Promotional strategies and channel cannibalization in multichannel retail

Abstract

Paper aims  This study introduces a data-driven approach to evaluate how promotional strategies redistribute demand across channels and are associated with cannibalization in multichannel retail.

Originality  Transitioning from descriptive analysis to a predictive machine learning approach, this research addresses a literature gap by empirically evaluating mitigation strategies, such as coordinated promotions and loyalty incentives, to provide a basis for strategic promotional planning.

Research method  Demand prediction models, including gradient boosting, linear, and neural network models, were benchmarked using historical sales data from a regional Brazilian supermarket. Model performance was evaluated using Root Mean Squared Error (RMSE) and R-squared (R²). The validated model was used to run counterfactual simulations of mitigation scenarios.

Main findings  eXtreme Gradient Boosting (XGBoost) demonstrated robust physical-channel forecasting, identifying cross-channel displacement associations of 11.23% (physical-to-online) and 19.34% (online-to-physical). Simulations suggest that while isolated promotions exacerbate channel conflict, coordinated promotions attenuate cannibalization by 30.04%. Furthermore, integrating loyalty incentives yielded the largest demand uplift (+3.5%), transforming conflict into synergy.

Implications for theory and practice  Theoretically, the study validated XGBoost paired with SHAP-based interpretation as a simulation framework for testing channel-synergy propositions. Practically, it offers a replicable, data-driven approach to mitigate demand displacement and foster channel synergy through integrated promotional planning.

Keywords:
Demand forecasting; Promotional cannibalization; Machine learning; XGBoost; Consumer behavior

1. Introduction

Promotional techniques originated during the 19^th-century Industrial Revolution, when mass production created the need to stimulate demand and clear surplus inventory (Allen, 2017; Beard, 2016). Early practices included Coca-Cola’s free coupons and department store sales events, which evolved into mass media advertising by the mid-20^th century (O’Barr, 2005).

In nowadays multichannel environment, promotions remain crucial but often trigger channel cannibalization, redistributing existing sales rather than expanding total demand (Aguilar-Palacios et al., 2019; De Giovanni & Ramani, 2017; Silva et al., 2016). The rise of e-commerce has introduced behaviors such as Research Online, Purchase Offline (ROPO) that shift demand between channels (Oliveira et al., 2026; Verhoef et al., 2015), with price disparities causing significant internal reallocations (Aguilar-Palacios et al., 2019; Gong et al., 2015; Oliveira et al., 2025). This behavior is elucidated by Prospect Theory (Kahneman & Tversky, 1979), under which consumers evaluate gains and losses relative to a reference point. Specifically, promotions lower prices below a consumer’s willingness-to-pay threshold, creating a perceived gain that drives channel-switching behavior and cannibalization (Deleersnyder & Koll, 2012).

Existing literature has documented the channel cannibalization phenomenon across different retail contexts. Studies show that broadening online assortments (Ma, 2016), launching brand-owned stores (Van Crombrugge et al., 2024), adopting live-stream shopping (Gong et al., 2022), and introducing mobile apps (Lim et al., 2022) can trigger this effect. While these studies have advanced the literature primarily through descriptive analyses, the application of predictive Machine Learning (ML) models to actively forecast and mitigate promotion-induced cannibalization remains underexplored.

This limitation is particularly critical given the dynamic and nonlinear nature of consumer responses to promotions, which requires analytical models capable of predicting demand shifts before strategic decisions are implemented (Gupta & Cooper, 1992). Recent advances in ML and simulation-based optimization provide powerful tools to address this challenge, enabling accurate demand forecasting and data-driven promotional design (Mitra et al., 2022; Pereira & Frazzon, 2021).

Accordingly, this research proposes a data-driven framework that leverages predictive ML models to provide model-based estimates of how promotions redistribute demand across channels and to quantify the extent of the resulting channel cannibalization, interpreted as predictive associations rather than causal effects. Additionally, it simulates and compares mitigation strategies that aim to convert channel conflict into synergy. The framework is validated through an empirical use case of a multichannel supermarket located in southern Brazil. Theoretically, this study contributes by extending cannibalization research from descriptive analysis to predictive modeling. Practically, it offers actionable insights for designing coordinated promotional strategies that mitigate channel demand displacement.

2. Related works

Differences in promotional strategies across retail channels often foster conflict and unintended sales cannibalization. Therefore, the overall success of any multichannel strategy is largely determined by the balance between channel synergy and demand displacement (Neslin, 2022; Timoumi et al., 2022).

Although channel cannibalization presents a tangible risk in which sales in one channel may diminish those in another (Deleersnyder & Koll, 2012; Chen et al., 2019; Lim et al., 2022; Shriver & Bollinger, 2022), expanding the channel mix can also generate positive synergy effects. Synergy occurs when the presence of one channel enhances the performance of another, leading to overall sales growth (Neslin et al., 2006; Fornari et al., 2016; Wang et al., 2021; Lim et al., 2022). The net outcome is driven by the interplay between demand expansion and cannibalization effects (Shriver & Bollinger, 2022). Table 1 summarizes how different mechanisms contribute to positive interactions between online and offline channels, ultimately boosting overall brand performance.

Table 1
Key drivers of channel synergy.

Mechanism	Description	References
Greater availability and convenience	More touchpoints facilitate consumer engagement and purchasing behavior. Specifically, e-commerce and m-commerce improve both convenience and accessibility.	Huang et al. (2016); Lim et al. (2022); Neslin et al. (2006).
Strengthened brand presence and recognition	Physical retail locations, in particular, can act as “living outdoors”, increasing visibility and potentially driving traffic to online channels. The mere presence of a physical store can cultivate consumer trust and credibility.	Jill et al. (2013); Fornari et al. (2016); Gong et al. (2022); Shriver & Bollinger (2022); Van Crombrugge et al. (2024); Wang & Goldfarb (2017).
Channels information search	Consumers occasionally engage in “research purchases” using one channel for information gathering and another for purchase. This includes webrooming (research online, purchase offline) and showrooming (research offline, purchase online). Showrooms explicitly facilitate this practice, and even Buy Online, Pick-up in Store (BOPS) systems can incentivize webrooming by signaling product availability.	Gallino & Moreno (2014); Gong et al. (2022); Neslin (2022); Timoumi et al. (2022); Verhoef et al. (2007).
Market expansion	New channels can attract new consumers or fulfill previously unmet needs, leading to incremental sales rather than merely reallocating existing demand. Further, offering larger online assortments, despite cannibalization risks, can stimulate sales.	Brynjolfsson et al. (2013); Li (2021); Ma (2016); Shriver & Bollinger (2022).
Complementary channel capabilities and value transfer	Different channels excel at different competencies (e.g., digital platforms for broad selection, physical stores for experiential engagement). An integrated offering allows consumers to leverage the strengths of each channel synergistically.	Bridges & Florsheim (2008); Neslin et al. (2006).
Enhanced pricing power	In some cases, the presence of a complementary channel may enable retailers to implement higher prices in existing channels, as the new channel provides a “compensating substitute” that mitigates demand loss when prices increase elsewhere.	Li (2021)

Empirical evidence suggests that synergy may prevail, leading to increased overall performance, despite some cannibalization (Neslin, 2022; Timoumi et al., 2022). Studies have found a positive causal effect from adopting online channels on physical store performance, primarily through increased purchase frequency via travel platforms (Wang et al., 2021) and mobile applications (Huang et al., 2016; Lim et al., 2022). Conversely, adding physical stores to online operations can also yield long-term synergy (Jill et al., 2013). However, the net result is highly dependent on the retail context (Timoumi et al., 2022), as channel expansion can sometimes merely shift existing sales rather than generating overall growth.

The interplay between cannibalization and synergy is influenced by several factors related to the channels, the product, the market, and the retailer’s strategy (Timoumi et al., 2022). These factors, detailed in Table 2, jointly determine whether synergy or cannibalization prevails.

Table 2
Elements driving the balance between synergy and cannibalization in retail channels.

Category	Description	References
Channel attributes	The degree of differentiation between channels in price, service, and assortment is critical; greater overlap can increase cannibalization, while distinct value propositions foster complementarity. Channels have unique capabilities (e.g., online for search, physical for experience), and higher integration typically leads to better performance by meeting consumer expectations for consistency and synchronization across touchpoints.	Cao & Li (2015); Chen et al. (2019); Deleersnyder & Koll (2012); Herhausen et al. (2015); Huang et al. (2016); Li (2021); Ma (2016); Neslin (2022); Soysal & Krishnamurthi (2016); Timoumi et al. (2022); Yeh et al. (2022).
Market and consumer factors	Consumer traits like demographics and channel preferences segment shoppers across channels, where observed differences may stem from self-selection rather than channel adoption itself. Local market conditions, such as store availability, further shape this segmentation.	Chen et al. (2019); Herhausen et al. (2015); Li (2021); Lim et al. (2022); Neslin (2022); Soysal & Krishnamurthi (2016).
Retail strategy and management	The way a retailer manages its channels, including pricing, the degree of operational integration, and the sequence of channel rollout (e.g., web-first vs. store-first) impacts outcomes.	Fornari et al. (2016); Herhausen et al. (2015); Hübner et al. (2016); Kim & Chen (2018); Li (2021); Neslin (2022); Shriver & Bollinger (2022); Van Crombrugge et al. (2024).

Beyond these structural factors, promotion-induced cannibalization manifests through distinct behavioral mechanisms. First, cross-channel demand displacement occurs when consumers redirect purchases from a non-promoted channel to a promoted one (Gong et al., 2015; Shriver & Bollinger, 2022). Second, promotions are frequently associated with forward buying, where short-term campaigns encourage consumer stockpiling, thereby reducing future demand (Ailawadi & Gupta, 2014; Gupta & Cooper, 1992). Third, cross-product cannibalization can reallocate demand within a category, diverting sales from higher-margin items without generating incremental revenue (Bekal & Bari, 2021; De Giovanni & Ramani, 2017).

To mitigate these displacement effects, customizing promotional offers across heterogeneous consumer segments – using purchase history, demographics, or channel preference – refines targeting and helps moderate cross-channel cannibalization (Li, 2021; Konus et al., 2008). Strengthening this approach with dynamic pricing allows for real-time adjustments based on demand, inventory, and competitive dynamics (Fruchter & Tapiero, 2005). Together, personalized targeting and adaptive pricing interact synergistically, ensuring that promotions are both relevant to distinct consumer behaviors and optimally calibrated to market conditions.

Complementing these strategies, analyzing the optimal duration and spacing of promotions allows firms to identify the most effective promotional length and the appropriate recovery interval between consecutive offers. This temporal calibration helps moderate excessive demand shifts and cross-product interference. Such decisions are critical because demand often exhibits high volatility during promotional periods and seasonal peaks. Consequently, predictive modeling capable of anticipating these fluctuations is essential for maintaining product availability, guiding promotion design, and managing cross-channel cannibalization (Shak et al., 2024). Accurate forecasts during these periods improve marketing planning and promotional evaluation, thereby enhancing demand and inventory planning (Krishna et al., 2018).

Demand forecasting translates historical data and market intelligence into actionable insights, thereby supporting informed decision-making rather than relying on intuition (Mitra et al., 2022). This analytical foundation is essential for strategic planning, operational competitiveness, and ensuring consumer satisfaction through reliable product availability (Krishna et al., 2018; Mitra et al., 2022; Shak et al., 2024).

Among ML techniques for demand forecasting, Gradient Boosting models, especially XGBoost, have shown a strong ability to capture complex, non-linear interactions in retail demand data, often outperforming traditional statistical methods (Krishna et al., 2018). These models can identify intricate patterns, including demand volatility across products and channels during promotions. In addition to XGBoost, CatBoost and LightGBM also outperform at modeling complex, non-linear relationships. Their outputs provide insights into how promotions and pricing variables are associated with demand, helping characterize sales volatility and cannibalization dynamics (Mitra et al., 2022; Shak et al., 2024). Beyond these tree-based approaches, other advanced techniques are also applied in the field; Convolutional Neural Networks (CNNs) extract local temporal features, while hybrid models (such as ARIMA-ANN) leverage the complementary strengths of different methodologies (Mitra et al., 2022; Chen & Lu, 2017).

This proliferation of approaches has fostered extensive comparative studies evaluating ML techniques against each other and traditional benchmarks (Krishna et al., 2018). These applications span general retail chains (Mitra et al., 2022; Shak et al., 2024) and specific product categories such as computers (Chen & Lu, 2017), apparel (Cheriyan et al., 2018), and vegetables (Priyadarshi et al., 2019), as well as adjacent domains such as credit scoring (Brito Filho & Artes, 2018). These models integrate diverse predictive features associated with demand, including historical sales, promotional indicators, holidays, seasonality, pricing variables, store characteristics, and exogenous factors such as weather and fuel prices (Mitra et al., 2022; Shak et al., 2024). A recurring finding in the literature is that ensemble and deep learning models typically outperform simpler classical techniques, although the optimal model selection remains highly context-dependent.

Beyond forecasting, interpretable tree-ensemble models such as XGBoost can support cannibalization analysis by examining feature importance and interaction effects to reveal substitution patterns among products or channels (Mitra et al., 2022; Shak et al., 2024). Explainable ML techniques further enhance this capability by opening the black box of complex forecasting models and translating predictive outputs into managerial insights, thereby increasing trust and facilitating adoption in operational planning contexts (Arboleda-Florez & Castro-Zuluaga, 2023). A prominent example is SHAP (SHapley Additive exPlanations), a game-theoretic method that quantifies the marginal contribution of each input feature, such as price, promotional flags, and lagged sales, to an individual prediction. Recent studies show that SHAP-based explanations improve the transparency and managerial usability of gradient boosting models in retail forecasting, enabling decision-makers to interpret how promotions, inventory, and channel indicators jointly shape demand (Maione et al., 2023; Nabati et al., 2022). Although not designed to directly estimate a cannibalization factor, ML-generated baselines enable the comparison between predicted non-promotional demand and actual promotional sales. This difference helps characterize model-estimated promotional impacts and identify which product combinations or promotion types are most strongly associated with cannibalization, improving strategic decision-making (Krishna et al., 2018).

To complement these empirical models, retailers need to continuously monitor the key moderators of channel interaction, such as product attributes (Gong et al., 2022;Li, 2021), evolving consumer preferences, and segment heterogeneity (Kim & Chen, 2018; Lim et al., 2022), alongside shifting competitive dynamics (Van Crombrugge et al., 2024). Finally, evaluating how these factors are associated with consumer choices allows for the dynamic adjustment of mitigation strategies.

3. Data-driven approach

Retail environments are defined by intricate, non-linear interdependencies among demographics, channel usage, and promotional timing. Therefore, a data-driven approach is essential to decode these patterns, especially during high-volatility promotional cycles (Cavalcante et al., 2019). In this scenario, ML models are well-suited to reveal the subtle consumer preference shifts across channels that traditional analytical approaches often fail to detect.

Within this study, the data-driven approach aims to characterize how promotional strategies redistribute demand across channels in multichannel retailers and the model-estimated extent of their association with channel cannibalization. Sales data serves as an empirical foundation, capturing price variation, promotion periods, and seasonal behavior to support predictive modeling and interpretive analysis. The structure of the proposed approach is presented in Figure 1.

Figure 1
Proposed approach step-by-step.

A multichannel supermarket retailer in southern Brazil, which operates both physical stores and an e-commerce platform, was selected for model validation using empirical data. The dataset comprises 77 weeks of observations (Jan 2024 – Jun 2025), tracking the weekly sales of a single representative product across both channels. Key recorded features – including promotion periods, channel designation, and weekly inventory levels – enable a granular examination of product performance and channel-specific demand interactions.

Specific methodological boundaries were established to ensure analytical clarity and operational feasibility. The scope was intentionally limited to a single product and retailer to enable a detailed investigation of the underlying mechanisms governing sales and cannibalization dynamics. Price, promotion, and seasonality were incorporated as the primary predictive variables, with promotional effects represented through binary or categorical features rather than granular promotional mechanics. These decisions reflect the available data scope and the strategic intent of developing a manageable and reproducible modeling framework.

Exploratory Data Analysis (EDA) was conducted to uncover foundational patterns and inform subsequent modeling. Sales trends, seasonality, and volatility across channels were examined through time-series decomposition, with particular attention to promotional periods, which were compared against established baselines to identify potential associations with demand displacement. The temporal dependence of weekly sales within each channel was also assessed using autocorrelation functions to characterize persistence and cyclicality. This step confirmed the dataset’s suitability for capturing multichannel dynamics and informed the feature engineering process, such as the inclusion of lagged variables and promotional interaction terms, which are essential for modeling cross-channel interactions.

In the predictive modeling step, models were trained independently for both physical and online channels. Gradient boosting techniques were adopted, as they integrate spatiotemporal signals, making them suitable for environments where geography and dynamic promotions shape demand patterns (De Giovanni & Ramani, 2017). Specifically, XGBoost was employed as the primary model due to its capability to capture complex, non-linear relationships within retail data (Mitra et al., 2022). Its performance was benchmarked against alternative algorithms, including CatBoost, LightGBM, ElasticNet, Bayesian Ridge, and Multilayer Perceptron (MLP). To ensure robustness and prevent overfitting, hyperparameters were tuned using a grid search methodology with 5-fold time-series cross-validation, alongside depth constraints, regularization terms, and early stopping.

The physical and online sales models underwent performance evaluation using a temporal holdout set and rolling-origin time-series cross-validation to ensure predictive robustness across multiple out-of-sample periods. A suite of regression metrics was employed for a comprehensive assessment. Root Mean Squared Error (RMSE) was utilized to quantify the average magnitude of prediction errors. The R-squared (R²) score was used to measure the proportion of sales variance explained by the model, indicating its overall fit to complex retail data (Krishna et al., 2018; Shak et al., 2024). Additionally, predictions generated under active promotion conditions were directly compared with observed sales to determine baseline model error. This step was essential to ensure that differences observed in the counterfactual analysis reflect demand reallocation rather than prediction inaccuracy.

Feature importance analysis was employed to identify the key drivers of sales predictions and to examine potential cross-channel interactions. SHAP values were computed to quantify the marginal contribution of each feature to individual predictions, enabling assessment of how price and promotional features influenced demand within and across channels.

Beyond this attribution analysis, the validated model was used to quantify cross-channel cannibalization directly. For each promotional period, baseline demand was predicted as if the competing channel ran no promotion, and the gap between this baseline and the observed sales was taken as the estimated cannibalization effect, following the three-step procedure detailed in Table 3.

Table 3
Demand forecasting approach to measure sales cannibalization.

Step	Description
1. Baseline scenario prediction	For each week a promotion was active in Channel A (e.g., online), the model for Channel B (e.g., physical stores) was used to predict sales in Channel B as if the promotion in Channel A was not active (i.e., setting the promotional flag for Channel A to 0). This provided a baseline sales forecast for Channel B in the absence of Channel A’s promotion.
2. Actual/promotional scenario prediction	The actual sales data for Channel B during the promotion in Channel A was recorded. Alternatively, the model for Channel B could predict sales with Channel A’s promotion active (which should be close to actual if the model is good).
3. Cannibalization measuring	The difference between the baseline predicted sales (no cross-promotion) and the actual sales (with cross-promotion) in Channel B represented the estimated impact of Channel A’s promotion on Channel B’s sales.
	Cannibalization Amount (Units) = Baseline Predicted Sales_ChannelB - Actual Sales_ChannelB (during Channel A’s promotion);
	Cannibalization Factora (%) = (Cannibalization Amount / Baseline Predicted Sales_ChannelB) * 100.
	aThe cannibalization factor estimated the percentage change in sales in one channel attributable to a promotion in the competing channel operated by the same retailer. This analysis was conducted reciprocally for promotions in physical stores affecting online sales, and vice-versa.

Following the estimation of the baseline effect, mitigation strategies were defined. Each strategy was grounded in retail theory and designed to alter promotional variables or create new consumer incentives to moderate channel conflict. These strategies were simulated using the XGBoost algorithm through the modification of relevant input features in the dataset, which generated new sales predictions for both channels under each scenario.

This counterfactual simulation assumes that the demand relationships captured during training remain locally stable when promotional indicators are modified, which is a standard assumption in short-term, data-driven scenario analysis. Specifically, treating promotional indicators as independently controllable levers assumes that behavioral responses are additive and that the underlying patterns observed in the training data are robust for localized perturbations. While consistent with standard practice in short-term promotional planning models (Shak et al., 2024; Krishna et al., 2018), this assumption does not account for complex feedback loops or strategic consumer behaviors, such as anticipatory purchasing, loyalty program learning, or heterogeneous responses across consumer segments. Consequently, simulation outputs should be interpreted as directional estimates of expected demand redistribution rather than as precise forecasts.

Finally, the proposed mitigation strategies were evaluated and compared. The primary evaluation metrics comprised the predicted change in total sales volume and the model-estimated change in the cannibalization factor, defined as the percentage shift in demand reallocation, relative to the baseline scenario. This dual-metric comparison enabled a holistic assessment of each strategy’s effectiveness in simultaneously stimulating demand and moderating channel conflict.

Given the deliberately narrow scope adopted in this study, analyses were restricted to internal data, excluding multi-product or cross-brand interactions and exogenous variables such as competitor promotions, which were not available in the historical dataset. Furthermore, the study does not provide a broad comparison of forecasting algorithms, prioritizing instead the development of an interpretable framework tailored for small and medium-sized retailers. Because the research design relies on observational data, without randomized conditions or instrumental variables to control for potential confounders, the estimated cannibalization effects should be interpreted as conditional, correlational associations rather than causal relationships (Timoumi et al., 2022). The directions of demand redistribution identified in this study are consistent with established theoretical frameworks and contextual evidence, but definitive causal claims would require randomized or quasi-experimental designs that were not feasible in this setting.

4. Modeling and simulation

The data-driven approach for modeling sales performance and simulating strategic mitigation interventions was structured in a multi-stage framework. Fisrt, EDA was conducted to uncover underlying patterns and dependencies within the sales data. Subsequently, ML models were developed and validated to identify the most robust predictive tool. This model was then leveraged to quantify demand associations – specifically cannibalization – between physical and online channels. Finally, mitigation strategies were designed, simulated, and compared to identify the most suitable approach for maximizing total sales volume while moderating channel conflict.

4.1. Exploratory data analysis

Understanding consumer responses to pricing, seasonality, and promotional intensity across channels is critical for developing robust ML models and mitigation strategies. To this end, the underlying characteristics of the sales time series data were explored. Figure 2 shows the decomposition of sales data into trend and seasonal components for both channels, which serves to reveal structural patterns that may affect forecasting accuracy and the optimal timing of promotional campaigns.

Figure 2
Trend and seasonality decomposition by channel.

The trend component exhibits a U-shaped pattern in physical channel sales, characterized by mid-period declines followed by an end-period recovery. Such fluctuations may be associated with inherent retail cycles, macroeconomic factors, or year-end campaigns. Conversely, the online trend component, while irregular, remains predominantly ascending, potentially reflecting ongoing digital adoption and intensified strategic investment. The seasonal component reveals regular waves in physical sales, likely linked to predictable consumer behaviors such as monthly pay cycles or recurring in-store events. In contrast, online sales exhibit sharp peaks amid flatter troughs, suggesting intermittent spikes driven by short-term digital campaigns. This divergence in temporal dynamics highlights distinct channel rhythms –campaign-driven demand in online channel versus stable, periodic patterns in the physical channel – requiring coordinated promotion scheduling to mitigate the risk of temporal overlaps that may dilute promotional impact.

The temporal dependence of weekly sales was further examined using autocorrelation functions (ACFs). For physical sales, the ACF reveals a strong positive correlation at short lags (e.g., ~0.6 at lag 1), which declines and becomes negative around a monthly cycle (reaching -0.3 near lag 40), indicating a pattern of mean reversion. In contrast, online sales exhibit even stronger short-term persistence (~0.7 at lag 1) combined with a more pronounced negative trough (to -0.4 at lag 40), potentially reflecting sharper post-promotion demand contractions. These results confirm that sales in both channels exhibit significant temporal dependence on their own past values, which is a common retail phenomenon frequently associated with consumer habits and campaign carryover effects, thereby validating the inclusion of lagged variables in the predictive models. Furthermore, the distinct cyclicality of each channel is characterized by smoother, more predictable oscillations in physical sales, whereas online sales are marked by stronger immediate persistence followed by sharper corrections. This evidence further supports the independent modeling of each channel due to their different underlying dynamics.

The temporal dynamics of total sales across both retail channels reveal initial volumes of approximately 1,300 units (comprising approximately 400 units in the physical and 900 units in the online channel), followed by a progressive decline in both channels. Thereafter, demand exhibits fluctuations at intermediate levels. In the final weeks, total sales peak again at approximately 1,400 units, potentially reflecting the influence of seasonal year-end campaigns. Online promotions, observed at frequent intervals (i.e., weeks 5–10, 15–30, 35–60, 65–70), are concentrated during troughs and recovery periods, suggesting an alignment with strategic demand stimulation efforts. These patterns highlight the relevance of promotional timing, seasonality, and inter-channel synchronization for moderating demand displacement across channels.

An analysis of sales volumes from January 2024 to June 2025 revealed a distinct event-driven sensitivity. Clustered promotional events in September and November-December 2024, as well as campaigns around Mother’s Day and mid-year periods in May-June 2025, corresponded to prominent expansions in demand, coinciding with pronounced sales peaks observed particularly within the physical channel. Distinct inter-channel dynamics were also identified within the database; while the analyzed period commenced with a post-holiday normalization, especially in the online channel, high-density event intervals were characterized by a notable alignment between both platforms. Although physical sales exhibited greater response amplitude, both channels experienced concurrent lifts during major promotional clusters. This pattern suggests that well-structured, coordinated promotions are associated with an overall elevation in demand across the entire multichannel system, temporarily attenuating baseline channel disparities.

Overall, the timeline analysis indicates that event planning and its alignment with promotions are strongly associated with variations in sales volume within the empirical scope of this study, particularly when coordinated across physical and digital retail spaces, thereby facilitating the contextualization of demand fluctuations that might otherwise appear random in non-temporal analyses.

4.2. Modeling and evaluation

Predictive models were trained using the XGBoost, CatBoost, LightGBM, ElasticNet, Bayesian Ridge, and MLP algorithms, with the implementation details provided in Appendix A. Following training and validation, a performance comparison across channels and architectures was conducted to evaluate predictive accuracy and generalization capability using RMSE and R² metrics. Figure 3 illustrates this comparative assessment for both physical and online sales channels. The left panel presents the resulting R² scores, measuring the proportion of variance explained by each model, while the right panel displays the RMSE, quantifying the average magnitude of the prediction errors.

Figure 3
Comparative predictive performance of machine learning models by channel.

Among the evaluated architectures, XGBoost demonstrated the strongest performance for physical sales, yielding an R² of 0.92 and the lowest RMSE (33.6), signaling a robust capacity to capture complex store-level patterns. In contrast, the model’s explanatory power for online sales was limited (R² ≈ 0), though the algorithm still outperformed other tree-based models such as CatBoost and LightGBM. For the online channel, the MLP achieved the best error metric (RMSE of 25.8), suggesting that neural networks may be better suited to accommodate its noisier and more dynamic nature.

This performance disparity highlights a fundamental difference between channels: physical sales appear to be well-explained by internal operational levers such as price and promotions, whereas the online channel is heavily influenced by unobserved exogenous variables omitted from the dataset, including platform traffic metrics, digital advertising expenditures, delivery constraints, and competitive pricing dynamics. Although linear models (specifically ElasticNet and Bayesian Ridge) yielded high metrics, this likely indicates overfitting to a structured dataset rather than robust, generalizable predictive power.

Because these primary demand drivers remain unobserved, model-based cannibalization estimates associated with the online channel should be interpreted as partial effects conditional on observed variables, rather than as definitive causal estimates. While the direction of demand redistribution identified by the algorithms remains informative, the quantified magnitude of online channel displacement is subject to higher statistical uncertainty, thereby bounding the generalizability of subsequent managerial insights. As emphasized by Mitra et al. (2022) and Shak et al. (2024), the integration of expanded digital demand signals substantially enhances model explanatory power within e-commerce settings, representing a critical avenue for future model refinement.

Consequently, XGBoost is established as the most robust modeling option for forecasting physical sales, offering an ideal balance between predictive accuracy and structural interpretability. For online sales, the empirical findings underscore the requirement for a channel-specific analytical framework, potentially involving the incorporation of enriched feature sets or alternative model architectures such as MLPs to achieve comparable predictive reliability.

To evaluate model behavior within a temporal context, actual sales were compared against the predictions generated by the XGBoost algorithm. This alignment is illustrated in Figure 4 across both physical and online sales channels.

Figure 4
Weekly actual vs predicted sales (XGBoost).

For physical sales (left panel), the predicted line closely aligns with observed historical sales across the entire timeline. The precision with which the tracking is executed reflects the model’s capacity to capture nonlinear dependencies, as well as its ability to accommodate trend, seasonality, and exogenous impact such as promotions or holidays. Even during abrupt increases, including end-of-year sales surges or campaign periods, minimal phase lag is maintained, demonstrating robust responsiveness to dynamic shifts. This performance suggests that the XGBoost algorithm successfully mapped autoregressive dependencies, interactions between promotional features, and correlations with calendar-based variables. Such adaptability is essential for operational planning, especially in retail settings where unexpected demand peaks can considerably affect logistics and inventory decisions.

Conversely, online sales (right panel) reveal a divergence between predictions and observed sales. Particularly during volatile intervals, the algorithm exhibits underestimation and smoothing tendencies. This performance constraint is primarily attributed to the omission of digital-specific operational levers or an insufficient density of high-magnitude sales events within the historical dataset. Nevertheless, the XGBoost model maps the overall trajectory and baseline movement of online sales, indicating that the underlying predictive architecture retains functional capability for trend tracking.

To facilitate the identification of demand displacement signals, sales volume and promotional periods were analyzed across both channels. Figure 5 provides a temporal visualization of these dynamics, mapping observed sales trajectories against concurrent promotional activity for both the physical and online retail channels.

Figure 5
Temporal visualization of sales volume and promotional periods by channel.

Physical store sales exhibit a generalized downward trend during the initial weeks, followed by stabilization and slight recovery in subsequent periods. Notably, during intervals of online promotional activity, physical sales demonstrate a tendency to decline, suggesting that digital campaigns for the online channel may correspond to demand displacement from the physical store consumer base. Conversely, physical promotion events are consistently accompanied by visible spikes in physical sales volume, supporting the association between these events and the stimulation of physical demand.

The online sales curve exhibits distinct temporal dynamics often contrasting with the physical channel. During intervals of physical promotional activity, online sales were observed to stabilize or experience slight contractions. Conversely, online promotional periods are associated with pronounced peaks in online sales, which suggests a notable sensitivity within this channel to targeted digital interventions. Furthermore, the occurrence of simultaneous promotions across both channels does not consistently yield additive demand effects. In some instances, sales expansions in one channel occurred without a proportional increase in the other, which may indicate potential competition for the same consumer segment rather than mutually reinforcing growth.

From a strategic standpoint, this evidence underscores the importance of coordinated promotional planning to moderate potential demand displacement. While channel-specific promotions have the potential to stimulate demand, asynchronous campaigns may primarily result in sales redistribution across channels rather than the generation of incremental growth. Accordingly, the optimization of campaign timing, offer design, and targeting is identified as a critical consideration to ensure that promotional investments yield positive outcomes across both channels.

To enhance interpretability during promotional periods, SHAP-based feature attribution analysis was performed for weeks with active campaigns. Promotion indicators represented the largest predictive contribution, accounting for approximately 35-45% of demand variation, followed by price-related features (20-25%), lagged sales effects reflecting temporal persistence (15-20%), and seasonal or calendar variables (10-15%). This quantitative breakdown identifies promotional intensity as the primary driver of demand shifts during campaign weeks. From a managerial standpoint, the dominant contribution of promotion indicators implies that the scheduling and coordination of campaigns should take precedence over price adjustment as a cannibalization-control lever. Furthermore, the price feature contribution indicates that cross-channel price alignment, rather than identical discounts, can be employed to further moderate demand redistribution (Li, 2021).

Quantifying cannibalization further clarifies trade-offs in multichannel strategies. Empirical findings indicate that physical-store promotions correspond to an estimated 11.23% reduction in online sales, while online campaigns correspond to a larger displacement in physical sales (19.34%), a dynamic potentially driven by the relative convenience of digital purchasing channels. It must be noted that these magnitudes are specific to the specific product and retailer analyzed and, consequently, should not be generalized beyond this empirical setting without further validation. From a managerial perspective, these model-based estimates serve as a foundational baseline to simulate net campaign effects, anticipate demand redistribution patterns, and inform the design of coordinated promotions intended to mitigate revenue displacement and improve resource allocation.

4.3. Mitigation strategies

In view of the observed displacement demand between physical and online channels, mitigation strategies were evaluated with the objective of fostering positive synergy, which occurs when one channel enhances the performance of another (Fornari et al., 2016; Neslin et al., 2006).

The mitigation strategies were evaluated through the adjustment of input variables in the validated XGBoost model to facilitate counterfactual simulations of each scenario. These interventions are designed to mitigate the negative consequences of demand migration while preserving or increasing total revenue across both channels. Consequently, four quantified mitigation strategies are presented in Table 4, encompassing their respective objectives, implementation protocols, and their alignment with the key drivers of channel synergy outlined in Table 1. The two scenario parameters – a 10% seasonality uplift (strategy iii) and a 5% cross-channel price reduction (strategy iv) – were set from conservative benchmarks in the retail promotional literature (Ailawadi & Gupta, 2014; Li, 2021) and constrained to the dataset’s observed variation range; results may vary under alternative assumptions.

Table 4
Proposed mitigation strategies and their associated channel-synergy drivers.

Mitigation strategy	Objective	Implementation	Associated key drivers of channel synergy
(i) Coordinated promotions	Align promotions across channels to minimize attractiveness gaps driving consumer migration, maintaining competitiveness without substitution.	Run simultaneous promotions in both channels with differentiated discounts based on price sensitivities. Trigger parallel promotions and optimize discounts using historical elasticity data. Reflect in model by activating indicators with adjusted parameters.	Complementary channel capabilities and value transfer;
			Enhanced pricing power.
(ii) Staggered promotions	Use temporal separation to prevent simultaneous substitution, allowing independent promotional benefits per channel.	Schedule promotions at least two weeks apart, shifting online calendar after physical ones. In model, adjust promotion flags for temporal offset to influence decisions sequentially.	Market expansion;
			Complementary channel capabilities and value transfer.
(iii) Coordinated promotions with loyalty bonus	Synchronize promotions and add loyalty incentives to reward multi-channel engagement, turning substitution into complementary behavior.	During active promotions in both channels, increase the seasonality factor by 10% to simulate loyalty uplift, based on benchmark data.	Channels information search;
			Complementary channel capabilities and value transfer;
			Strengthened brand presence and recognition.
(iv) Cross-channel promotion incentives	Offer small discounts in one channel during promotions in the other to encourage cross-purchasing instead of full shifts.	When a promotion is active in one channel, reduce the price in the other by 5% and incorporate it into the demand model to assess the effect on sales.	Channels information search; Market expansion; Complementary channel capabilities and value transfer.

This controlled, data-driven simulation framework enables the identification of measures that shift promotional dynamics from a zero-sum logic toward a synergistic system. Within this configuration, net outcomes balance demand expansion against cannibalization (Shriver & Bollinger, 2022) and may ultimately support total revenue growth. After simulation, predicted sales outcomes were assessed against the baseline scenario to quantify each strategy’s impact. The comparative results are presented in Table 5.

Table 5
Simulated cannibalization reduction relative to baseline scenario by mitigation strategy.

Strategy	Physical channel cannibalization (%)	Online channel cannibalization (%)	Physical channel reduction (%)	Online channel reduction (%)
(i)	0.31	-10.75	10.92	30.04
(ii)	6.62	7.7	4.61	11.64
(iii)	7.11	1.99	4.12	17.35
(iv)	6.64	7.71	4.59	11.63

Coordinated promotions (Strategy i) demonstrated substantial potential for mitigating the cannibalization effect, particularly in scenarios where online promotions coincide with contractions in physical store sales. This simulation indicates a reduction in cannibalization by 30.04% from a baseline of 19.34%. These results suggest that incentive alignment across channels, by minimizing price disparity, represents an effective mechanism for protecting the physical channel, shifting the online-channel effect toward synergy (-10.75%). Furthermore, the strategy coincided with an increase in total sales of +1.8%. Consequently, these findings imply that synergy, rather than conflict, may be achieved through coordinated promotional planning, moving towards a more integrated retail strategy (Neslin, 2022).

The coordinated strategies (i and iii) consistently reduced demand displacement in both directions, indicating that differentiating the promotional offer serves as a mechanism to minimize direct channel substitution. Their impact on total sales, however, differed. While the standard coordinated strategy (i) was associated with a sales increase of +1.8%, the strategy incorporating a loyalty bonus (iii) yielded the highest overall uplift among the tested scenarios, at +3.5% in total demand. These results indicate that combining coordinated promotions with integrated loyalty rewards represents an effective approach for simultaneously mitigating displacement and facilitating revenue expansion.

Conversely, the staggered promotions (Strategy ii) demonstrated reduced mitigation performance compared to the coordinated approach. Although it reduced online demand displacement by 11.64%, it was the only strategy to cause a decline in total sales (-0.5%). This finding implies that the desynchronization of promotional intervals may correlate with a suppression of overall demand, potentially arising from consumer confusion, delayed purchase decisions, or a failure to capitalize on campaign momentum. Therefore, rather than optimizing demand across channels, this configuration did not support overall revenue growth in the simulated scenario, limiting its utility for promotional strategy.

Cross-channel promotion incentives (Strategy iv) produced outcomes comparable to the staggered promotions (Strategy ii) regarding mitigation efficiency. It reduced physical channel displacement by 4.59% and online displacement by 11.63%. While these reductions suggest a partial dampening of channel conflict (lowering the online displacement rate to 7.71%), the impact magnitude remained below that of Strategy i and comparable to Strategy ii. The similarity to Strategy ii suggests that this configuration functions predominantly as a stabilizing measure rather than a primary driver of cross-channel synergy.

Although all strategies reduced cannibalization relative to the baseline scenario, they resulted in different outcomes regarding total sales. The loyalty bonus policy (Strategy iii) demonstrated the highest effectiveness within the simulated scenario. It generated the highest total incremental demand growth of all tested strategies (+3.5%) while still substantially reducing online cannibalization (a 17.35% reduction); the single largest cannibalization reduction, however, was obtained by coordinated promotions (Strategy i), at 30.04%. This dual outcome suggests that the strategy not only moderates displacement but also stimulates additional purchases, potentially by increasing consumer engagement and the perceived value associated with the loyalty incentive. These results align with Relationship Marketing theory (Ailawadi & Gupta, 2014), which posits that rewarding existing behaviors strengthens consumer retention and enhances long-term value.

Finally, the comparison reveals that the most effective strategies are those that embrace channel integration and enhance consumer value, thereby creating net positive growth effects. Strategies focused exclusively on operational separation are associated with potential risks regarding overall revenue performance. Therefore, for the regional multichannel grocery retailer examined in this use case, the implementation of a loyalty bonus program integrated with coordinated promotional activities is indicated as a viable approach to moderate demand displacement and support sustainable growth.

5. Discussion

The empirical investigation elucidates the magnitude of channel cannibalization in a regional multichannel retailer and the extent to which coordinated promotional design can attenuate it. The validated XGBoost model yielded model-based cannibalization associations of 11.23% (physical-to-online) and 19.34% (online-to-physical), suggesting that fragmented, channel-specific promotions redistribute existing demand rather than expand total market volume. Among the simulated strategies, coordinated promotions reduced the baseline displacement by 30.04% alongside a modest total sales increase. Incorporating a loyalty bonus produced the highest overall demand uplift (+3.5%) while mitigating cross-channel friction, whereas staggered promotions, by contrast, were the only configuration to suppress total sales. This echoes the literature on promotional timing, which holds that the spacing and duration of offers should be calibrated to safeguard baseline demand (Shak et al., 2024; Krishna et al., 2018). As these outcomes are derived from counterfactual simulations calibrated with conservative, literature-based parameters, these magnitudes warrant cautious interpretation and remain conditional upon the underlying modeling assumptions.

The overall pattern suggests that channel conflict stems less from the coexistence of multiple channels than from their uncoordinated promotional management. Consequently, transitioning toward an integrated, value-driven approach is identified as central to converting inter-channel rivalry into synergistic growth. This perspective aligns with documented synergy mechanisms, whereby a single channel can potentially enhance rather than erode another’s performance (Neslin et al., 2006; Fornari et al., 2016). Furthermore, the simulated loyalty-bonus scenario operationalizes complementary-capabilities and value-transfer drivers. Rewarding multichannel engagement may reframe consumer behavior from channel substitution toward complementary channel use, which is consistent with the simulated reduction in displacement and the resulting demand expansion (Shriver & Bollinger, 2022; Timoumi et al., 2022).

From a managerial standpoint, the empirical findings support a shift toward channel-aligned promotional strategies. Operationally, the framework serves as a structured decision-support routine. Channel-specific models are trained on historical sales, pricing, and promotion data; SHAP attribution identifies the features driving each channel; and counterfactual simulations toggle promotional levers – such as synchronizing discounts or incorporating loyalty bonus – to evaluate performance against the baseline across total sales and estimated demand displacement metrics simultaneously (Mitra et al., 2022). This pre-deployment screening enables the prioritization of campaigns that expand demand without accelerating channel displacement.

The simulation outcomes indicate that minimizing cross-channel price disparities protect total sales volume more effectively than staggered promotional timing, which may suppress aggregate demand. However, these predictive outputs warrant cautious interpretation. The counterfactual simulations assume locally stable, additive demand responses and omit behavioral dynamics, such as anticipatory purchasing, loyalty-program learning, or heterogeneous responses across consumer segments. Consequently, projected gains may fade as consumer segments adapt over time. Furthermore, model assertiveness hinges on data quality, given that fragmented or low-granularity digital metrics can introduce predictive bias, while overcoming organizational silos is identified as a prerequisite for implementation (Neslin et al., 2006). Accordingly, these analytical outputs are best utilized as directional guidance to be validated through controlled field pilots, while continuously monitoring contextual moderators including product attributes, consumer preferences, and competitive dynamics (Gong et al., 2022; Kim & Chen, 2018; Van Crombrugge et al., 2024).

For an academic perspective, empirical evidence of channel cannibalization is provided within an underexplored regional context. Moreover, the utility of XGBoost algorithm is demonstrated as a simulation tool to evaluate theoretical propositions on channel synergy. These associations support the channel-attributes perspective, which posits that minimizing cross-channel price and assortment overlaps fosters complementarity over channel substitution (Cao & Li, 2015; Herhausen et al., 2015; Neslin, 2022). Methodologically, the integration of SHAP-based feature attribution aligns this framework with the stream of explainable ML, increasing transparency in retail forecasting architectures (Arboleda-Florez & Castro-Zuluaga, 2023; Maione et al., 2023). By transitioning from descriptive analysis to a predictive and interpretable approach, a replicable methodological template is offered for complex multichannel retail dynamics.

6. Conclusion

This study set out to develop a data-driven framework that uses predictive ML models to evaluate how promotional strategies redistribute demand across retail channels, to quantify the resulting displacement, and to simulate strategies for converting channel conflict into synergy. The application of this approach to a multichannel supermarket context located in southern Brazil yielded two main outcomes. First, coordinated promotions were associated with a 30.04% reduction in the baseline cannibalization effect alongside a modest total sales increase. Second, the integration of a loyalty bonus corresponded to the highest overall demand uplift (+3.5%) while concurrently mitigating cross-channel friction.

While these empirical estimates are specific to the analyzed product and retailer, the underlying methodological framework remains replicable. The core logic combines interpretable demand prediction with scenario-based simulation, remaining independent of the specific product category, retailer size, or market structure examined. Therefore, the approach can be transferred to alternative retail formats and extended to multi-product and multi-region settings. Such expansions can be executed through cross-product displacement matrices or hierarchical modeling frameworks that account for store-level heterogeneity, establishing a robust foundation for strategic promotional planning across multichannel environments.

Despite these contributions, this study has limitations that open avenues for future investigations. The analysis is constrained to a single product and a single regional retailer, limiting the generalizability of the reported rates. Additionally, while the one-year dataset captures seasonality, long-term macroeconomic trends are excluded. The online-demand model’s lower explanatory power also reflects the absence of digital-side drivers such as website traffic, online advertising, delivery conditions, and competitor activity. Assessing cannibalization solely through sales volume excludes profitability variations. Furthermore, structural stability in consumer behavior is assumed, omitting potential long-term adaptations such as promotional cycle learning or channel preference shifts. Finally, given the observational nature of the dataset, all estimates remain associative rather than strictly causal.

Consequently, future research should therefore replicate the framework across diverse retail environments and multi-product settings to establish universal benchmarks. Additional research avenues include integrating exogenous variables to improve model robustness, incorporating margin-based outcomes, and performing parameter-based sensitivity analyses to confirm the stability and direction of strategy rankings. Finally, developing dynamic feedback loops to capture behavioral adaptations over time and adopting experimental or quasi-experimental designs can facilitate a transition toward causal inference regarding consumer responses to promotional strategies.

Appendix A Algorithm implementation details.

import pandas as pd

import numpy as np

import matplotlib.pyplot as plt

import seaborn as sns

from sklearn.model_selection import train_test_split

from sklearn.metrics import mean_absolute_error, mean_squared_error, r2_score

import xgboost as xgb

from catboost import CatBoostRegressor

from lightgbm import LGBMRegressor

from sklearn.neural_network import MLPRegressor

from sklearn.linear_model import BayesianRidge, ElasticNet

from statsmodels.tsa.seasonal import seasonal_decompose

from mpl_toolkits.mplot3d import Axes3D

from pandas.plotting import autocorrelation_plot

import networkx as nx

from scipy import stats

import matplotlib.dates as mdates

from datetime import datetime

import warnings

warnings.filterwarnings('ignore')

df = pd.read_csv('dados_varejo.csv')

df['Cannibal_Effect'] = np.where(

(df['Promo_Phys'] == 1) & (df['Promo_Online'] == 0),

df['Online_Sales'] * 0.9,

np.where(

(df['Promo_Online'] == 1) & (df['Promo_Phys'] == 0),

df['Physical_Sales'] * 0.88,

0

)

)

df['Evento_Especial'] = df['Evento_Especial'].apply(lambda x: 1 if str(x).strip() != '' else 0)

X = df[['Promo_Phys', 'Promo_Online', 'Seasonality', 'Evento_Especial',

'Preco_Fisico', 'Preco_Online', 'Estoque_Fisico', 'Estoque_Online']]

y_fisico = df['Physical_Sales']

y_online = df['Online_Sales']

X_train, X_test, y_fisico_train, y_fisico_test = train_test_split(

X, y_fisico, test_size=0.2, shuffle=False

)

X_train, X_test, y_online_train, y_online_test = train_test_split(

X, y_online, test_size=0.2, shuffle=False

)

def evaluate_model(y_true, y_pred, model_name, channel):

return {

'Modelo': model_name,

'Canal': channel,

'MAE': mean_absolute_error(y_true, y_pred),

'MSE': mean_squared_error(y_true, y_pred),

'RMSE': np.sqrt(mean_squared_error(y_true, y_pred)),

'R2': r2_score(y_true, y_pred)

}

results = []

xgb_fisico = xgb.XGBRegressor(n_estimators=100, learning_rate=0.1, random_state=42)

xgb_fisico.fit(X_train, y_fisico_train)

y_fisico_pred_xgb = xgb_fisico.predict(X_test)

results.append(evaluate_model(y_fisico_test, y_fisico_pred_xgb, 'XGBoost', 'Physical'))

xgb_online = xgb.XGBRegressor(n_estimators=1000, learning_rate=0.02, random_state=11)

xgb_online.fit(X_train, y_online_train)

y_online_pred_xgb = xgb_online.predict(X_test)

results.append(evaluate_model(y_online_test, y_online_pred_xgb, 'XGBoost', 'Online'))

cat_fisico = CatBoostRegressor(iterations=2000, learning_rate=0.009, verbose=0)

cat_fisico.fit(X_train, y_fisico_train)

results.append(evaluate_model(y_fisico_test, cat_fisico.predict(X_test), 'CatBoost', 'Physical'))

cat_online = CatBoostRegressor(iterations=1500, learning_rate=0.4, verbose=0)

cat_online.fit(X_train, y_online_train)

results.append(evaluate_model(y_online_test, cat_online.predict(X_test), 'CatBoost', 'Online'))

lgb_fisico = LGBMRegressor(n_estimators=50, max_depth=3, num_leaves=7, learning_rate=0.1)

lgb_fisico.fit(X_train, y_fisico_train)

results.append(evaluate_model(y_fisico_test, lgb_fisico.predict(X_test), 'LightGBM', 'Physical'))

lgb_online = LGBMRegressor(n_estimators=50, max_depth=3, num_leaves=7, learning_rate=0.1)

lgb_online.fit(X_train, y_online_train)

results.append(evaluate_model(y_online_test, lgb_online.predict(X_test), 'LightGBM', 'Online'))

en_fisico = ElasticNet(alpha=0.1, l1_ratio=0.5)

en_fisico.fit(X_train, y_fisico_train)

results.append(evaluate_model(y_fisico_test, en_fisico.predict(X_test), 'ElasticNet', 'Physical'))

en_online = ElasticNet(alpha=0.1, l1_ratio=0.5)

en_online.fit(X_train, y_online_train)

results.append(evaluate_model(y_online_test, en_online.predict(X_test), 'ElasticNet', 'Online'))

br_fisico = BayesianRidge()

br_fisico.fit(X_train, y_fisico_train)

results.append(evaluate_model(y_fisico_test, br_fisico.predict(X_test), 'Bayesian Ridge', 'Physical'))

br_online = BayesianRidge()

br_online.fit(X_train, y_online_train)

results.append(evaluate_model(y_online_test, br_online.predict(X_test), 'Bayesian Ridge', 'Online'))

mlp_fisico = MLPRegressor(hidden_layer_sizes=(50,50), max_iter=1000)

mlp_fisico.fit(X_train, y_fisico_train)

results.append(evaluate_model(y_fisico_test, mlp_fisico.predict(X_test), 'MLP', 'Physical'))

mlp_online = MLPRegressor(hidden_layer_sizes=(50,50), max_iter=1000)

mlp_online.fit(X_train, y_online_train)

results.append(evaluate_model(y_online_test, mlp_online.predict(X_test), 'MLP', 'Online'))

results_df = pd.DataFrame(results)

print(results_df)

Data availability

Research data is only available upon request.

• How to cite this article:
  Rosa, L. G. C., Oliveira, B. R., & Frazzon, E. M. (2026). Promotional strategies and channel cannibalization in multichannel retail. Production, 36, e20250127. DOI: https://doi.org/10.14488/1980-5411.20250127
• Financial Support
  This research was funded by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq). The CNPq was not involved in the collection, analysis, or interpretation of the data, or the writing of the manuscript.
• Ethical Statement
  The authors declare that this research does not require ethical approval.

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Edited by

• Editor(s):
  Adriana Leiras
  Rodrigo Caiado

Publication Dates

• Publication in this collection
  18 Sept 2026
• Date of issue
  2026

History

• Received
  19 Dec 2025
• Accepted
  19 Aug 2026