Introducing a predictive-oriented multi-stakeholder recommender system model.

Introducing a predictive-oriented multi-stakeholder recommender system model - PMC Skip to main content An official website of the United States government Here's how you know Here's how you know Search Log in Primary site navigation Search Log in Search PMC Full-Text Archive Search in PMC Journal List User Guide As a library, NLM provides access to scientific literature. Inclusion in an NLM database does not imply endorsement of, or agreement with, the contents by NLM or the National Institutes of Health. Learn more: PMC Disclaimer | PMC Copyright Notice Sci Rep . 2026 Apr 13;16:17097. doi: 10.1038/s41598-026-37793-4 Introducing a predictive-oriented multi-stakeholder recommender system model Reza Davoudabadi 1 , Ahmad Makui 1, ✉ , Mohammad R Rasouli 1 Author information Article notes Copyright and License information 1 School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran ✉ Corresponding author. Received 2025 Oct 15; Accepted 2026 Jan 27; Collection date 2026. © The Author(s) 2026 Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ . PMC Copyright notice PMCID: PMC13230954  PMID: 41974732 Abstract Most conventional recommender systems (RSs) rely on past user behavior to predict future preferences. They fail to account for changing user expectations and variable organizational performance. To overcome this limitation, this study proposes a predictive-oriented, multi-stakeholder recommender system (RS). It measured two indices: how flexible users were, based on past interactions, and how flexible organizations were, based on the gap between what they had and what they needed. A weight adjustment function balances user and organizational influence based on these indices. The function ensures that neither stakeholder is ignored; it adjusts the weights so that higher user flexibility increases organizational preference weights, and higher organizational flexibility increases user weights. To model adaptive user expectations, the proposed RS model integrates principles from Prospect Theory and the Peak-End Rule, constructing a dynamic reference point based on the user’s peak and most recent experiences. The proposed RS model was evaluated through a simulation of 100 user profiles interacting with 30 characterized products. The results showed a 17.6% improvement in balanced resource utilization compared to a user-centric strategy. The study introduces a new paradigm for RSs that aligns long-term sustainability with user satisfaction. Keywords: Recommender systems, Organizational flexibility, Multi-stakeholder, Predictive-oriented approach Subject terms: Business and management, Business and management, Information systems and information technology, Mathematics and computing Introduction Over the past decade, the adoption of recommender systems (RSs) has increased significantly. These systems facilitate the decision-making process for users by assisting them and reducing their information overload. Despite extensive research across various domains, these systems still require further development. The focus of RSs research to date has been on end-users and consumers. These systems have attempted to recommend items that would yield the highest user satisfaction by predicting users’ ratings for unrated items. Beyond the accuracy of predictions, it is essential to consider other stakeholders. Sole focus on one stakeholder can exacerbate risks such as biased recommendations and reduced system transparency, and also deviate from fairness. Focusing on a single stakeholder while neglecting other key stakeholders can adversely affect and erode long-term customer satisfaction by undermining the ability to fulfill customer needs. Moreover, algorithms that operate based on predicting user ratings for items are retrospective and rely solely on historical data. This is clearly a major weakness, as consumers continually adapt their preferences based on new information and experiences. In addition, these algorithms, at best, can model the past and fail to understand users’ future needs. Thus, these algorithms essentially predict past events, performing what can be described as “ Post-Dict ” rather than forecasting future ratings. More specifically, they accurately estimate the rating a user has given to an item historically, but this does not necessarily imply that they can reliably predict the rating that will be assigned in the future. Consequently, RSs should extend beyond predictions derived solely from historical data. By inferring patterns in user behavior, RSs can customize recommendations in accordance with identified behavioral trajectories. In contrast, the proposed RS model extends beyond simple analysis of historical data, which is reflected in the user profile. Instead of solely relying on historical data to generate recommendations, the system also considers potential future consequences and outcomes by analyzing past data alongside the current organizational context. This integration allows the recommender system (RS) to incorporate not only past preferences but also the anticipated impacts of recommendations, thereby enabling more informed and context-aware suggestions. Moreover, within the proposed framework, organizational constraints and expectations are explicitly modeled, acknowledging that organizations are key stakeholders in the recommendation process. The organizational preferences and flexibility are factored into the recommendation process: when an item significantly deviates from organizational expectations and the organization has limited flexibility to respond, the importance of organizational utility in the final recommendation increases. Conversely, if an item diverges markedly from organizational expectations but the organization exhibits high flexibility, indicating that accommodating user demands would not harm organizational interests, then the user’s utility is given greater weight in the final recommendation. This approach ensures a balanced and transparent consideration of both organizational and user interests. Based on this framework, the proposed RS model evaluates and offers recommendations by assessing four key factors: User priorities and expectations, Organizational priorities and expectations, The RS’s predicted flexibility of the user, The RS’s predicted organizational flexibility. These components collectively enable the RS to deliver recommendations that are both personalized and aligned with organizational constraints and goals. Having established the theoretical framework, the remainder of this paper is organized as follows: Sect. 2 reviews relevant literature, Sect. 3 describes preliminaries Sect. 4 describes the methodology. Section 5 presents the computational complexity analysis, Sect. 6 presents simulation experiments for method validation, while Sect. 7 provides the comparative performance analysis. finally, Sect. 8 provides a conclusion. Related work This section examines the existing literature with a dual focus on multistakeholder Recommendations and supply chain constraints—the two domains most relevant to the methodology proposed in this study. Multistakeholder recommendations Academic research on RSs has predominantly focused on the user-centric approach, emphasizing the end-user (customer) experience and optimizing user satisfaction. While this approach has advanced personalized recommendations, it tends to limit the systematic exploration of other relevant aspects such as fairness, balance, and profitability, often overlooking the concerns and priorities of additional stakeholders 1 . Although considering the interests of multiple stakeholders has long been part of RS studies, the explicit identification and investigation of multistakeholder recommendations—with practical implications across various application domains—has only recently emerged as a distinct research area 2 . According to 2 , stakeholders encompass any groups or individuals who can impact, or be impacted by, the delivery of recommendations to users. Therefore, RSs must be capable of recognizing and supporting the preferences of all key stakeholders 3 . proposed a multi-stakeholder RS that emphasizes fairness and personalized diversity. Rather than focusing solely on recommendation accuracy, their approach also takes into account the interests of both users and suppliers, aiming to achieve a balanced trade-off between these two stakeholder groups. The study 4 addressed multi-stakeholder RSs by proposing dedicated utility functions for four key stakeholders—users, producers, cast, and the system itself—moving beyond traditional single-stakeholder approaches. To balance conflicting stakeholder objectives, the authors employed evolutionary optimization (NSGA-II), enabling a trade-off recommendation solution that enhanced utility gains while maintaining personalization 5 . proposed a Cascade Hybrid Many-Objective Recommendation (CHMAOR) algorithm. Their work is distinguished by the introduction of a comprehensive Provider Visibility Model (PCRE), which moves beyond traditional provider coverage metrics. The PCRE model integrates three specific indicators: Provider Coverage (PC), User Reach Coverage (URC), and Provider Entropy (PE), offering a more holistic measure of provider exposure. Their methodological framework employs a hybrid recommendation list generated from four classic algorithms and optimizes it using a novel Multi-parent Probabilistic Heuristic Genetic Algorithm (MPPHX). This approach simultaneously balances four key objectives: recommendation accuracy, diversity, novelty, and the defined provider visibility. Experimental validation on real-world datasets indicated that their model successfully reconciled user and provider goals, notably enhancing visibility for long-tail providers while maintaining competitive user-centric performance 6 . introduced an independent producer–item interaction framework and leveraged deep neural networks to learn non-linear user-item features and to fuse consumer and producer preferences. The core innovations include: (1) a deep neural network–based model for aggregating cross-stakeholder preferences; (2) a multi-criteria rating mechanism that explicitly captures producer preferences over items; and (3) an end-to-end training scheme that produces a cumulative preference matrix by integrating consumer and producer signals. In the literature, three main stakeholder groups have been highlighted: consumers, providers (suppliers), and the system itself. Consumers, as the end-users, anticipate recommendations that align with their needs and preferences, while providers are responsible for supplying the recommended items. The system, representing the platform or organization, serves as the intermediary linking consumers to the items and is subject to requirements such as supply chain constraints, product lifecycle, profit margins, alignment with organizational strategy, and minimization of overhead costs. For providers, considerations include lead times, inventory status, and contractual terms related to product supply, whereas for consumers, factors such as product appeal, fit with personal taste, and purchase history are most significant. A critical challenge arises when RSs exhibit supplier bias, potentially undermining provider interests by reducing the visibility of their products in recommendation lists. This may lead to diminished provider engagement or even their withdrawal from the platform. Beyond consumers and providers, the system itself may pursue objectives distinct from those of the other two groups, such as maximizing profit margins or delivering recommendations tailored to specific pedagogical goals on educational platforms. The context of these platforms can vary widely, including online retailers, e-commerce websites, brokers, and other environments where recommendations are offered. Supply chain constraints Evidence from prior research suggests that recommending products without accounting for supply chain constraints can introduce additional costs or inefficiencies into the supply chain. Such inefficiencies may result in recommendations that are suboptimal in terms of fulfillment time or cost, affecting both customers and the extended supply chain. For example, recommending products with protracted preparation or shipping times can complicate supply chain operations 7 . proposed a framework that explicitly integrates delivery constraints into product recommendations, aiming to shift demand towards items that can be fulfilled using existing delivery networks, within an acceptable profit margin and minimal additional resources over a specific time window. Their approach seeks to adjust user preferences towards certain products by personalizing recommendations while considering delivery limitations. This conceptual framework does not represent an entirely new theory, but rather provides a novel linkage between RSs, supply chain management, and inventory control. Another study by 8 investigated the integration of supply chain restrictions with RSs in contexts where both product availability constraints and customer interaction strategies are crucial. The study, focused on an online grocery retailer, confronted challenges such as overstocked, high-margin items with low sales velocity, as well as products with limited availability. Instead of issuing blanket discounts, the objective was to identify target customers for “nudge” strategies designed to shift excess inventory. Candidate customers were selected using Support Vector Machine (SVM) methods, with a novel use of Type I error as a criterion for identifying target customers for nudges. In this context, customers associated with Type I errors—those who did not purchase a focal product potentially due to a lack of awareness about its availability—were viewed as promising targets for promotional interventions. This approach to utilizing Type I errors for nudge targeting is innovative and largely unexplored in previous research 9 . investigated how to improve apparel e-commerce recommendations by using unsupervised machine learning to enhance customer segmentation and supply chain management. Their approach began with dimensionality reduction via Principal Component Analysis (PCA), and then applied K-Means clustering to segment customers according to their purchasing behavior, emphasizing brand, product, and price-range relationships. The study also presented a SKU-based product segmentation model derived from sales volume and revenue, intended to help retailers optimize inventory and marketing strategies. The overarching goal was to support a sustainable, profitable, and scalable e-commerce business model that accounted for environmental, social, and economic dimensions 10 . introduced an interactive visual RS to advance decision-support in circular supply chain management (CSCM). They addressed the gap of transparent tools that impeded the identification of circular business opportunities by combining algorithmic filtering with interactive visualization in a hybrid framework. This design enhanced user control and decision transparency, moving beyond traditional black-box recommenders. The system enabled exploration of industrial-symbiosis opportunities via hierarchical visualizations aligned with standardized waste (EWC) and industry (NACE) taxonomies. The work demonstrated that visual-interactive RSs could promote more sustainable supply chains and facilitate the adoption of circular economy practices 11 . proposed a two-tier blockchain-based intelligent RS (BLC-IRS) to enhance supply chain resilience. It first develops an IRS to rapidly suggest internal and external resources during disruptions, and then decentralizes data sharing with blockchain to improve reliability and security of the recommendations. Methodological limitations in prior studies Recent studies in the field of RSs has increasingly focused on designing multi-stakeholder paradigms. These paradigms aim to satisfy end users’ preferences while also considering the requirements of other actors, such as suppliers, platforms, and supply chains. Additionally, they address broader objectives like fairness, sustainability, and resilience. This shift signals a gradual move from purely user-centric RSs toward multi-stakeholder RSs, whose aim is to deliver recommendations that balance the interests of all stakeholders. Nevertheless, existing research has largely exhibited a limited focus on specific stakeholder needs, with each study developing concrete balancing mechanisms tailored to those needs. Among the most prominent development strands in these studies, the following can be highlighted: Accounting for delivery and inventory constraints, Reducing operational costs, Achieving the organization’s strategic objectives, Equitably representing products belonging to different suppliers on a single platform, and. Enhancing system resilience in the face of disruptions. The present study proposes a holistic approach that captures an organization’s priorities as a key stakeholder, moving beyond the detailed modeling frameworks used in previous studies. Rather than predetermining a fixed and pre-specified set of modeling domains (such as inventory, margin, operating costs, or strategic objectives) that prior studies have focused on, this paper offers a framework enabling organizations to leverage it in accordance with their evolving needs and priorities across different time horizons. Preliminaries In real-world scenarios, when a RS interacts with diverse users, it inevitably encounters varying levels of user expectations. Each user’s expectations are shaped by their previous purchase experiences and past choices, resulting in substantial heterogeneity across the user base. Consequently, RSs must address a spectrum of expectation levels: a certain product selection may exceed one user’s expectations, while for another user, it may fall short. This raises the critical question of how users can be categorized according to their levels of expectation. Inspired by Prospect Theory—a psychological theory describing how people make decisions based on perceived gains and losses—this article presents a RS model that moves beyond traditional, rationality-based models toward a Behavioral RS. Unlike conventional models that focus on optimizing objective metrics (e.g., predictive accuracy) and assume users are rational agents with static preferences, our approach embraces the Prospect Theory premise that human evaluation is relative, reference-dependent, and subject to framing effects. Consequently, it dynamically adjusts recommendations based on each user’s evolving psychological state. Here, the Reference Point (RP) functions as the user’s mental frame—a benchmark continuously updated through experience, which redefines how a given recommendation is perceived as a “gain” or the “loss”. This RP is not static; rather, in accordance with the Peak-End Rule, it is intelligently constructed as a composite of the user’s most intense past experience (the Peak) and their most recent interaction (the End). The Peak-End Rule posits that the overall evaluation of an experience (such as purchasing a product) is shaped more by its peak emotional moment and its end than by the totality of the experience. Prior to presenting the methodology, the two foundational theoretical concepts —Prospect Theory and the Peak-End Rule—that underpin the proposed model are introduced in this section. Peak-end rule Human memory has an inherent limit in how much it can store and remember complete details from every experience, especially given the endless flow of information and stimuli we face. Over time, experiential memory tends to fade, shifting from feelings—episodic memory—to beliefs—semantic memory—as people summarize and interpret their experiences. Because recall is imperfect, individuals often use heuristics to summarize their experiences and form perceptions, which bridges the gap between episodic and semantic memory. However, this can create a mismatch between what was experienced and what is remembered, known as the memory-experience gap. A key heuristic explaining this is the peak-end rule (PER), which suggests that the overall judgment of an experience is disproportionately shaped by the most emotionally intense moment, like a sudden burst of joy or sadness, and the final moment, like the last note of a song, rather than by the entire duration or average of all moments during the experience. Peak emotional moments act as thresholds that influence how we interpret the experience, while the end point is often more memorable because of its recency or its role in marking completion, especially in goal-oriented activities 12 . This psychological mechanism illustrates how a negative ending, as emphasized by the PER, can disproportionately affect the overall perception of an experience. According to the PER, not all moments within an experience carry equal weight; rather, the most salient peak and the final moments play a crucial role in shaping our overall memory and judgment. In contrast, other intermediate moments and the overall duration tend to have negligible influence on the retrospective evaluation of an experience 13 . For each user ℎ, the utility function , which represents the overall subjective evaluation at time t , is defined as Eq. ( 1 ). 1 where: indicates the subjective assessment of user ℎ regarding the most intense moment (the peak) experienced up to time t. represents the subjective evaluation of the end moment of the experience. θ: is a weight parameter ranging between 0 and 1, reflecting the relative influence of the peak and the end on the user’s overall utility. In essence, when evaluating an experience, the user does not consider all moments equally but instead assigns greater importance to the most emotionally salient (peak) and concluding (end) moments. The overall assessment is thus a weighted combination of these two points, encapsulating the core principle of the PER. This concept aligns with findings from 14 , who integrated the PER from behavioral economics with the Decision-Based Evidence Theory. Traditionally, the PER suggests that individuals’ overall evaluations of an experience are primarily influenced by the most intense (peak) and the final moments. The authors extended this principle to consumer evaluation of similar products, such as different television shows, by introducing a similarity function to quantify the resemblance between two products. Specifically, they proposed to measure the similarity between the current product ​and the peak experience, as well as ​ to measure similarity with the end experience. These similarity functions assess how closely the current experience aligns with prior peak and end moments, influencing the consumer’s overall evaluation. As illustrated in Fig. 1 , for each individual, similarity between the current situation and the peak and end experiences is first estimated, and these measures are then incorporated into the overall decision-making and preference formulation. Fig. 1. Open in a new tab Method of 14 . This Fig. schematically demonstrates how the positions of the peak and end points influence the decision-making process of the support system. Prospect theory Prospect theory is a behavioral economic model that describes how individuals make decisions under conditions of uncertainty and risk. This theory posits that people evaluate potential outcomes relative to a reference point, rather than based on absolute values, and categorize these outcomes as either “gains” or “losses.” The perceived value of a change is thus determined by its distance from the reference point, not by its absolute magnitude. The value function in prospect theory is characterized by its nonlinearity and asymmetry: it is concave for gains, convex for losses, and losses are weighted more heavily than gains (typically by a factor of about 2). This structure accounts for the psychological sensitivity to relative changes, explaining why a monetary loss of a given amount generally evokes stronger negative feelings than the equivalent monetary gain elicits positive feelings; that is, losses have a greater psychological impact than comparable gains. Furthermore, prospect theory suggests that individuals tend to be risk-averse when dealing with gains but become risk-seeking when facing potential losses 15 , 16 . Proposed methodology Parameters and required data The proposed RS model begins with a predefined set of candidate items, denoted as, , where M=|X| represents the total number of available items. The set of users is represented by , while the set of user-centeric evaluation features, used to assess items, is represented by . The normalized user-centric feature matrix encodes the normalized evaluation scores assigned to each item i concerning criterion j . The normalized user-centric feature matrix is constructed based on assessments provided by organizational experts. Additionally, user preferences regarding the importance of item features constitute one of the primary inputs to the proposed method and are represented by the weight matrix , where represents the weight of criterion j from the perspective of user ℎ. The feature vector of the for user h is denoted by . Furthermore, denotes the subset of items that user ℎ has previously purchased or interacted with, based on historical data. Conversely, signifies the set of items that user ℎ has not yet engaged with or purchased. Recommendation model In the proposed RS model, computations are divided into two separate but concurrent sections: one performed on the organization’s side and the other executed on the user’s side. At the end of this process, the outputs from both sections are collected, and in the final aggregation step, optimal recommendations are provided to the user. All computational steps are conducted in real-time; that is, with each user login and purchase, all components of the algorithm are immediately activated, resulting in an appropriate response. This requirement arises from the fact that each new purchase can alter the “current state” of the organization, and such changes directly impact the results. User-Centric computational steps Step1. User History Monitoring and Peak–End Identification At this step, the behavioral history of each user is monitored at the time of the request (i.e., at time t ), and based on the PER, two key points are identified for each user h at this moment: Peak Point : The highest level of utility that the user has experienced up to time t . End Point : The utility of the user’s most recent choice, i.e., at time . Given the user-centric feature matrix and the weight matrix , we first calculate the experienced utility for each item within the historical interaction set of user h . In this study, we employ the Simple Additive Weighting (SAW) utility function. Consequently, the utility of purchasing product m by user h is expressed as . The peak point occurs when the user perceived the highest utility in the past. The Peak Point perceived utility is defined as the maximum perceived utility across all items purchased by the user up to the current moment t. Hence, the peak utility for user h up to time t is denoted by , where item g corresponds to the item that has provided the maximum utility for user h until time t . On the other hand, the End Point is precisely defined as the user’s most recent interaction with the organization. We are currently at time t , while denotes the time of the user’s most recent interaction. Furthermore, ​ denotes the utility derived from the user’s previous selection, experienced at time . This value is referred to as the end point utility, and the corresponding item is denoted as item e . Step2. User Reference Point Construction User preferences regarding the importance of item features constitute a primary input to the proposed method. In this step, we aim to establish the RP for each user. The RP is of particular significance because, during the decision-making process, the user evaluates different items against it. Items whose utility falls below that of the RP are categorized as “loss items,” whereas those with higher utility are classified as “gain items.” In other words, the RP—or the user’s current state—serves as an anchor, and the utility of other recommendations is assessed based on their distance from this anchor. The feature vector of the RP for user h at time t is denoted by and is computed based on Eq. ( 2 ). 2 where, quantifies the importance afforded to the peak point relative to the end point. Step 3. Computation of Relative Distances to the Reference Point In this step, for each item that user h has not yet selected, we compute its similarity to the RP based on the method of 17 using Eq. ( 3 ). 3 here, and denotes the cardinality of set and respectively. Subsequently, by applying the EXPTODIM method proposed by 10 , the adjusted distance between each item and the RP is determined according to the gain and loss domains. Specifically, denotes the distance of item from user h ’s RP at time t , and is computed as given in Eq. ( 4 ). 4 where, the parameter O serves as the threshold separating the domains of gain and loss; that is, if the similarity between ​ and the RP falls below this value, the user will assess the utility of the corresponding item as lower than that of the RP (or the current state). Conversely, if the similarity exceeds this threshold, the utility is perceived as higher. The parameter governs the user’s sensitivity to variations. Higher values of ρ correspond to users who are more responsive to changes. Lower values of ρ yield curves with gentler curvature, indicating reduced sensitivity to minor differences among options. Conversely, higher values of ρ produce sharply curved profiles, reflecting heightened user responsiveness to small disparities. Step 4. User Flexibility Computation In this step, user flexibility functions as a leading indicator, acting as a primary measure that can significantly enhance the RS’s proficiency in engaging with users. Leading indicators are predictive metrics that provide early signals about future trends or outcomes, often emerging before the actual changes become observable. Leading indicators are widely used for forecasting developments, identifying opportunities and risks, and supporting data-driven policy formulation. By Recognizing this aspect, the RS can operate with greater awareness and adjust its recommendations more effectively. Specifically, by understanding that the flexibility indicator reflects the user’s propensity for adaptable behavior, the RS, endowed with heightened awareness, can recalibrate its recommendation strategies accordingly. We characterize a user’s flexibility based on the variability in their past choices; specifically, the more diverse their purchase history, the greater their capacity to accept and adapt to new recommendations. The flexibility of user h , denoted as ​, is computed via Eq. ( 5 ). 5 where, denotes the cardinality of set . Organization-Centric computational steps The objective of this section is to assess the impact of the selection of each item on the organization’s operational goals, thereby enabling organizational priorities to inform recommendations provided to users. Additionally, the organization’s flexibility is evaluated based on its current status and the gap between its present condition and its ideal state. Figure 2 offers a comprehensive overview of the calculations involved in this section, with detailed explanations provided in the subsequent steps. Fig. 2. Open in a new tab Comprehensive overview of the organizational calculations. This Fig. illustrates the three core operations carried out concerning the organization: (1) Organizational Expectations (OEs) computation, (2) quantification of the influence of item selection on OEs, and (3) organizational flexibility computation. Step 1. Organizational Expectations Computation In this step, the organization needs to specify its expectations derived from its strategic and operational plans. the OEs should be defined by assigning values to those features based on which products are evaluated. the set of organization-centric evaluation features, used to assess items, is represented by . These features are designed for organizational-level computations. As a result, we define the organization-centric normalized feature matrix , where each row denotes the feature vector of the i -th item (i = 1,…,M) and the entries are filled in by domain experts. The organizational expectation vector is defined as , where denotes the organization’s expected level for feature . Here, , indicating that the organization does not necessarily need to define expectations for all features which is consider in matrix ; instead, it may focus only on the most relevant or important ones. Step 2. Quantifying the Influence of Item Selection on OEs The similarity between each item and the OEs is evaluated by analyzing the impact of selecting that item on the organization’s current state. This process involves examining how each item would alter the organization’s existing configuration and comparing the resulting future state with the ideal or desired state. The degree of similarity is then quantified: a higher similarity score indicates that the item’s characteristics closely match the OEs. This approach facilitates identifying items that are most aligned with organizational goals, based on the extent to which they restore or maintain the preferred capacity distribution. The similarity between each item and OEs is assessed by analyzing how the selection of that item transforms the organization’s current state into a future state. This process begins with a predefined current-state vector , designed based on the criteria specified in the organizational expectation vector . Each item modifies to produce a distinct future-state vector , representing the organization’s projected configuration after adopting item i . The degree of alignment between and is then quantified using a similarity metric, where a higher similarity score indicates that the item’s impact on the organization’s capacity distribution more closely matches the predefined OEs. This method enables the systematic identification of items that best harmonize with organizational objectives, prioritizing those that either restore or sustain the desired equilibrium across critical operational dimensions. The impact of item selection on the OEs is modeled using the similarity index presented in Eq.( 6 ). A higher value of this index indicates a greater alignment between the item and the OEs, since it reflects a larger similarity between the OEs and the anticipated future state resulting from the item selection. 6 Step 3. Organizational Flexibility Computation The distance between the and signifies the level of flexibility in its capacity to accept recommendations. A smaller distance suggests that the organization is close to its capacity limits, indicating reduced flexibility, whereas a larger distance signifies greater flexibility, as there is still significant capacity available. This measure provides insight into the organization’s current operational leeway, allowing the RS to tailor suggestions accordingly. In this study, we employ the Eclidean distance metric to quantify the disparity between the and . This choice is motivated by two critical considerations: Non-Compensatory Nature of Organizational Resource Allocation Resource distribution across all operational features is deemed equally critical. Deviations from expected performance in any single feature cannot be offset by superior performance in another. The Euclidean distance inherently enforces this non-compensatory framework by squaring individual deviations before aggregation, ensuring that no single criterion’s shortfall is trivialized by others’ overperformance. Sensitivity to Extreme Deviations The Euclidean distance emphasizes larger discrepancies by squaring deviations, which aligns with organizational priorities where significant gaps in key metrics pose disproportionate risks to operational objectives. By amplifying the effect of extreme deviations, this metric ensures that high-impact discrepancies are explicitly penalized within the flexibility index. The organizational flexibility derived from Euclidean distance between the and is presented in Eq. ( 7 ). 7 Gathering information and providing recommendations Up to this point, four key pieces of information have been obtained: Relative distances to the RP. User flexibility. Influence of item selection on OEs. Organizational flexibility. The greater the user’s flexibility, the more prominently organizational preferences are considered. Conversely, the higher the organizational flexibility, the more user preferences are taken into account. However, it is important to note that even if a user possesses the highest level of flexibility among all users, their preferences should not be entirely disregarded. The same applies to the organization; that is, if the organization is in a state of maximum flexibility, its preferences should not be completely overlooked. To account for this, a weight adjustment function is defined, which, given an input flexibility value, produces an adjusted coefficient. Mathematically, the weight adjustment function is expressed in Eq. ( 8 ): 8 where and are the lower and upper thresholds, respectively. Based on this approach, Eq. ( 9 ) calculates the final score for each item , which serves as the basis for providing recommendations. As illustrated in Fig. 3 , the decision-making process for providing recommendations involves assessing the extent to which each item aligns with the preferences of both the organization and the user. These two scores are then combined, weighted according to the flexibility inherent to each stakeholder. Fig. 3. Open in a new tab Schematic representation of item proximity to user and OEs. This Fig. illustrates multiple items plotted based on their proximity to the preferences of both the user and the organization. Item is closer to the organizational preferences, whereas Item aligns more closely with the user’s preferences. Item represents a midpoint, demonstrating the varied degrees of alignment among the items relative to both stakeholders. 9 The score serves as the basis for making recommendations; that is, the top N items with the highest scores are recommended to each user. Analysis of computational complexity To evaluate the scalability and practical efficiency of the proposed RS model, a detailed analysis of its computational complexity is essential. In general, there are two kinds of algorithm complexity: time complexity and space complexity. The time complexity, denoted by T(n), is calculated based on the number of computational stages required to execute the algorithm’s operations. The time complexity is broken down for each major step of the proposed RS model. Table 1 provides a summary of the number of arithmetic operations and the asymptotic time complexity involved in processing a single user request under the worst-case scenario. In this context, M represents the total number of items, N denotes the number of user-centric features (i.e., product attributes considered in user-related computations), R indicates the number of organization-centric features (i.e., product attributes considered in organization-related computations), and denotes the subset of items that user ℎ has previously purchased or interacted with. Table 1. Step-wise asymptotic time complexity analysis of the proposed RS model. Step Operation Count (per user) Asymptotic Time Complexity User History Monitoring and Peak–End Identification User RP Construction 5 N Computation of Relative Distances to the RP User Flexibility Computation Quantifying the Influence of Item Selection on OEs 5R + 1 Organizational Flexibility Computation 4R + 2 Gathering Information and Providing Recommendations Open in a new tab The algorithm’s overall time complexity is primarily influenced by Step 4: User Flexibility Computation, which scales quadratically with the number of items (M²) and linearly with the number of user-centric features (N), as detailed in the accompanying table. This step requires calculating pairwise similarities among all items in the user’s purchase history. However, it is important to understand that a user’s flexibility, defined as their ability to adapt to new recommendations, is a latent trait that evolves slowly over time. Consequently, this computationally intensive calculation can be performed offline in a periodic manner (e.g., daily), and its result cached for subsequent user sessions. All other steps scale linearly or near-linearly with M, N, or R. By implementing a strategy that combines both online and offline computations, the real-time complexity for processing a user request is effectively reduced to , governed by the linear-scaling steps (“User History Monitoring and Peak–End Identification” and “Computation of Relative Distances to the RP”). This complexity is comparable to that of standard collaborative filtering or content-based filtering methods. Therefore, despite its sophisticated multi-stakeholder and predictive-oriented design, the proposed RS model maintains computational tractability, making it suitable for deployment in large-scale RSs such as e-commerce platforms or streaming services. Simulation experiments This section develops a simulated scenario designed to assess the demand management capabilities of our proposed RS model in a practical setting. By testing the model’s demand management capabilities under controlled conditions, this simulation provides insights into its efficiency, scalability, and adaptability in real-world scenarios. To this end, we modeled a hypothetical manufacturing company with a diverse product portfolio comprising 30 distinct items, chosen to reflect the complexity and variety the RS model is designed to handle. Each product was characterized by four attributes: C1 (price), C2 (quality), C3 (delivery time), and C4 (innovative design), to realistically emulate the diverse spectrum of offerings available in the marketplace. For the simulation, we created profiles for 100 individual users, each tailored with unique attributes to reflect realistic consumer behavior. These profiles included details such as the users’ prior purchases from the company and the relative weights they assigned to different product features. Furthermore, we assumed that all 100 users had an established purchase history with the company, with each having acquired at least three products in the past, to ensure the simulation accurately reflects ongoing consumer relationships and loyalty patterns. To construct the user-centric feature matrix P , we adopted an approach that emphasizes product diversity, ensuring the matrix captures a wide range of attribute combinations across the 30 items. To further enrich the simulation and facilitate more granular analysis, we organized the 30 products into five distinct groups based on their characteristic feature profiles. These product groups, detailed in Table 2 , were designed to reflect a range of strategic positions commonly observed in manufacturing portfolios, such as products that emphasize premium quality, cost-effectiveness, rapid delivery, or innovative design. Table 2. Stratified product groups based on feature profiles ( – ). Group Item sets Description 1 Products with high scores in (delivery time) and (innovative design), but relatively low scores in price and quality. These items are characterized by their rapid availability and attractive design features, making them suitable for customers who prioritize quick delivery and modern aesthetics. 2 Products with low pricing ( ) and high quality ( ), but with longer delivery times and average design. These items appeal to consumers seeking a balance of affordability and quality while being less sensitive to delivery speed and design innovation. 3 Products with exceptional quality ( ) and innovative design ( ), but priced at a premium and subject to moderate delivery times. These products are tailored to users who value cutting-edge design and top-tier quality, and are willing to pay more for these features. 4 Products with very competitive pricing ( ) and fast delivery ( ), but with average quality and basic design. Targeted at price-sensitive customers needing quick turnaround, these items offer practical but less sophisticated solutions. 5 Balanced products with moderate scores across all four features. These items aim to satisfy broad customer segments without emphasizing any single attribute, representing all-purpose offerings in the company’s portfolio. Open in a new tab Figure 4 presents a histogram visualizing the distribution of user purchasing behaviors derived from simulated historical data for 100 users, providing insights into consumer trends and engagement levels. The x-axis denotes the quantity of purchased items (ranging from 3 to 30 products, as specified by the simulation parameters), while the y-axis quantifies user frequencies per bin. This distribution reveals pronounced heterogeneity in user engagement patterns, indicating varied levels of customer loyalty and purchasing frequency across the population. The underlying data were synthesized via a right-skewed normal distribution, with parameters rigorously calibrated to emulate empirically observed customer loyalty dynamics. Fig. 4. Open in a new tab Histogram of user purchase history. To more accurately reflect empirical customer behavior, the distribution of user purchase history demonstrates a right-skewed pattern. This skewness is intentionally engineered to simulate realistic customer loyalty dynamics, wherein the majority of users exhibit relatively low purchase counts, and the number of highly loyal customers with extensive purchase histories is substantially smaller. In this study, an organization-centric feature matrix was constructed based on three distinct attributes, , where each ​ represents the number of person-hours required to manufacture a single item in the i-th workshop. The person-hour requirements corresponding to 30 individual items in each workshop, along with their normalized values, are presented in Table 3 . This formulation captures the specific resource demands associated with each production facility. To establish the organization’s capacity profile, the maximum nominal person-hour capacities for the three workshops—namely, 150, 200, and 400 person-hours per month—were identified and assembled into an organizational expectation vector. Consequently, the normalized organizational expectation vector was defined as = [38.36, 40.32, 67.34], where each element represents the maximum available normalized person-hours per month for the respective workshop. Table 3. Organization-centric feature matrix with normalized values. Item Normalized Normalized Normalized 3.51 3.04 0.97 0.898 0.613 0.163 0.61 1.66 0.68 0.156 0.335 0.115 1.66 4.84 5.47 0.425 0.976 0.921 3.12 4.5 2.88 0.798 0.907 0.485 2.75 1.11 5.11 0.703 0.224 0.86 1.09 0.2 4.85 0.279 0.04 0.817 3.83 3.61 1.12 0.980 0.728 0.188 2.40 4.36 1.48 0.614 0.880 0.249 1.37 0.76 0.32 0.350 0.153 0.054 2.52 0.38 3.65 0.645 0.077 0.614 3.70 3.07 4.66 0.947 0.619 0.785 3.63 3.10 3.06 0.929 0.625 0.515 2.18 2.67 0.16 0.558 0.538 0.027 2.04 0.23 5.94 0.522 0.046 1.00 1.59 3.50 3.00 0.407 0.706 0.505 0.69 4.74 1.99 0.177 0.956 0.335 3.13 4.39 1.04 0.801 0.885 0.175 0.96 0.74 3.75 0.246 0.149 0.631 1.74 1.90 3.45 0.445 0.383 0.581 1.88 1.36 4.50 0.481 0.274 0.758 3.59 2.88 0.92 0.918 0.581 0.155 0.57 3.14 2.14 0.146 0.633 0.36 3.45 1.64 0.86 0.883 0.331 0.145 1.50 4.03 5.10 0.384 0.812 0.859 1.37 4.01 2.02 0.350 0.808 0.340 2.20 3.94 1.65 0.563 0.795 0.278 3.05 1.88 0.03 0.780 0.379 0.005 1.20 0.46 4.81 0.307 0.093 0.810 1.25 3.60 2.98 0.320 0.726 0.502 3.91 4.96 3.22 1.00 1.00 0.542 Open in a new tab Table 4 presents the results obtained for each user. For every user, the table reports their weight matrix , , , , and, finally, the item recommended by the RS. Furthermore, Fig. 5 shows the histogram of the users’ flexibility index. Figure 6 illustrates the variations in organizational flexibility as successive users enter the system, alongside the plot of function α. The parameters of the function α are set as follows: and . As depicted in Fig. 6 , upon the entry of the 65th user, the organizational flexibility drops below 0.2 (specifically, 0.1928). Consequently, for all users entering the organization after the 64th user, the assigned user scores are fixed at 0.2. Table 4. User information and recommended item overview. User Recommendation 1 [0.14,0.12,0.60,0.14] [0.02, 0.05, 0.41, 0.12] {29,22,2,17,27,16,5,14} 0.68 3 2 [0.30,0.24,0.15,0.31] [0.17, 0.20, 0.02, 0.24] {9, 27, 3, 22, 18, 30, 4, 25, 29, 15, 14, 16} 0.45 11 3 [0.09,0.35,0.32,0.25] [0.02, 0.07, 0.28, 0.15] {7,2,23,18,10,1,26,20,27} 0.78 4 4 [0.31,0.07,0.03,0.59] [0.16, 0.06, 0.00, 0.44] {28,30,29,9,12,27,7,16} 0.79 19 5 [0.15,0.28,0.27,0.30] [0.07, 0.25, 0.04, 0.22] {8, 25, 3, 4, 7, 28, 9, 18, 27, 11, 5, 30} 0.45 13 6 [0.30,0.23,0.26,0.22] [0.16, 0.18, 0.04, 0.16] {25, 16, 10, 22, 3, 17, 11, 30, 18, 9, 19} 0.59 28 7 [0.40,0.38,0.15,0.07] [0.22, 0.30, 0.02, 0.05] {20, 30, 7, 17, 26, 12, 11, 16, 28, 15, 27, 19} 0.40 8 … … … … … 94 [0.32,0.06,0.43,0.18] [0.17, 0.02, 0.19, 0.16] {26,3,13,4,12,19,29,27,16,5,14} 0.45 17 95 [0.07,0.13,0.21,0.59] [0.03, 0.03, 0.18, 0.39] {10,16,7,18,26,19,11,2,22,3,20,21} 0.39 5 96 [0.09,0.32,0.46,0.13] [0.02, 0.06, 0.40, 0.08] {16,8,22,21,2,19,24,11,29,26,13,5,4,1,17,23,27} 0.14 3 97 [0.28,0.19,0.38,0.15] [0.13, 0.10, 0.22, 0.08] {22,11,15,27,19,5,29,12} 0.80 24 98 [0.22,0.25,0.27,0.25] [0.06, 0.22, 0.08, 0.18] {28,26,12,5,7,15,13} 0.87 19 99 [0.27,0.38,0.10,0.25] [0.16, 0.32, 0.01, 0.21] {2,20,30,1,18,23,4,28,11} 0.71 14 100 [0.40,0.22,0.07,0.31] [0.35, 0.14, 0.03, 0.07] {15,18,12,14,13,1,22,26,20,4,11,21,6} 0.40 10 Open in a new tab Fig. 5. Open in a new tab Histogram of user flexibility index. This distribution, similar to the customer purchase distribution, is left-skewed, indicating that only a small fraction of customers exhibit very low flexibility, while the majority demonstrate moderate to high flexibility. Fig. 6. Open in a new tab Organizational flexibility dynamics. This Fig demonstrates how organizational flexibility evolves with the sequential entry of users, alongside the plot of with and . Comparative performance Analysis To analyze the impact of the proposed RS model, we first computed recommendations based solely on Eq. ( 10 ). This equation represents an allocation strategy that is entirely aligned with customer preferences, which we refer to as the Customer-Driven Recommendation Strategy (CDRS). These results were then directly compared with those generated by the proposed method, as shown in Fig. 7 . Fig. 7. Open in a new tab Workshop capacity utilization: proposed method vs. CDRS. This Fig illustrates the comparison between the proposed method (solid lines) and the CDRS (dashed lines). Under CDRS, Workshops 1 and 2 exceed capacity (54.5% and 36.9% expansions, respectively), while Workshop 3 shows 34.8% idle capacity. The proposed method reduces overcapacity by 18.7% (Workshop 1) and 17.1% (Workshop 2), and cuts idle time in Workshop 3 to 18.8%, resulting in a 17.6% average improvement in organizational efficiency. Dashed lines highlight CDRS-induced imbalances, underscoring the method’s enhanced resource equilibrium. 10 As depicted in Fig. 7 , the implementation of the CDRS results in notable operational discrepancies between the actual capacities of the workshops and the suggested production loads. Specifically, Workshops 1 and 2 are compelled to operate beyond their normalized monthly person-hour limits of 38.36 and 40.32, respectively, reaching 59.28 and 55.22 person-hours. This represents capacity expansions of approximately 54.5% and 36.9%, which exceed the feasible thresholds determined by available resources. Conversely, Workshop 3 demonstrates significant underutilization, with only 65.2% of its capacity being utilized and 34.8% remaining idle. This underutilization indicates suboptimal resource deployment, potentially leading to inefficiencies, elevated operational costs, and issues related to labor shortages or underemployment. In contrast, the proposed method demonstrates a balanced and sustainable approach. Under the proposed RS model: Workshop 1, previously overloaded with the highest demand, experiences a significantly reduced requirement for expansion, needing only an 18.7% increase in capacity (down from 54.5% under CDRS), reflecting a notable 35.8% improvement in utilization efficiency. Workshop 2 sees its overcapacity burden mitigated, requiring only a 17.1% increase instead of 36.9%—a revised capacity demand that represents a meaningful 19.8% efficiency gain. Workshop 3, the most underutilized under the CDRS, achieves a substantial improvement from 34.8% idleness to 18.8%, resulting in a 16% reduction in idle capacity. Overall, the proposed RS model achieves an average increase of 17.6% in organizational capacity utilization, effectively mitigating the inefficiencies associated with purely customer-driven strategies. This underscores the method’s ability to intelligently reallocate resources, reduce load imbalances among workshops, and ensure that the anticipated person-hour capacities are neither exceeded nor underutilized. Consequently, this contributes to improved operational resilience and heightened cost-effectiveness. Conclusion This study introduces a novel RS that simultaneously accounts for the preferences of both the organization and the user as key stakeholders. Unlike traditional approaches, the proposed system does not rely on the entire historical data of user interactions; instead, it leverages the peak-end rule, focusing solely on the most significant moments—namely, the peaks and endpoints. This methodological choice reduces computational complexity and addresses issues related to data sparsity and large-scale data processing. Additionally, the system incorporates leading indicators, which can forecast future trends by signaling changes before they manifest in actual performance or environmental shifts. Specifically, user and organizational flexibility are utilized as such indicators, providing insight into the novelty of recommendations and the organization’s capacity to fulfill orders. In cases where organizational flexibility is limited, disregarding the organization’s preferences may lead to a subsequent decline in user satisfaction, as the user is likely to receive their goods over a longer period or with reduced quality. Furthermore, this work presents a systematic, dynamic approach for assessing the organizational benefit of a product, emphasizing real-time implementation. The method necessitates continuous updates with the latest organizational data, enabling responsive and context-aware recommendations at every interaction. The outcomes of the simulation demonstrated that the proposed methodology significantly enhances organizations’ ability to achieve effective resource leveling. On average, there was a 17.6% improvement in the utilization of organizational capacities compared to scenarios where this approach was not applied. Author contributions Ahmad Makui: Supervision, Guidance, Reviewing, and Editing. Reza davoudabadi: Methodology Design, and Writing – Original Draft Preparation. Mohammad R. Rasouli: Advisory Role. Data availability Data generated during the current study are available from the corresponding author upon reasonable request. Declarations Competing interests The authors declare no competing interests. Footnotes Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. References 1. Sitar-Tăut, D. A. & Mican, D. MRS OZ: managerial recommender system for electronic commerce based on Onicescu method and zipf’s law. Inf. Technol. Manage. 21 (2), 131–143 (2020). [ Google Scholar ] 2. Abdollahpouri, H. & Burke, R. Multistakeholder RSs. In (eds Ricci, F., Rokach, L. & Shapira, B.) RSs Handbook. Springer. (pp. 647-677) (2022). 3. Ranjbar Kermany, N., Zhao, W., Yang, J., Wu, J. & Pizzato, L. A fairness-aware multi-stakeholder recommender system. World Wide Web . 24 (6), 1995–2018 (2021). 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[ Google Scholar ] Associated Data This section collects any data citations, data availability statements, or supplementary materials included in this article. Data Availability Statement Data generated during the current study are available from the corresponding author upon reasonable request. Articles from Scientific Reports are provided here courtesy of Nature Publishing Group ACTIONS View on publisher site PDF (3.3 MB) Cite Collections Permalink RESOURCES Similar articles Cited by other articles Links to NCBI Databases Follow NCBI NCBI on X (formerly known as Twitter) NCBI on Facebook NCBI on LinkedIn NCBI on GitHub NCBI RSS feed Connect with NLM NLM on X (formerly known as Twitter) NLM on Facebook NLM on YouTube National Library of Medicine 8600 Rockville Pike Bethesda, MD 20894 Web Policies FOIA HHS Vulnerability Disclosure Help Accessibility Careers NLM NIH HHS USA.gov Back to Top

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