooling. And the cluster of margin-, inventory-, and acquisition-related issues is not coincidental: each is a symptom of a missing decision-support apparatus, and each is addressed by a distinct branch of the technical literature surveyed in the rest of this report.

Table 1 contrasts the typical SMB tooling stack with what platform-scale retailers use. The pattern is consistent across surveys: SMB tooling is dominated by spreadsheets, marketplace dashboards, and rule-based repricers, while platform-scale tooling is dominated by purpose-built optimization, machine learning, and continuous experimentation infrastructure. The capability gap (Figure 2) is largest in causal attribution and experimentation—precisely the layers that compound, because they are the layers that allow every other model to improve over time.

3. Pricing — from heuristics to learning systems

Pricing is the single highest-leverage lever in retail because every dollar of price flows directly to contribution. McKinsey estimates that even a basic dynamic-pricing program adds 1–5% margin across categories [27], and well-instrumented field experiments have shown gross-profit lifts of 80% or more relative to rule-based heuristics [29]. A modern pricing system has three components, treated below in turn: a demand model that maps prices to expected sales; an optimizer that maximizes contribution subject to business rules; and an exploration policy that updates the demand model as new data arrives. The literature treats these as separable, but they interact: the optimizer's structure determines what the demand model needs to predict, and the exploration policy determines what the demand model can be identified from.

3.1 Demand modeling

A demand model is a function Q(p, x) predicting expected unit sales at price p and covariates x (seasonality, competitor prices, marketing spend, inventory position). The choice of functional form matters because it determines what the optimizer can do, how much data is needed for stable estimation, and what kind of identification problem must be solved. Six families of demand model are in routine industrial use.

Linear and log-linear demand

The linear specification Q = a − bp + γ′x + ε is the simplest workable model. It is fast to estimate by ordinary least squares, transparent, and admits a closed-form revenue maximum at p^* = (a + γ′x) / (2b) when marginal cost is zero. The log-linear specification log Q = α − β log p + γ′x is more useful in retail because the slope coefficient β is the price elasticity of demand—directly interpretable, dimensionless, and stable across price levels in many categories. Both forms are vulnerable to price endogeneity: prices in observational data are not random; they reflect the seller's beliefs about demand. Naive regression therefore conflates the demand curve with the supply response. The standard remedies are instrumental variables (cost shocks, competitor cost shocks [6]), within-product fixed effects with exogenous price changes (e.g., calendar-driven promotional waves), or a deliberate randomization policy that supplies its own identification, which is why the bandit machinery in §3.3 is more than a curiosity: it is the cleanest way to estimate elasticity at all.

Constant-elasticity demand

The constant-elasticity form Q(p) = A · p^ε, with ε < 0, admits closed-form revenue R(p) = A · p^(1+ε) and a profit maximum that satisfies the classical Lerner condition (p^* − c) / p^* = 1 / |ε|. The form is appealing for two reasons. First, the optimal markup over marginal cost is a simple function of one parameter, which makes the model auditable. Second, in panel data with cost variation, ε is identified from the slope of log-quantity on log-price, holding fixed effects constant. The form's main weakness is that it assumes elasticity is constant across price levels, which is rarely true near psychological thresholds (e.g., $9.99, $19.99) or near competitor caps. Production implementations use a piecewise-constant-elasticity model with breakpoints at salient prices [32], or fall back to logit and ML alternatives below.

Discrete-choice (logit, nested logit, mixed logit)

When customers choose among substitutes—the typical online-shopping decision—a discrete-choice model is the structurally appropriate object. The multinomial logit (MNL) gives the share of product j in category C as s_j(p) = exp(α_j − β_j p_j) / (1 + Σ_k∈C exp(α_k − β_k p_k)). The MNL is the workhorse of marketing and retail assortment optimization [42, 47], but inherits the Independence of Irrelevant Alternatives (IIA) property: the relative odds of two products are unaffected by the presence of a third, which is empirically false for close substitutes (red vs. blue versions of the same shirt). The nested logit relaxes IIA across nests (color/size within product) by introducing a within-nest correlation parameter. The mixed (random-coefficients) logit allows the price coefficient β to vary across customers as a draw from a population distribution, capturing taste heterogeneity that no aggregate model can. Estimating the mixed logit on aggregated market data is the BLP problem [6], which combines a contraction mapping for shares with GMM for parameters and is the structural foundation of modern industrial-organization studies of pricing. For sellers with customer-level data, hierarchical Bayesian estimation is more practical and is the bridge to the next family.

Hierarchical Bayesian demand

A wide catalog with short per-SKU history is the typical SMB regime. Hierarchical (multi-level) Bayesian models exploit the structure that, within a category, SKU-level parameters are exchangeable draws from a category-level prior. Concretely, log Q_j,t = α_j − β_j log p_j,t + γ_j′ x_j,t + ε_j,t with (α_j, β_j, γ_j) ∼ N(μ_c, Σ_c) where c indexes the category. The model is fitted with MCMC (Stan, PyMC) or variational inference. The benefit is partial pooling: SKUs with thin data are shrunk toward the category mean, while SKUs with abundant data dominate their own posterior. Empirically this delivers calibrated posteriors with as little as 6–8 weeks of data per SKU when the catalog has a few hundred comparable items [2], which is the regime where every SMB seller actually operates. The downside is computational: fitting a thousand-SKU panel with full MCMC is non-trivial, but variational inference and stochastic gradient samplers have largely closed the gap in practice.

Black-box ML demand models

Gradient-boosted trees (LightGBM, XGBoost) and deep nets can fit Q(p, x) non-parametrically, capturing seasonality, holiday effects, weather, and feature interactions that a parametric form would miss. The technical risk is that maximum-likelihood estimation does not respect the downstream optimization: a model with low MSE on the demand surface can still produce poorly conditioned profit landscapes. Two responses to this have crystallized in the literature. Decision-focused learning (the Smart-Predict-Then-Optimize, SPO+, framework) trains the predictor under a loss function that scores end-task decisions rather than predictions [15, 8]. And predictive-to-prescriptive analytics [5] uses the predictor to weight historical scenarios in a sample-average optimization, sidestepping calibration issues at the cost of richer scenario data. For pricing specifically, ML demand models work best when paired with bandit-driven exploration so the model is identified, not just fitted.

3.2 Optimization given a demand model

Once demand is estimated, prices are chosen by solving a constrained optimization problem. The simplest case—single product, constant elasticity, marginal cost c, no constraints—gives the Lerner condition by setting the derivative of profit (p − c)·A·p^ε to zero:

The same logic generalizes. Under linear demand the closed form is p^* = (a + bc) / (2b), and under MNL with constant marginal costs the optimal price for product j satisfies p_j^* = c_j + 1 / (β_j (1 − s_j^*)), a fixed-point equation in the equilibrium share [42]. These closed forms are what make the constant-elasticity and logit families durable: even when a black-box ML model fits the data better, sellers often run the optimizer on a parametric approximation in the neighborhood of the current operating point because the parametric form admits a defensible, interpretable optimum.

Constrained single-SKU pricing

Production pricing systems do not solve unconstrained problems. Margin floors (p ≥ c · (1 + m_min)), Manufacturer-Authorized-Price (MAP) rules, competitor caps (p ≤ p_comp + δ), and price-ending requirements (p ∈ {x.99, x.95}) narrow the feasible set. The standard approach is to evaluate the unconstrained Lerner-implied price, then project onto the feasible set; for non-convex constraints (price endings) this is a small enumeration. KKT conditions tell us when binding constraints distort the optimum, which is operationally useful: a category whose Lerner-implied price is consistently above the MAP cap is one where the seller is leaving margin on the table because of vendor policy, not demand.

Joint multi-SKU pricing under cannibalization

When products are substitutes, the optimal price for one is a function of the prices of all close substitutes. Under linear demand Q_j = a_j − Σ_k B_jk p_k the optimization is a quadratic program with closed form p^* = (B + B^T)^-1 (a + Bc). Under logit demand the structure is non-trivial but well behaved: the seller's problem on a single nest reduces to choosing a single markup multiplier across the nest [42], which dramatically simplifies estimation. Modern implementations cluster SKUs into demand-similar groups and solve the joint program at the group level, then back out individual prices. The mathematical pay-off of joint optimization is largest in categories with high cross-elasticity (apparel sizes, color variants); in categories with low cross-elasticity (specialty hardware), separable single-SKU optimization captures most of the benefit.

Mixed-integer programs for promotion-aware pricing

Many production pricing problems are intrinsically discrete: the seller chooses, for each SKU and each week, whether to promote, by how much, and through which mechanism (TPR, multibuy, coupon, bundle). The natural formulation is a mixed-integer program (MIP) over binary promotion variables and continuous depth variables, with vendor-funded budget constraints, category caps, and pantry-loading penalties to discourage same-customer reuse. Cohen et al. [11] formalize this and report empirical lifts of 3–5% in retail trials when MIP-based promotion planning replaces calendar-based heuristics. The LP relaxation is typically very tight in this problem class, which is why LP solutions—rounded with a small post-processing step—are the practical workhorse rather than full branch-and-bound.

Robust and distributionally robust pricing

All of the above takes the demand model as given. In practice elasticity estimates have wide credible intervals, and over-fitting the optimizer to a point estimate can produce large losses when the world deviates. Robust optimization hedges by maximizing the worst-case profit over a credible set of demand functions; distributionally robust optimization (DRO) does the same over a Wasserstein or moment-based ambiguity set around the empirical demand distribution [53]. The practical effect is that DRO solutions are biased toward prices in the interior of the historical price support, where data is densest. For a seller deploying pricing for the first time, this is exactly the right inductive bias.

Dynamic pricing with finite inventory

Single-period pricing ignores the trade-off between selling now and saving units for later. The Gallego–van Ryzin formulation [17] treats price as a control of a Poisson sales process over a finite horizon with given starting inventory, and derives an optimal price that decreases as remaining inventory grows and increases as remaining time shrinks. The same machinery underlies airline yield management and retail markdown systems [39]. In e-commerce, the most common application is end-of-season clearance: the optimizer schedules a sequence of markdowns that draws inventory toward zero by season end while maximizing expected residual revenue.

3.3 Online learning — exploration policies

The optimizer of §3.2 requires an estimated demand function. Where does the estimate come from? In principle, from historical data; in practice, that data has been generated by the seller's own past pricing rules, which makes it a censored, non-experimental sample. The cleanest solution is to treat pricing as a sequential learning problem: a multi-armed bandit in which arms are candidate prices, rewards are realized contributions, and the seller's job is to balance exploitation of the currently best-estimated arm against exploration of arms that may turn out to be better. The bandit literature dates to Robbins (1952) [34], and the modern theory begins with the Lai–Robbins lower bound [24], which establishes that any policy with logarithmic regret in the number of trials is asymptotically optimal.

ε-greedy

At each step, the seller plays the empirically best arm with probability 1 − ε and a uniformly random arm with probability ε. Implementation is trivial; the regret bound is O(εT) + O((K log T) / Δ), which is sublinear only if ε decays appropriately. ε-greedy is therefore the right baseline, not the right policy. Its main use in production is as a smoke test for the rest of the pipeline: if ε-greedy with ε = 0.1 cannot find a better-than-status-quo price within a few thousand customer arrivals, the data plumbing or the demand structure is the problem, not the algorithm.

Upper Confidence Bound (UCB)

UCB1 [4] plays the arm that maximizes p̂_k + √(2 log t / n_k), where p̂_k is the empirical mean reward and n_k is the number of pulls. The intuition is optimism in the face of uncertainty: the seller picks the arm whose plausibly highest reward is the largest. UCB has provably O(log T) regret, and—important for retail compliance—is fully deterministic given the data, which makes audit trails straightforward. The reliability cost is that UCB often over-explores high-variance arms early, which can be expensive when one arm has a large negative cost (e.g., a much-too-low price). KL-UCB and Bayes-UCB are tighter variants that perform better in practice.

Thompson Sampling

Thompson Sampling [37, 35] maintains a posterior over each arm's reward parameter and at each step draws a sample, choosing the arm whose sampled reward is highest. For Bernoulli rewards (purchase / no purchase), the Beta(α_k, β_k) posterior is conjugate and the algorithm is two lines of code. Agrawal & Goyal [3] establish O(√(KT log T)) regret bounds; in practice Thompson Sampling outperforms UCB on most benchmarks because its randomized exploration is naturally tempered by the posterior's shape: an arm with a tight, high posterior gets drawn often; an arm with a wide posterior gets explored. For pricing specifically, Misra et al. [29] report a field-experiment gross-profit lift of 86% versus a price-discrimination heuristic, and recover more than 80% of the oracle policy's profit within roughly two months. Figure 4 shows the same qualitative behavior in a deliberately simple simulated marketplace.

Contextual bandits

If the optimal price depends on the customer (returning vs. new), the channel (organic vs. paid), or the basket composition, the seller is in a contextual bandit. LinUCB [25] posits a linear reward model r = θ_a^T x + ε for each arm a, maintains a ridge-regression estimate of θ_a, and selects the arm with the highest UCB on its predicted reward. Disjoint LinUCB allows arm-specific θ_a; hybrid LinUCB shares parameters across arms. Neural-Thompson and neural-UCB extend the same idea with deep feature representations. Contextual bandits are also the dominant pattern for ranking and personalization at large platforms (see §7), where each arm is a candidate item rather than a candidate price.

Reinforcement learning

When the seller's actions affect future state—inventory levels, customer lifetime value, brand perception—the bandit framing is incomplete and a Markov decision process is more accurate. The state s_t encodes inventory, demand history, and competitor state; the action a_t is a price; the reward r_t = (p_t − c_t) Q_t − h_t I_t includes contribution net of holding cost. Policies are learned by Q-learning, policy gradients, or actor–critic methods. RL is most useful for inventory-coupled pricing (markdown sequences, ride-share surge) and least useful for routine catalog pricing where the bandit framing is sufficient. The operational risk is that off-the-shelf RL agents are notoriously sample-hungry, so most retail RL deployments learn in a high-fidelity simulator and use the bandit framing in production.

Off-policy evaluation and counterfactual learning

A persistent obstacle to deploying any new policy is that the seller cannot afford to A/B-test every candidate. Off-policy evaluation (OPE) lets the seller estimate, from logged data generated by an old policy, the expected reward of a new policy. Inverse-propensity scoring weights each logged event by the ratio of new-policy to old-policy action probabilities; doubly-robust estimators [14] combine IPS with an outcome model and remain consistent if either is correct; balanced policy evaluation [20] reduces variance by reweighting toward covariate balance. For seller teams, OPE is what turns ‘which model is best?' from a question that requires months of experimentation into a question answerable on logged data overnight.

The exploration policies above sit on top of the demand models of §3.1 and feed the optimizers of §3.2. The integration choice—what model is updated at what cadence with what data—is more important than the choice of algorithm: a daily Thompson-Sampling run on a hierarchical demand model with 24-hour observation lag is, in our experience, more reliable than a real-time contextual bandit on a black-box predictor.

4. Forecasting — making demand legible

Demand forecasting feeds inventory, pricing, promotion, and capacity decisions, so the marginal value of accuracy compounds across the stack. Forecasting accuracy is also one of the few metrics whose lift is empirically additive: a 10% reduction in MAPE typically translates into a 1–3% reduction in inventory carrying cost at constant service level [40], because the safety stock that protects against forecast error scales with the forecast standard deviation. Selection across forecasting methods comes down to three questions: how dense is the per-SKU history, how stationary is the underlying process, and does the downstream task need a point estimate or the full predictive distribution?

4.1 Classical statistical forecasters

Exponential smoothing and the ETS family

Exponential smoothing decomposes a series into level, trend, and seasonal components, each updated by an exponentially weighted moving average of past observations. The state-space ETS class formalizes this with explicit Error, Trend, Seasonality components in additive or multiplicative combinations, providing a likelihood for parameter estimation and a closed form for prediction intervals. ETS is robust, fast, and routinely beats more complex methods on dense, well-behaved series; it remains the right baseline for any single-SKU forecast and is the default in commercial planning software.

ARIMA and SARIMAX

ARIMA(p, d, q) models a series as a function of its own lags and lagged shocks after differencing. The seasonal extension SARIMAX adds seasonal differencing and exogenous regressors. ARIMA is the right tool when the series exhibits clean autoregressive structure and few external drivers; in retail it is more useful at the category aggregate than at the SKU level, because individual SKUs are too sparse and too promotion-driven for the ARIMA family's stationarity assumptions to hold.

Bayesian Structural Time Series (BSTS) and Prophet

BSTS expresses a series as y_t = trend_t + season_t + regression_t + ε_t, with each component evolving as a Gaussian state-space process and parameters fitted by MCMC or Kalman smoothing. The major operational benefit is calibrated uncertainty in every component, which lets a planner attribute forecast revisions to specific causes. Prophet [43] is a deliberately simpler relative—it fits a piecewise-linear trend with Fourier seasonality and a holiday-effect regressor, with priors that make it robust to messy data—and has become a popular default for analyst-facing forecasting.

4.2 Hierarchical and reconciled forecasts

Retail forecasts live in a natural hierarchy: SKU within category within store within region. Forecasting each level independently produces inconsistent numbers (the SKU forecasts will not sum to the category forecast). Reconciliation methods enforce consistency. Bottom-up sums SKU forecasts; top-down disaggregates the aggregate forecast by historical proportions; the optimal MinT reconciliation [19] is a generalized-least-squares projection that minimizes total trace of the reconciled forecast covariance subject to coherence constraints. MinT-reconciled forecasts deliver lower MAPE at every level than any single forecast, which is why hierarchical reconciliation is now the default for any organization that plans at multiple aggregations.

4.3 Machine-learning forecasters

Gradient-boosted trees with engineered features

LightGBM and XGBoost dominate Kaggle retail-forecasting competitions and underpin many production systems. The recipe is to engineer lag features (sales 1, 7, 14, 28 days back), rolling statistics (mean, max, min over moving windows), calendar features (day-of-week, month, holidays), and price/promo features, then train a global model on the entire panel with ID embeddings. Tree boosting handles non-linearities and interactions natively, scales to millions of series, and supports quantile regression directly via pinball loss. The main weakness is that the model has no internal notion of time and can extrapolate unevenly outside the training distribution; the standard remedy is to retrain on a rolling window and to monitor extrapolation by feature coverage.

Quantile regression and conformal prediction

Inventory does not need a point forecast; it needs a quantile (typically the 90–98th percentile of demand over the lead-time-plus-review interval). Quantile regression—either as a separate model per quantile or as a single multi-quantile network—targets these directly. Conformal prediction wraps any base predictor with a non-parametric calibration step that produces prediction intervals with finite-sample coverage guarantees, and is increasingly the right choice for inventory-grade forecasts where the calibration must be defensible.

4.4 Deep-learning forecasters

DeepAR

DeepAR [36] is an autoregressive recurrent network with parameters shared across all series in the panel. At each step the network outputs a distribution over the next value (negative-binomial for counts, Gaussian for continuous), conditioned on the series' lagged values, an embedding vector that identifies the series, and exogenous covariates. The shared parameters let the model transfer information from data-rich SKUs to data-poor ones, which is precisely the regime where SMB sellers operate. Probabilistic outputs are produced by Monte Carlo rollout. Production deployments at AWS, JD, and others have reported MAPE reductions of 10–25% over ETS baselines on retail panels.

Temporal Fusion Transformer (TFT)

TFT [26] is an attention-based architecture that handles the three covariate types found in retail forecasting: static metadata (category, brand), time-varying known-future inputs (planned promotions, holidays), and time-varying observed inputs (price, weather). Variable-selection networks gate which inputs contribute at each step, and an interpretable multi-head attention block surfaces which past timesteps drive each forecast. TFT typically beats DeepAR on covariate-rich problems and is the right choice when explainability of the forecast is part of the production requirement.

N-BEATS and N-HiTS

N-BEATS [31] is a stack of fully-connected residual blocks that decomposes the series into interpretable basis functions (trend, seasonality) without recurrence or convolution. The architecture is simple, trains fast, and competitive on benchmarks like M4. N-HiTS adds multi-rate sampling for long-horizon forecasting. Both are useful when the panel is too small to support a transformer but too large to forecast series-by-series.

Forecasting foundation models

A new class of pre-trained, zero-shot forecasters has emerged in 2023–24: Chronos, TimesFM, Lag-Llama. They are trained on broad corpora of time series and produce reasonable forecasts on unseen series with no fine-tuning. For SMB sellers, the immediate value is in cold-start: a brand-new SKU with no history can be forecast on day one by analog matching against the foundation model's prior, then refined as data accumulates. The maturity of these models is still uneven and they should be treated as a strong prior, not a final answer—but they have already become the default cold-start tool inside the larger demand-planning vendors.

4.5 How to choose

5. Inventory — matching supply to demand under uncertainty

Inventory translates a demand distribution into orders. The core idea is the newsvendor: in a single period with stochastic demand D ∼ F, per-unit overage cost c_o (= cost minus salvage), and per-unit underage cost c_u (= price minus cost), the expected-profit-maximizing order quantity Q^* satisfies the critical-fractile equation:

The derivation is short. Expected profit is E[π(Q)] = c_u · E[min(D, Q)] − c_o · E[(Q − D)⁺]; differentiating with respect to Q gives c_u (1 − F(Q)) − c_o F(Q) = 0, which rearranges to the critical fractile. The strength of the framing is that it converts a strategic question (how cautious should I be?) into a parameter (the ratio c_u / (c_u + c_o)) that has a defensible value as soon as the unit economics are written down.

5.1 Multi-period and continuous-review variants

(s, S) policies

When ordering incurs a fixed cost K in addition to per-unit cost, the optimal policy is of the (s, S) form: order up to S whenever inventory drops below s, and otherwise do nothing. The optimality is established under stationary demand and was generalized by Scarf and others to broader classes [40]. In practice, s is determined by service-level targets (typically the demand-over-lead-time α-quantile), and S − s trades off ordering cost against holding cost.

Base-stock policies

When the fixed ordering cost is negligible (typical for digital purchase orders to a single vendor), the optimal policy collapses to a base-stock rule: continuously raise inventory to a fixed target. The base-stock target is the critical fractile of the lead-time demand distribution, which is the multi-period generalization of the newsvendor.

Multi-echelon optimization

Real retailers hold inventory across DCs, regional warehouses, and stores. Local optimization is suboptimal because it double-counts safety stock. Clark and Scarf [52] established the optimality of echelon base-stock policies for serial supply chains, and the modern multi-echelon literature extends this to assembly and distribution systems. The structural advantage of platform-scale retailers is precisely that they coordinate inventory across the network rather than at each node, which is why same-day delivery is feasible without holding store-level worst-case stock for every SKU.

Joint replenishment

When several SKUs share a vendor and a fixed ordering cost (case-pack purchase from a single supplier), the joint replenishment problem chooses a common ordering frequency and SKU-specific multipliers. Closed-form solutions exist for special cases; in general the problem is solved by a Lagrangian or by enumeration over a small set of candidate frequencies. SMB sellers buying from a single overseas supplier are an obvious application.

Distributionally robust inventory

Newsvendor solutions are sensitive to demand-distribution misspecification. Scarf's min-max [51] is the classical worst-case-distribution solution given only the mean and variance of demand. Modern Wasserstein-based DRO [53] replaces this with a tractable convex program over an ambiguity set centered on the empirical distribution, with the ambiguity radius tuned by cross-validation. DRO is attractive when forecast errors are heavy-tailed or when the seller's history covers an unusual macro regime.

RL-based inventory

When demand is non-stationary, lead times are stochastic, and the network is multi-echelon, deep RL can learn policies that beat analytic baselines. Production deployments include sub-systems of large fulfillment networks. The pattern is similar to RL pricing: train in a high-fidelity simulator that has been calibrated against real demand, deploy a constrained policy that always respects safety-stock floors, and instrument continuous off-policy evaluation against the analytic baseline.

5.2 Markdowns and clearance

End-of-season inventory liquidation is a joint pricing-inventory problem: the seller must draw inventory toward zero by season end while maximizing residual revenue. Smith and Achabal [39] formalize this as an optimal-control problem in which price decreases over time as the urgency of selling rises, and derive structural properties of the optimal markdown trajectory. Modern implementations layer demand-forecasting and bandit-based exploration on top of the same backbone, and treat the markdown schedule as a sequence of small price experiments that update the seller's elasticity estimate as the season progresses.

6. Promotions and discounting — where causality matters

Promotion decisions are intrinsically causal. The relevant question is not ‘did customers who received a coupon buy more?' but ‘would they have bought without it?'. Conventional propensity-weighted regression conflates the two, and as a result chronically over-credits promotions to customers who would have purchased anyway. The relevant statistical object is the conditional average treatment effect (CATE):

Estimating τ is hard because, by the fundamental problem of causal inference, we never observe both Y(w) and Y(0) for the same unit. Identification requires either randomized assignment of w (an experiment) or an unconfoundedness assumption that (Y(0), Y(w)) ⊥ w | X. Most production uplift modeling rests on the second route, so the choice of features X is part of the modeling decision, not a preprocessing step.

6.1 Meta-learners for CATE

S-learner

The S-learner fits a single model μ̂(x, w) of the outcome on covariates and treatment, then estimates τ̂_S(x) = μ̂(x, 1) − μ̂(x, 0). The simplicity is its strength and its weakness: regularizing the base learner shrinks both the prognostic and treatment-effect signals, and the latter is usually much smaller, so the S-learner is biased toward zero treatment effect when the prognostic signal is large. It remains a sensible default for small samples and weak treatments.

T-learner

The T-learner fits two models, one per arm: μ̂_w(x) on the subsample with treatment w, then τ̂_T(x) = μ̂₁(x) − μ̂₀(x). The T-learner is flexible but inherits high variance in the smaller arm, which in retail is usually the treated arm because the seller does not give discounts to everyone. It is also at risk of differential overfitting between arms.

X-learner

Künzel et al. [23] propose the X-learner: fit T-learner-style outcome models, then impute counterfactual treatment effects D_i for each unit using the opposite arm's model, and finally regress D_i on covariates separately within each arm to produce arm-specific CATE estimates. A propensity-weighted combination of the two estimates yields the final CATE. The X-learner outperforms S- and T-learners when arm sizes are imbalanced, which is the typical retail regime.

R-learner

Nie & Wager [30] formulate CATE estimation as residualized regression: fit nuisance models for the conditional outcome m̂(x) = E[Y|X = x] and propensity ê(x) = P(W = 1|X = x), then minimize Σ ((Y − m̂(X)) − (W − ê(X)) τ(X))² in a flexible class. The result has quasi-oracle properties: the CATE estimator behaves as if the nuisance functions were known, provided they are estimated at sufficient rates. The R-learner has become a strong default in modern uplift work because the residualization decouples nuisance estimation error from CATE estimation.

Doubly robust learners (AIPW, DR-learner)

Augmented inverse-propensity weighting (AIPW) constructs a pseudo-outcome that is consistent for the CATE if either the outcome model or the propensity model is correctly specified. The DR-learner regresses this pseudo-outcome on covariates to get an explicit CATE function. Doubly robust estimators are the right starting point in observational settings where neither the outcome nor the propensity model is fully trusted.

Causal forests and generalized random forests

Wager & Athey [46] adapt random forests to CATE estimation by enforcing honesty (using disjoint subsamples for split selection and leaf estimation) and recasting splits to maximize heterogeneity in treatment effects rather than outcome variance. Causal forests yield asymptotically normal CATE estimates with valid confidence intervals, and they handle high-dimensional X without manual feature selection. The implementation in EconML is a practical default for tabular retail data.

Deep CATE estimators

When covariates include dense embeddings (session features, product images, text), neural CATE estimators—TARNet, CFRNet, Dragonnet—are appropriate. These typically share a representation across arms and add arm-specific heads, with regularization to limit treatment-imbalance bias in the shared representation. They require larger samples than tree-based methods and are most useful in personalization-adjacent settings where the relevant features are not naturally tabular.

6.2 From CATE to assignment — the optimization layer

Given a CATE estimator and a budget, the assignment problem is a 0/1 knapsack:

with m the contribution margin per unit. At retail scale the problem becomes a mixed-integer program with vendor-funded budgets, pantry-loading constraints, category caps, and customer-frequency caps. The LP relaxation is typically very tight, so a column-generation approach with simple rounding is the production workhorse [11]. The structural insight is that the value of better targeting (a tighter τ̂) is proportional to budget pressure: when the budget is unconstrained, even mediocre targeting captures most of the lift; under tight budgets, the value of accurate uplift modeling rises sharply.

6.3 Measurement

Last-touch attribution remains the default in most marketplace UIs but systematically over-credits bottom-of-funnel channels, leading to under-investment in awareness. Three modern alternatives have stabilized in industry practice. Bayesian media-mix models regress geo-week revenue on geo-week spend across channels with informative priors on saturation and adstock, producing channel-level marginal-ROI curves. Geo-randomized experiments (GeoLift, synthetic controls) randomize spend at the geography level and identify incrementality from the gap between treated and synthetic-control units. Switchback designs alternate the treatment on/off in time within a single unit to handle two-sided-marketplace interference. The trend is unmistakably toward continuous experimentation rather than periodic measurement studies, which is why the experimentation layer in §8 is non-negotiable.

7. Personalization and recommendation

Recommender systems convert browsing into purchases by ranking items per user. Bezos [7] famously attributed substantial Amazon GMV to recommendations; downstream estimates place direct lift in the 20–35% range for mature implementations. The architectural arc has run from collaborative filtering through matrix factorization to two-tower neural retrieval and multi-task neural ranking. Three structural choices distinguish industrial recommenders: how candidate items are retrieved from a catalog of millions; how those candidates are ranked at low latency; and how the system continues to learn from logged data.

7.1 Retrieval

Collaborative filtering

User-based and item-based collaborative filtering compute similarities (cosine, Pearson) over the user-item interaction matrix, then recommend items similar to those the user has interacted with. CF is the original recommender approach and remains a strong baseline, especially with implicit-feedback corrections. Its weaknesses are scalability (similarity matrices are O(n²)) and cold-start (no recommendations for new users or new items).

Matrix factorization

Matrix factorization [22] decomposes the user-item rating (or implicit-feedback) matrix into low-rank user and item embeddings U and V, with predicted score ŝ_ui = u_u^T v_i. For implicit feedback (clicks, purchases, no explicit rating), the standard objective is weighted least squares over observed and (down-weighted) unobserved interactions, solved by alternating least squares (ALS-WR) or stochastic gradient descent. Bayesian Personalized Ranking [33] replaces this with a pairwise ranking loss that directly optimizes AUC on observed-vs-unobserved pairs. Matrix factorization is still in production at many sellers, particularly as a strong cold-start fallback.

Two-tower neural retrieval

Industrial-scale retrieval has converged on the two-tower architecture: a user encoder f(u) and an item encoder g(i) produce embeddings whose dot product is the predicted relevance [49]. The model is trained with sampled softmax over the catalog, with sampling-bias correction to compensate for the fact that popular items appear disproportionately often as negatives. At serving time, item embeddings are pre-computed and indexed with an approximate-nearest-neighbor structure (FAISS, ScaNN), so retrieval is sub-millisecond on catalogs of millions. The two-tower pattern is the dominant industry recipe and has the operational advantage that the user and item towers can be retrained on different cadences.

Graph neural networks

GNNs exploit the bipartite user-item graph and item-item co-purchase graph by propagating embeddings along edges. PinSage [48] is the canonical web-scale recipe; LightGCN [18] strips out non-essential transformation and activation layers and trains a much simpler weighted aggregation, often outperforming heavier architectures. GNNs are particularly useful for cold-start (new items inherit embeddings from their neighbors) and complementary-product recommendation (items frequently co-purchased rather than substituted).

7.2 Ranking and re-ranking

Pointwise vs. pairwise vs. listwise

Once a few hundred candidate items are retrieved, the ranker reorders them. Pointwise rankers predict per-item scores (logistic regression on engagement); pairwise rankers (RankNet, LambdaRank) optimize ordered pairs; listwise rankers (LambdaMART, ListNet) optimize the full list using metrics like NDCG. Listwise approaches generally win on engagement metrics but are more expensive; LambdaMART remains a workhorse for tabular feature sets.

Multi-task neural rankers

Industrial rankers must balance competing objectives—click, add-to-cart, purchase, return rate—because optimizing a single objective leads to clickbait. Multi-task architectures (shared bottom, MMoE, PLE) [12] maintain shared representations with task-specific heads, and weighted task losses reflect the seller's value function. The Deep Interest Network [50] adds an attention mechanism over the user's past behaviors that gates which historical signals are relevant for the current candidate, improving CTR meaningfully on large e-commerce platforms.

Sequence and session models

User intent is more legible from a recent sequence of clicks than from an aggregate profile. SASRec [21] applies self-attention to the user's interaction history; BERT4Rec [55] replaces the autoregressive objective with a masked-item prediction more analogous to BERT in NLP. Session-based recommenders win in domains with thin user histories and strong intra-session intent (apparel, electronics).

7.3 Learning from logs — bandits and counterfactual evaluation

Production recommenders cannot afford to A/B-test every candidate model, and online metrics are noisy. The right architectural pattern is contextual-bandit ranking: each ranking decision logs the action probability, and the system continuously learns from the resulting reward. Top-K off-policy correction [10] adapts policy-gradient training to the multi-action setting required for a list of recommendations. Counterfactual evaluation [20, 14] lets teams compare candidate models on logged data, which is essential because the catalog and user distribution drift on weekly time scales. Mature recommenders treat exploration as a first-class concern—not as a randomization gimmick, but as the data-collection mechanism that keeps the model identified.

8. Putting it together — a reference decision-intelligence stack

The methods above are necessary but not sufficient. The binding constraint for most sellers is the absence of a system that ingests their data, runs the relevant models, and surfaces actionable decisions. Figure 6 sketches a five-layer reference architecture that we treat as the minimum viable stack for a seller crossing into the ‘growing' or ‘scaled' regime of Table 3.

8.1 Data layer

Connectors to marketplaces (Amazon SP-API, Shopify GraphQL, Walmart Marketplace, eBay Trading API), the seller's warehouse-management system, ad platforms (Meta Marketing API, Google Ads, Pinterest), and competitive scrapers. The output is an event log with consistent SKU, customer, and time keys, partitioned and stored in a columnar format (Parquet on object storage, or a warehouse like Snowflake or BigQuery). Without this layer, every downstream layer regresses to spreadsheet quality. The hardest single problem at this layer is identity resolution across marketplaces, which determines whether ‘the customer' is a usable abstraction.

8.2 Feature store

A small but disciplined feature store containing SKU embeddings (text via a pre-trained encoder, image via a vision encoder, taxonomy via learned look-ups), customer recency-frequency-monetary features, price and competitor-price histories, and seasonal and holiday calendars. Each feature has an explicit freshness budget (intraday for pricing; daily for forecasting; weekly for cohort features) and an SLA for serving latency. The feature store is what makes models reproducible and what lets the same feature vector flow into pricing, forecasting, and ranking.

8.3 Model layer

A demand forecaster (hierarchical Bayesian or DeepAR/TFT for the catalog), an elasticity estimator with bandit-driven exploration for pricing, an uplift model (R-learner or causal forest) for promotions, an inventory optimizer that consumes the forecaster's predictive distribution, and a two-tower ranker for personalization. Crucially, models are decoupled from decisions: the same forecaster feeds both pricing and inventory, the same SKU embeddings feed retrieval and uplift, and the model registry is the unit of versioning rather than the decision endpoint.

8.4 Optimization and decision layer

A linear- or mixed-integer-programming solver translates model outputs into decisions, subject to business constraints (margin floors, MAP, brand consistency, vendor budgets). Decision proposals are not auto-executed: a thin review UI exposes the recommendations, the model evidence, and the constraint shadow prices to a human merchandiser. The shadow prices in particular are commercially valuable—they tell the seller how much margin is left on the table because of a binding constraint, which is exactly the conversation a merchandiser should be having with a vendor or a category manager.

8.5 Experimentation and off-policy evaluation

A switchback or geo-randomized experimentation framework wraps every decision so that the marginal contribution of each model is observable. Off-policy evaluation lets the team rank candidate models on logged data before promoting any of them to a live A/B, which is essential when the seller's traffic is too thin to support many simultaneous experiments. This layer is what converts the architecture from a one-off consulting deliverable into a continuously improving asset [5], and it is the layer where SMB sellers most consistently under-invest.

9. How to select techniques by seller stage

Capability should track the seller's data volume, decision frequency, and operational maturity. Table 3 maps a pragmatic technique progression that we have found durable across categories.

10. Risks, governance, and considerations

Pricing fairness and regulation

Dynamic and personalized pricing have a poor reputation for reasons that are partly justified: surge pricing on essentials, opaque discrimination across geographies, and the perception of being ‘gouged' all impose long-run brand cost. Regulators in the EU (the Omnibus Directive) and several U.S. states now require disclosure of personalized pricing, and the Federal Trade Commission has signaled active interest in price discrimination by digital intermediaries. Sellers should prefer context-level optimization (channel, time-of-day, basket composition) over identity-level optimization until the legal landscape stabilizes, and should design their pricing system so that the price actually shown to a customer is a deterministic function of disclosable inputs.

Cold start

New SKUs and new customers have no per-entity history. Hierarchical Bayes (§3.1, §4.2), embedding-based analog matching, and forecasting foundation models (§4.4) are the right architectural responses. The wrong response is to wait until enough data accumulates—by then the cold-start window has closed and the seller has ceded margin to whichever competitor was willing to make a guess.

Data drift and silent failure

Promo cycles, macro shocks, and platform algorithm changes invalidate models built on stationary assumptions. The mitigation is continuous evaluation: holdout reservoirs that the production model never sees, conformal prediction intervals that flag unusual coverage breaches, and KS-style monitoring of feature distributions against training-set baselines. A model that has not been re-evaluated in 90 days should be treated as suspect by default.

Algorithmic monoculture

When every seller deploys the same repricer or recommender, equilibrium prices and assortments collapse to a narrow strip and the platform's overall consumer surplus falls. The platforms that actively allow multiple algorithms to compete (and that publish realistic counterfactual data so vendors can train differentiated models) tend to retain healthier ecosystems. From the seller's side, monoculture is a reason to instrument differentiation against the platform default, not a reason to abandon optimization.

Human-in-the-loop and auditability

Auto-execution amplifies errors. The stable production pattern is decision proposals reviewed before they hit the catalog, with audit logs for every override and for every model decision (input features, model version, output, applied constraints). Auditability is also increasingly a regulatory requirement and is the difference between a defensible system and one that simply works most of the time.

11. Conclusion

Large retailers have, for a decade, used the techniques surveyed in this report to move pricing, inventory, promotions, and personalization from intuition to inference. The techniques themselves are no longer the moat. The moat is integration: connectors, feature stores, optimization, experimentation, off-policy evaluation, and a human-in-the-loop UI assembled into a single workflow. For an SMB seller, the highest-return investment is no longer hiring a single data scientist; it is adopting—or, where the right product does not yet exist, building—an integrated decision stack of which that data scientist would be one component. Closing this gap is the most concrete way to move e-commerce from a winner-take-most market toward one in which a much wider set of merchants can earn fair returns on the capital and labor they invest.

The techniques are no longer the moat. Integration is the moat.

FAQ

Six questions sellers, operators, and engineers ask most often when deciding whether — and how — to adopt the techniques surveyed in this report.

References

[1] Amazon.com Inc. (2024). 2023 Annual Report and Form 10-K.

[2] Athey, S., & Imbens, G. W. (2019). Machine learning methods that economists should know about. Annual Review of Economics, 11, 685–725.

[3] Agrawal, S., & Goyal, N. (2012). Analysis of Thompson sampling for the multi-armed bandit problem. COLT 2012.

[4] Auer, P., Cesa-Bianchi, N., & Fischer, P. (2002). Finite-time analysis of the multiarmed bandit problem. Machine Learning, 47, 235–256.

[5] Bertsimas, D., & Kallus, N. (2020). From predictive to prescriptive analytics. Management Science, 66(3), 1025–1044.

[6] Berry, S., Levinsohn, J., & Pakes, A. (1995). Automobile prices in market equilibrium. Econometrica, 63(4), 841–890.

[7] Bezos, J. (2017). Letter to Shareholders. Amazon.com Inc.

[8] Chen, N., & Mišić, V. V. (2022). Decision-focused learning of revenue-management policies. Management Science, 68(8), 5921–5947.

[9] Chen, X., Owen, A. B., Pixton, C., & Simchi-Levi, D. (2015). Statistical learning of dynamic pricing strategies. Operations Research, 63(2), 326–339.

[10] Chen, M., Beutel, A., Covington, P., et al. (2019). Top-K off-policy correction for a REINFORCE recommender system. WSDM 2019.

[11] Cohen, M. C., Leung, N.-H. Z., Panchamgam, K., Perakis, G., & Smith, A. (2021). The impact of linear optimization on promotion planning. Operations Research, 69(1), 105–124.

[12] Covington, P., Adams, J., & Sargin, E. (2016). Deep neural networks for YouTube recommendations. RecSys 2016.

[13] Donoho, D. (2017). 50 years of data science. Journal of Computational and Graphical Statistics, 26(4), 745–766.

[14] Dudík, M., Erhan, D., Langford, J., & Li, L. (2014). Doubly robust policy evaluation and optimization. Statistical Science, 29(4), 485–511.

[15] Elmachtoub, A. N., & Grigas, P. (2022). Smart ‘predict, then optimize'. Management Science, 68(1), 9–26.

[16] Fisher, M., Gallino, S., & Li, J. (2018). Competition-based dynamic pricing in online retailing. Management Science, 64(6), 2496–2514.

[17] Gallego, G., & van Ryzin, G. (1994). Optimal dynamic pricing of inventories with stochastic demand. Management Science, 40(8), 999–1020.

[18] He, X., Deng, K., Wang, X., et al. (2020). LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation. SIGIR 2020.

[19] Hyndman, R. J., Ahmed, R. A., Athanasopoulos, G., & Shang, H. L. (2011). Optimal combination forecasts for hierarchical time series. Computational Statistics & Data Analysis, 55(9), 2579–2589.

[20] Kallus, N. (2018). Balanced policy evaluation and learning. NeurIPS 2018.

[21] Kang, W.-C., & McAuley, J. (2018). Self-attentive sequential recommendation. ICDM 2018.

[22] Koren, Y., Bell, R., & Volinsky, C. (2009). Matrix factorization techniques for recommender systems. IEEE Computer, 42(8), 30–37.

[23] Künzel, S. R., Sekhon, J. S., Bickel, P. J., & Yu, B. (2019). Meta-learners for estimating heterogeneous treatment effects using machine learning. PNAS, 116(10), 4156–4165.

[24] Lai, T. L., & Robbins, H. (1985). Asymptotically efficient adaptive allocation rules. Advances in Applied Mathematics, 6(1), 4–22.

[25] Li, L., Chu, W., Langford, J., & Schapire, R. E. (2010). A contextual-bandit approach to personalized news article recommendation. WWW 2010.

[26] Lim, B., Arık, S. O., Loeff, N., & Pfister, T. (2021). Temporal Fusion Transformers for interpretable multi-horizon time series forecasting. International Journal of Forecasting, 37(4), 1748–1764.

[27] McKinsey & Company. (2023). The Multiplier Effect: How dynamic pricing is reshaping retail. McKinsey Insights.

[28] McKinsey & Company. (2024). The State of Small and Medium-Sized Businesses Report.

[29] Misra, K., Schwartz, E. M., & Abernethy, J. (2019). Dynamic online pricing with incomplete information using multi-armed bandit experiments. Marketing Science, 38(2), 226–252.

[30] Nie, X., & Wager, S. (2021). Quasi-oracle estimation of heterogeneous treatment effects. Biometrika, 108(2), 299–319.

[31] Oreshkin, B. N., Carpov, D., Chapados, N., & Bengio, Y. (2020). N-BEATS: Neural basis expansion analysis for interpretable time series forecasting. ICLR 2020.

[32] Phillips, R. L. (2005). Pricing and Revenue Optimization. Stanford University Press.

[33] Rendle, S., Freudenthaler, C., Gantner, Z., & Schmidt-Thieme, L. (2009). BPR: Bayesian personalized ranking from implicit feedback. UAI 2009.

[34] Robbins, H. (1952). Some aspects of the sequential design of experiments. Bulletin of the American Mathematical Society, 58(5), 527–535.

[35] Russo, D., Van Roy, B., Kazerouni, A., Osband, I., & Wen, Z. (2018). A tutorial on Thompson sampling. Foundations and Trends in ML, 11(1), 1–96.

[36] Salinas, D., Flunkert, V., Gasthaus, J., & Januschowski, T. (2020). DeepAR: Probabilistic forecasting with autoregressive recurrent networks. International Journal of Forecasting, 36(3), 1181–1191.

[37] Scott, S. L. (2010). A modern Bayesian look at the multi-armed bandit. Applied Stochastic Models in Business and Industry, 26(6), 639–658.

[38] Shopify. (2024). Commerce Trends 2024 Report.

[39] Smith, S. A., & Achabal, D. D. (1998). Clearance pricing and inventory policies for retail chains. Management Science, 44(3), 285–300.

[40] Snyder, L. V., & Shen, Z.-J. M. (2019). Fundamentals of Supply Chain Theory (2nd ed.). Wiley.

[41] Statista Research Department. (2024). Global retail e-commerce sales 2014–2027.

[42] Talluri, K. T., & van Ryzin, G. J. (2004). The Theory and Practice of Revenue Management. Springer.

[43] Taylor, S. J., & Letham, B. (2018). Forecasting at scale. The American Statistician, 72(1), 37–45.

[44] U.S. Census Bureau. (2024). Quarterly Retail E-Commerce Sales, 4th Quarter 2023.

[45] Jungle Scout. (2024). The State of the Amazon Seller 2024.

[46] Wager, S., & Athey, S. (2018). Estimation and inference of heterogeneous treatment effects using random forests. Journal of the American Statistical Association, 113(523), 1228–1242.

[47] Wedel, M., & Kannan, P. K. (2016). Marketing analytics for data-rich environments. Journal of Marketing, 80(6), 97–121.

[48] Ying, R., He, R., Chen, K., et al. (2018). Graph convolutional neural networks for web-scale recommender systems (PinSage). KDD 2018.

[49] Yi, X., et al. (2019). Sampling-bias-corrected neural modeling for large corpus item recommendations. RecSys 2019.

[50] Zhou, G., Zhu, X., Song, C., et al. (2018). Deep Interest Network for click-through rate prediction. KDD 2018.

[51] Scarf, H. (1958). A min-max solution of an inventory problem. Studies in the Mathematical Theory of Inventory and Production.

[52] Clark, A. J., & Scarf, H. (1960). Optimal policies for a multi-echelon inventory problem. Management Science, 6(4), 475–490.

[53] Mohajerin Esfahani, P., & Kuhn, D. (2018). Data-driven distributionally robust optimization using the Wasserstein metric. Mathematical Programming, 171(1–2), 115–166.

[54] Chen, T., Sun, Y., Shi, Y., & Hong, L. (2017). On sampling strategies for neural network-based collaborative filtering. KDD 2017.

[55] Sun, F., Liu, J., Wu, J., et al. (2019). BERT4Rec: Sequential recommendation with bidirectional encoder representations from Transformer. CIKM 2019.