The impact of information disclosure and smart technology integration on e-retailing performance: A production delivery policy framework

Tayyab, Muhammad; Tahir, Hira; Habib, Muhammad Salman Article The impact of information disclosure and smart technology integration on e-retailing performance: A production delivery policy framework Operations Research Perspectives Provided in Cooperation with: Elsevier Suggested Citation: Tayyab, Muhammad; Tahir, Hira; Habib, Muhammad Salman (2025) : The impact of information disclosure and smart technology integration on e-retailing performance: A production delivery policy framework, Operations Research Perspectives, ISSN 2214-7160, Elsevier, Amsterdam, Vol. 14, pp. 1-26, https://doi.org/10.1016/j.orp.2025.100328 This Version is available at: https://hdl.handle.net/10419/325805 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Contents lists available at ScienceDirect Operations Research Perspectives journal homepage: www.elsevier.com/locate/orp The impact of information disclosure and smart technology integration on e-retailing performance: A production delivery policy framework Muhammad Tayyab a,b,c, Hira Tahir c, Muhammad Salman Habib d,∗ aInformation Systems and Operations Management Department, King Fahd Business School, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia bInterdisciplinary Research Center for Finance and Digital Economy, King Fahd Business School, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia cInterdisciplinary Research Center for Smart Mobility and Logistics, King Fahd Business School, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia dInstitute of Knowledge Services, Center for Creative Convergence Education, Hanyang University, ERICA Campus, Ansan-si, Gyeonggi-do, 15588, South Korea A R T I C L E I N F O Keywords: E-retail management Information disclosure Green technology integration Multi-shipment policy Smart production system A B S T R A C T The electronic retailers face distinct challenges in information sharing compared to their purely offline counterparts, particularly in transparently communicating their environmental practices to increasingly ecoconscious consumers. This complexity increases in e-retailing due to the absence of direct interaction and makes it difficult for consumers to evaluate the sustainability efforts of retailing channel’s stakeholders. In response to it, manufacturers and e-retailers are leveraging social media and blockchain technology for personalized advertising to bridge this information transparency gap. This research presents a sustainable multiitem integrated model for manufacturer–retailer collaboration in e-retailing by incorporating multiple delivery policies and investments in technology aimed at information disclosure and environmental footprint reduction. The manufacturer adopts a smart production system and reuse returned goods in the manufacturing process while investing in Green Emissions Reduction Technology. Meanwhile, the e-retailer enhances product demand through Information Disclosure Technology on social media and blockchain by showcasing their environmental protection efforts. By employing a hybrid analytic-metaheuristic approach, we determine optimal production and delivery policies to improve green consumer service under varying budgetary and spatial constraints. The results demonstrate a 4.39% increase in online consumer demand through information sharing and a 3.86% improvement in profitability of the collaborative retailing system under single-setup multi-delivery policy that confirms robustness of the proposed model. Scenario analysis further provides decision-makers with actionable insights by showcasing 8.44% increment in the system profit by converting traditional production into smart production system. Moreover, the sensitivity of the proposed model to balancing the technology investments among emission control and information disclosure efforts suggests keeping track of the efficiency parameters of these investment options before making technology budget allocations. 1. Introduction In the recent years, consumers have shown growing concern over the global energy crisis and resultant global warming. Consequently, they have been compelled to prioritize environmental conservation and the use of low-carbon commodities [1]. The 2030 Agenda regarding Sustainable Development (SD) from the UN makes sustainable consumption a strategic goal, saying that the individuals should contribute to the altering unsustainable consumption and production patterns. Therefore, the production and retail chains of daily consumables are making efforts to mitigate greenhouse gas emissions and communicating their efforts to the potential customers through various channels. However, determining the sustainability of a product is challenging for customers due to the subjective nature of environmental sustainability as a belief-based characteristic. E-retailers face exceptional difficulties in communicating their environmental practices to eco-conscious consumers in a transparent manner. This issue originates from the lack of direct physical interaction inherent in online sales settings. This opacity in the information disclosure makes it difficult for the product consumers to evaluate the sustainability efforts of e-tailers and their respective supply chain partners. For instance, ∗Corresponding author. E-mail address: [email protected] (M.S. Habib). https://doi.org/10.1016/j.orp.2025.100328 Received 31 October 2024; Received in revised form 7 February 2025; Accepted 8 February 2025 Operations Research Perspectives 14 (2025) 100328 Available online 27 February 2025 2214-7160/© 2025 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). M. Tayyab et al. while a brick-and-mortar store can simply display certifications like Fair Trade labels directly on the products, online retailers can rely on digital representations only that can be easily manipulated or overlooked. Furthermore, explaining complicated environmental initiatives including carbon offsetting or sustainable packaging choices requires detailed descriptions that may not effectively translate to the online environment. Consider a fast fashion industry where the online retailers like ASOS and Boohoo have faced scrutiny for ‘‘greenwashing’’ to promote environmentally friendly collections without sufficient evidence of genuine sustainable practices. Another obvious case is of Amazon, which faces inquiry about its carbon footprint and has responded to it by commencing initiatives including ‘‘Climate Pledge Friendly’’ with the objective of highlighting sustainable products [2]. Similarly, a globally famous retail chain named Patagonia has faced communication challenges in leveraging its ecommerce platform to transmit its environmental efforts information by showcasing detailed lifecycle analyses of its products. However, the lack of direct consumer interaction in e-retailing adds to the difficulty of verifying these claims which leads to skepticism about the greenwashing. This lack of transparency in information disclosure can directly wear away consumer trust and negatively impact the brand reputation. This highlights the practical implications of the green information-sharing challenges for the e-tailing industry. The continuous growth of information technology such as social media and blockchain has transformed individuals’ methods of communication and their decision-making processes about purchases, while also reshaping the digital marketing environment [3]. The emergence of personalized advertisements has prompted advertising personnel to investigate its efficacy, including its impact on customer attitudes, ad engagement (such as clicks or purchases), and the factors that influence it [4]. Therefore, blockchain and social media advertising offer powerful platforms for the retail sector to inform and educate their consumers about their initiatives to reduce carbon emissions by making investments in advanced low carbon technology. By virtue of this, production and retail industries have become capable of effectively drawing in a larger customer base and attract more demand. Production-delivery reliability in addition to the sustainability is of utmost importance in today’s globalized world. Failing to satisfy customer expectations may lead to a permanent loss of customers and a decrease in competitiveness. As a result, the supply chains must optimize their production and inventory systems to succeed in the long run despite the complicated global environment. Achieving success in manufacturing depends on effectively integrating production and inventories of the whole system. The major objective in the supply chains of integrated systems includes value creation through well-coordinated production quantities and delivery lot size decisions. The goal is to minimize total cost of the supply chain while making a wise trade-off among setup cost and inventory carrying costs of the system. However, basic inventory management models such as EOQ and EPQ presented by Harris and Taft in 1913 and 1918, respectively have certain limitations in terms of practical applicability [5]. Therefore, several studies have extended these models by incorporating many real world conditions. One of the recent addition is Vendor Managed Inventory (VMI) in the production inventory systems [6]. Several supply chains including NIKE, Procter & Gamble, and BOSCH implement Vendor Managed Inventory (VMI) to make decisions around delivery lot sizes and number of deliveries by taking full control of the retailer inventories. On the other hand, some production industries implement Just In Time (JIT) inventory control systems to develop a long-term economic viability through mutual cooperation with the downstream supply chain partners where the optimal lot size is broken down into smaller multi-shipments. In this way, the coordinated supply chains ensure higher service levels while maximizing economic sustainability. Recent applications of JIT have established that Single-Setup-Multi-Delivery-Policy (SSMD) has economic superiority over the Single-Setup-Single-Delivery (SSSD) policy [7]. However, there exists a high likelihood of shortages in the system, especially under the cases of rush deliveries and emergency deadlines faced in automotive industry such as Toyota and technology companies like DELL [8]. Therefore, the consideration of possible shortages in model formulation through deployment of a robust backordering policy is critical in determining optimal production delivery policies. Given the above key considerations, we propose a sustainable multi-item integrated production delivery model for a single-manufacturer singleretailer e-retailing management under SSMD policy and technology investments for advertisement and greenhouse gas emissions control. The manufacturer operates a smart production system and utilizes predetermined proportion of returned goods in producing the new products. He invests in green emissions reduction technology (GERT) in his production system, and the retailer invests in social media advertisement in the form of information disclosure technology (IDT) to communicate the emissions control efforts of the system to the customers in order to enhance product demand. Information Disclosure Technology (IDT) includes technological and digital platforms utilized to transparently communicate product and process information regarding sustainability efforts to the customers. This includes social media campaigns, interactive e-pages and websites, and product labeling initiatives that elaborates the supply chain’s environmental protection efforts. For instance, Patagonia uses its website and social media to share information about its sustainable raw-material sourcing and fair labor practices, whereas Unilever’s Sustainable Living Plan is communicated through various digital channels and product labels. In this research, IDT represents the retailer’s investment in social media advertising to inform consumers about the manufacturer’s greenhouse gas emissions reduction efforts. Further, Green Emissions Reduction Technology (GERT) refers to the investments in manufacturing and conversion processes, tools and equipment, and the technologies designed to minimize greenhouse gas emissions [7]. Some of the examples of GERT include carbon capture and storage systems, renewable energy integration in manufacturing plants such as solar panels or wind turbines and the utilization of energy-efficient equipment. In this study, GERT represents the manufacturer’s investment in technologies to reduce emissions during the production process which is then communicated to the customers through retailer’s IDT initiatives. Green technology investment plays a key role in supply chain dynamics, impacting costs, consumer behavior, and product demand. By implementing sustainable practices, the companies can not only lower operational costs through efficient use of resources and waste management but also increase profit of the system [9]. Consumers are increasingly willing to pay more for environmentally friendly products, encouraging manufacturers to adopt green technologies [10]. This shift in consumer behavior, particularly among those sensitive to carbon emissions, drives the need for firms to invest in sustainable practices. For example, Walmart’s investment in renewable energy and green supply chains has not only reduced costs but attracted eco-conscious consumers, and Tesla’s focus on electric vehicles and sustainable manufacturing has enhanced its market appeal [11]. Overall, green technology investments help businesses align with consumer preferences, driving demand and fostering sustainability [12]. To the best of author’s knowledge, no such sufficing model has been presented yet that considers this optimal e-advertisement and emissions control strategy while maximizing the system profit under shortage-prone SSMD product delivery mode. We develop two major cases in the proposed advertisement and emissions control efforts based sustainable integrated model. Case I develops a non-capacitated integrated model before advertisement and emissions control efforts which is solved through a combination of analytical optimization technique and a proposed heuristic approach. Further, Case II presents a capacitated integrated model with technology investments for IDT and emissions control which is solved through a metaheuristic approach to identify the optimal advertisement and emission control policy under the smart production rate. The proposed model cases are validated through numerical experiment and analysis to infer significant managerial insights. Operations Research Perspectives 14 (2025) 100328 2 M. Tayyab et al. Fig. 1. Contribution of the proposed study. 1.1. Research motivation Although the importance of flexibility, technology, and advertising [13] for enhancing profitability in offline retailing is studied, their integration within an SSMD policy adoption has not been well researched in e-retailing mechanisms. Further, as the SSMD policy adoption has shown economic benefits in JIT systems [14], it increase the likelihood of shortages in the integrated systems. Hence, consideration of backordering policy in such manufacturer–retailer coordinated arrangement is crucial. This study addresses the aforementioned research gap by presenting a comprehensive inventory model that incorporates technology investments for environmental protection and advertisement efforts within a multiitem supply chain comprising of a single manufacturer and a single retailer. Further, several global companies including Amazon faces inquiry about its carbon footprint and has responded to it by commencing initiatives including ‘‘Climate Pledge Friendly’’ with the objective of highlighting sustainable products [2] . Similarly, a globally famous retail chain named Patagonia has faced communication challenges in leveraging its ecommerce platform to transmit its environmental efforts information by showcasing detailed lifecycle analyses of its products. However, the lack of direct consumer interaction in e-retailing adds to the difficulty of verifying these claims which leads to skepticism about the greenwashing. This lack of transparency in information disclosure can directly wear away consumer trust and negatively impact the brand reputation. This highlights the practical implications of the green information-sharing challenges for the e-tailing industry. Therefore, this study examines the most effective combination of smart production, technological investments, and dynamic advertising methods to optimize overall profit in the presence of SSMD and planned backordering strategies under collaborative e-retailing. We investigate the strategic choices of technology budget distribution among IDT and GERT under various realizations of the budgetary and space constraints. Further, we identify the critical parameters through sensitivity analysis and devise recommendations to improve economic viability of the system under the variations in these parameters. The obtained managerial insights provide decision-makers with the necessary recommendations to deploy efficient strategies and attain environmental and economic sustainability. Therefore, our study aims to answer the below research questions: 1. How can the integration of smart production systems, technological investments, and dynamic advertising methods enhance the profitability of a manufacturer–retailer collaborative e-retailing system? 2. What is the optimal allocation of the technology investment budget between IDT for the retailer and GERT for the manufacturer to maximize overall profitability? 3. How does the adjustment of production rates within predefined ranges in response to fluctuating e-product demand contribute to the profitability and flexibility of the smart production system? 4. What is the economic role of advertising efficiency in enhancing the overall profitability of a sustainable integrated production-delivery strategy under e-retailing? 1.2. Contribution of the research On the basis of aforementioned discussion, this study contributes to the e-retailing literature in the following aspects. •This study highlights the significance of advertising efficiency by establishing a clear association between advertisement efficiency and profitability of the sustainable integrated production-delivery strategy under e-retailing. This understanding offers managerial recommendations on improving advertisement efforts in order to generate encouraging effects on overall profitability. •This study offers valuable insights into the strategic distribution of the technology investment budget among Information Disclosure Technology (IDT) for the e-retailer and Green Emissions Reduction Technology (GERT) for the manufacturer. This contribution enables managers and practitioners in improving economic viability through intelligent technology budget allocation under varied circumstances. •This study demonstrates a constructive impact of converting traditional fixed manufacturing systems into smart ones by allowing adjustment of production rates within the predefined ranges in response to varied e-product demand. Through an experimental study, we answer the question; What is the strategic role of flexibility in enhancing overall profitability of the system? •This study contributes to the literature by verifying the significant impact of incorporating parallel technological investments in Information Disclosure Technology (IDT) and Green Emissions Reduction Technology (GERT) to improve system profitability. This insight enables managers and practitioners in making strategic technology integration decisions for collaboration among the manufacturer and e-retailer. Fig. 1provides graphical representation of the major contribution of this research. Operations Research Perspectives 14 (2025) 100328 3 M. Tayyab et al. 1.3. Orientation of the research Rest of this research is structured as below. Section 2provides a thorough review of the research to identify the key milestones and need of the study in the field of production and retail management. Next section explains the problem and emphasizes the nomenclature and assumptions used to formulate the proposed mathematical model. Both cases of the proposed sustainable integrated production-delivery model are developed in the Section 4, and Section 5illustrates hybrid solution methodology for the proposed sustainable integrated inventory models. An experimental study is setup in Section 6to validate real world application of the model and the experimental outcomes are analyzed for various instances of the model to devise significant managerial insights. Eventually, Section 7presents conclusions, limitations, and future research avenues of the study. 2. Literature review This section presents an overview of the current literature in the field of e-retailing management with a focus on technology integration for green products manufacturing and delivery under a smart production management system. 2.1. E-retail management E-retail management is a process of managing online retail operations including sales, inventory, and customer engagement. For instance, Amazon uses AI-driven recommendations to personalize shopping experience and shopify platforms enable small businesses to set up and manage online stores. The businesses can establish their online presence with minimal effort and it has significantly lowered the barriers to entry into the e-retailing industry. The online marketplace including platform selling is primarily open to all types of businesses. However, this convenience to develop e-retailing channels has created a high degree of homogenization in this industry. The business models developed around e-retailing can be easily replicated due to their wide availability and affordability. This makes it even more complex to differentiate one online retailer from another in the same sector. This constructs a highly competitive landscape encompassing a high threat of new entrants, quite readily available distribution channels, reduced economies of scales, and eventually low customer switching costs. Further, the online retailers face persistent pressure to enhance their delivery process performance. This is due to the fact that online consumers have high expectations regarding product quality, delivery speed and quality, and the overall purchasing experience [15]. As a result, building a strong strategic position that offers a sustainable competitive advantage is important for the e-retailers. Current research on e-retailing has explored various aspects of improvement and has identified respective key factors for success in e-retailing [11,16–19]. Ani et al. [16] emphasize the importance of managing security concerns as a critical success factor in e-retailing. Further, Chen et al. [18] focused on the operational aspects of e-retailing and suggested that a successful e-retailing model should integrate simple information search, numerous communication channels, and safe trading and transaction processes. Cataldo et al. [17] has highlighted the importance of a highly integrated e-retailing application and a robust organizational operating system. Edghiem et al. [11] point out the crucial role of business networks in creating value. They have observed that e-retailers operate within highly interconnected business ecosystems that extend beyond their own organizational boundaries. Recently, Zhang et al. [19] emphasize the impact of key factors including responsiveness, personalization, ease of use, aesthetics, and perceived risk on the success of e-retailing businesses. 2.2. Information sharing in e-retailing Information disclosure through technology integration is a practice of sharing relevant business information with stakeholders to ensure transparency and build trust. Apple Inc. shares its annual environmental report to expose customers to its carbon footprint and sustainability efforts. Similarly, Tesla shares its quarterly earnings reports that provide insights into its financial performance and future plans. Green information disclosure efforts significantly impact consumer behavior by improving environmental awareness and promoting informed purchasing choices. According to the theory of planned behavior (TPB), consumer intentions to buy sustainable products are shaped by their attitudes, subjective norms, and the perceived behavioral control. Here, the environmental disclosure acts as a key factor in rationalizing behavioral decisions. Further, the Stakeholder theory highlights the mediating role of sustainability reporting in fostering stakeholder participation and improving sustainable information transfer [20]. In addition, the legitimacy and resource dependency theories emphasize that environmental reporting enhances corporate image of the firm, its legitimacy, and the consumer trust on the firm [21]. Now a days, increasing environmental consciousness is altering the preferences of consumers, placing more emphasis on sustainability and ethical manufacturing and delivery through e-retail channels. This transition requires clear and open communication about the green production and delivery practices. Customized advertising on technology platforms such as social media and Blockchain enables firms to directly convey their environmentally friendly activities, informing and involving customers in their efforts to reduce carbon emissions by using green technologies [22]. This not only cultivates customer loyalty but also broadens consumer demographics and stimulates demand for eco-friendly goods. However, the effectiveness of this communication relies on an efficient supply chain that guarantees product availability and fulfills consumer expectations. Therefore, environmentally responsive manufacturers and retailers including P&G, IKEA, and Walmart have expanded their operations from physical to digital platforms in response to the growth of e-commerce and are using AI-powered tools and IoT-based tracking systems. The online platform provides enhanced flexibility in response to consumer demands with regards to pricing, quality, selection, and convenience. The study conducted by Li et al. [23] explains that retailers operating in online settings have significantly improved demand related information capabilities due to considerable investments in information disclosure technology. Wei et al. [24] suggests that the retailers should be motivated to communicate sensitive demand information to the product suppliers to increase the green supply chain efficiency. The research conducted by Shang et al. [25] verify the sound impact that information sharing puts on supply chain decisions. In particular, Wang and Zhuo [26] states that retailers who possess advanced market intelligence can effectively negotiate more advantageous supply contracts and transaction terms with their suppliers by exchanging demand information. Cai et al. [27] have observed that the retailer’s choice of approach for disclosing information under voluntary information disclosure depends on the offered product price and the degree of greenness. Sarkar et al. [12] has focused on the impact of upstream asymmetric information and the bullwhip effect on profit and customer satisfaction under sustainable delivery practices like advanced transportation and automated inspection for defect management, but they ignored downstream information sharing. They demonstrated that information sharing among supply chain players enhances profits and reduces losses from information asymmetry with numerical examples validating these findings. Recently, Liu et al. [28] have examined the role of advertisement on supply and retail performance of the commodity products. Taking into account the positive effects of social media marketing in disseminating information regarding the environmentally conscious production of products to consumers and the subsequent rise in product demand, we consider IDT investment in advertisement of multi-product’s green manufacturing initiatives to the customers. Operations Research Perspectives 14 (2025) 100328 4 M. Tayyab et al. Table 1 Major contribution of the research. Author(s) Model type Advertisement investment Product type Product demand Production system Production delivery policy Product shortages Technology investment for emissions control Solution methodology Kang et al. [33] Nonintegrated production No Single-item Constant Smart SSSD Not allowed No Analytical optimization Sarkar et al. [34] Supply chain management No Single-item Constant Traditional SSMD Not allowed No Analytical optimization Taleizadeh et al. [35] Vendor managed inventory No Single-item Uncertain Traditional SSSD Partially backordered No Analytical optimization −heuristic Sana [36] Newsvendor No Single-item Price and emissions control efforts dependent Traditional SSSD Not allowed Yes Analytical optimization Sadeghi et al. [8] Integrate vendor–buyer No Single-item Constant Traditional SSMD Fully backordered No Analytical optimization −heuristic Dey et al. [37] Integrate vendor–buyer Yes Single-item Advertisement dependent Smart SSSD Fully backordered No Analytical optimization Tayyab et al. [38] Nonintegrated production No Single-item Constant Traditional SSSD Fully backordered No Analytical optimization Kar et al. [39] Nonintegrated production Yes Multi-item Price and advertisement dependent Smart SSSD Not allowed Yes Analytical optimization Umar et al. [7] Supply chain management No Single-item Constant Traditional SSMD Not allowed No Metaheuristic Saxena et al. [10] Integrate vendor–buyer No Single-item Random Smart SSSD Not allowed No Analytical optimization Datta et al. [40] Dynamic retailing model Yes Single-item Advertisement dependent Traditional NA Not allowed No Analytical optimization Morshedin et al. [41] Coordinated supply chain Yes Single-item Constant Demand Traditional SSSD Not allowed No Metaheuristic Sebatjane and Adetunji [42] Integrated production model No Single-item Price and freshness dependent Traditional SSSD Not allowed No Iterative procedure Sasanuma et al. [43] Retailer cost reduction No Multi-item Random demand Traditional SSSD Allowed No Analytical optimization Nobil et al. [44] Vendor economic decision No Single-item Constant demand Traditional SSSD Allowed No Analytical optimization This study Integrated manufacturer– retailer Yes Multi-item Price and advertisement dependent Smart SSMD Fully backordered Yes Analytical optimization −Metaheuristic 2.3. Multi-shipment policy Multi-shipment policy is a production and delivery strategy that allows manufacturers to produce the goods in a single-setup but deliver it in multiple shipments to improve logistics efficiency. Zara’s multi-shipment approach for international orders to optimize shipping costs and delivery times is one of the successful implementation of this strategy. The inventory management solutions such as Vendor Managed Inventory (VMI) and Single-Setup-Multi-Delivery (SSMD) policy play a key role in optimizing production and delivery strategies by ensuring timely deliveries and reducing the possibility of shortages. Ben-Daya et al. [29] presented a three-layer integrated supply chain model considering SSMD policy. Their research outcomes verified economic benefits of SSMD policy over the SSSD policy. Sarkar and Chung [30] presented a mathematical model to minimize total cost of a flexible manufacturing system. The research objective was to reduce system cost in the situations where demand during the lead time is considered as following a normal distribution. The experimental results verified the importance of making technology investments in developing a flexible manufacturing system by understanding its impact on total cost of the complete system. They implemented a classical optimization method along with a heuristic approach to derive exact and approximate solutions for the model variables. The sensitivity analysis indicated that their study has achieved lowest cost by optimizing the decision variables under the presence of technology investments and SSMD policy. A recent study conducted by Mridha et al. [31] seeks to enhance the efficiency of a multi-layer sustainable supply chain model by specifically addressing control of carbon emissions and maximizing profitability of the system under SSMD policy. They presented a smart manufacturing system that incorporates a model consisting of a single manufacturer, a single supplier, and multiple retailers. Their model effectively reduces imperfect production and carbon emissions by implementing a two-stage inspection policy, flexible production rate strategy, and selling prices based on demand. Their experimental results show positive environmental and economic impacts. Jauhari et al. [32] has developed an integrated inventory model for a supply chain involving a vendor and a buyer by accounting for stochastic demand, imperfect production, and a hybrid system combining regular and green production. By optimizing factors including shipment quantity, production allocation, and defect rate, their model minimizes supply chain costs while balancing environmental impact and production efficiency. However, they did not consider multi-shipment policy to minimize transportation costs Operations Research Perspectives 14 (2025) 100328 5 M. Tayyab et al. of the system. Chen et al. [45], Sarkar et al. [46], and Kang et al. [33] are among several other researchers who implement SSMD policy under manufacturer–retailer integrated supply chain management. Given the economic benefits of SSMD production delivery policy within a coordinated e-retailing, we incorporate this policy in the proposed sustainable integrated model to improve profitability of the system. 2.4. Green technology integration Green technology integration is the process of incorporating eco-friendly technologies into business processes to reduce its environmental impact. For instance, IKEA uses solar panels technology and energy-efficient lighting in its stores to reduce energy consumption, and Patagonia has adopted recycled materials in the clothing production. Technology investments mark outstanding contribution to improving global economy through effectively reducing carbon emissions in the global supply chains. As customer environmental awareness grows, manufacturers’ competition no longer just dependent on profits. It also includes their environmental performance. Thus, global production and retailing industries need carbon emissions reduction strategies and low-carbon product pricing. Song et al. [47] provided a multi stage stochastic optimization model to examine logistics capacity increase under various carbon emissions legislations. They showed that capacity investment cost volatility affects optimal capacity expansion decisions more than production cost for low and high carbon tax rates. Ganda [48] examined how innovation and technology investments affected Organization for Economic Co-operation and Development member nations’ carbon emissions from the year 2000 to 2014. Their analysis verified that renewable energy integration and R&D spending have a statistically significant negative correlation with the greenhouse gas emissions. They suggested that incorporating environmental responsibility in patents and training researchers in green skills may help them meet zero-emission ambitions. Sana [36] investigated a price competition between environmentally friendly and non-environmentally friendly manufacturers, taking into account product demand influenced by sales price, investments in technology for reducing carbon emissions, and corporate social responsibility index. Their results suggested continuous investments in greenhouse gas emissions reduction and consumer awareness may increase product demand in the longer run. Bose et al. [9] and Sarkar et al. [49] developed online-to-offline retailing models to optimize pricing, advertising strategy, customer care efforts and investment decisions to increase profit under the consideration of budget and space constraints, respectively, but they ignored green technology investments. Their research findings highlight that offering free home delivery and managing defective rates effectively can significantly enhance profitability of the system. Recently, Kang and Tan [50] have utilized an evolutionary-based model to investigate the technology investment choices made by suppliers and product manufacturers in a supply chain management under carbon cap-and-trade emissions control policy. They studied the fact that how revenue and cap-and-trade-related factors affect green technology investment choices. Their research provides insights for policy makers on how to handle the interplay between these investments and resulting revenues. Jauhari et al. [51] has developed a mathematical model for a closed-loop supply chain involving a manufacturer and retailer in different countries by considering stochastic conditions, imperfect production, and carbon emissions. By incorporating a carbon tax policy and green technology investments, their model aims to minimize total costs while addressing key factors like exchange rate uncertainty, production defectives and delivery decisions. Jauhari et al. [52] focused on minimizing emissions in a supply chain involving a vendor and a buyer by addressing carbon regulations through green technology investments, supported by government incentives and carbon tax policies. Their proposed model optimizes operational decisions and green investments to reduce costs and emissions, demonstrating improvements in both economic and environmental performance. However, they did not consider the impact of green investments on consumer demand through green information sharing. Given the technology investment benefits for environmental protection, our research incorporates technology investments for green emission reduction technology (GERT) as a strategic choice. 2.5. Smart production system Smart Production System is an advanced manufacturing system that uses automation, IoT, and data analytics to adjust production rates in order to enhance efficiency and productivity. For instance, Siemens uses digital twins to simulate and optimize production processes, and Tesla has fully automated its Gigafactories for electric vehicle manufacturing. Being able to adjust the production rates in a smart production system in accordance with the changes in demand and delivery time requirements is an essential factor that impacts manufacturing costs. Such smart production system can address issues associated to the random, uncertain and sometimes unpredictable characteristics of the market demand, and the resulting shortages. In this direction, Khouja and Mehrez [53] provided a method for determining the optimal lot size using Economic Production Quantity (EPQ) by considering both variable production rates and the dependent unit production costs. The production cost was taken into account as a function of the changes in production rate using that approach. This approach enables even more rigorous investigation of the cost components related to the production systems by taking in both flexibility of production rates and its impact on unit production cost. Further, several other researchers including AlDurgam et al. [54], and Sarkar and Chung [30] have implemented a similar type of approach by considering variability in the production rates to derive optimal inventory management policies to improve profitability of the whole production delivery system. Dey et al. [37] have considered the impact of flexible production rate on economic performance of the supply chain by incorporating the advantages of reducing lead time across various situations. The equation presented by them shows a precise relationship between total cost and lead time, indicating that the cost savings from reducing lead time drop as lead time increases. They research outcomes suggest making continuous investments to improve the reliability of the production process. Sadeghi et al. [8] provided an integrated inventory model with shortages to minimize system cost without considering flexible production rate. Recently, Kar et al. [39] presented a dual-channel advertisement and pricing model for multiple manufacturers and retailers while ignoring product shortages. They incorporated flexible production rate in their model and proved that such policy provides better economic benefits in comparison to the traditional fixed production rate systems. To acquire an in-depth understanding of how variable production rates impact the performance of inventory management systems, it is advised that interested readers refer to the research conducted by Glock and Grosse [55] as their study offers a comprehensive appreciation of this impact. Considering aforementioned discussion and analysis of the literature, we consider flexible production rate and planned backorders in our proposed sustainable integrated inventory model for a manufacturer and retailer coordinated system. Fig. 2presents the graphical illustration of the proposed study and Table 1presents contribution of this study. Operations Research Perspectives 14 (2025) 100328 6 M. Tayyab et al. Fig. 2. Graphical representation of the proposed collaborative e-retailing model. 3. Problem definition, notation, and assumptions This research proposes a sustainable multi-item integrated model to maximize total profit for the manufacturer–retailer coordinated decisionmaking under online sales mechanism. Within this collaborative system, a controllable production rate (𝑃𝑖∈ {𝑃𝑖,𝑚𝑖𝑛 −𝑃𝑖,𝑚𝑎𝑥}) for the manufacturer [38] is considered to take advantage of a smart production system in making production-delivery decisions under price and advertisement dependent product demand. The manufacturer invests in green emissions reduction technology (GERT) in his production system and the retailer invests in advertisement in the form of information disclosure technology (IDT) to communicate the emissions control efforts of the system to the customers in order to enhance product demand. Product demand is taken as a function of product price and advertisement efforts of the retailer. We use the dependent demand function as 𝐷𝑖=𝛥𝑖−𝛾𝑖𝑝𝑖+𝜓𝑖𝜂𝑖, where 𝛥𝑖is the initial market size of product type-𝑖,𝛾𝑖is the price sensitivity, and 𝜓𝑖is IDT sensitivity. Similar type of demand function has been utilized by Umar et al. [7] and Kar et al. [39] in their manufacturer–retailer optimization models. The e-retailer receives annual product-𝑖demand of 𝐷𝑖units and the manufacturer delivers products to the retailer in multiple equal shipments using SSMD policy, where the ordered lot size is 𝑄𝑖=𝑛𝑖𝑞𝑖. In this way, inventory holding cost of the retailer is reduced while compromising on the product transportation cost. We consider discrete IDT investment of 𝜂𝑖=𝛼𝑖𝑊𝑖,𝑇 𝑒𝑐 ℎ, where 𝛼𝑖is the proportion of discrete technology invesmtnet budget 𝑊𝑖,𝑇 𝑒𝑐 ℎallocated for product type-𝑖. The manufacturer invests in GERT technology to reduce the carbon emissions of the system during production. We consider a similar discrete GERT investment function of type 𝐸𝑖=𝛽𝑖𝑊𝑖,𝑇 𝑒𝑐 ℎ, where 𝐸𝑖is the GERT investment for product type-𝑖, and 𝐸𝑖=𝛽𝑖𝑊𝑖,𝑇 𝑒𝑐 ℎ. It is worth noting that 𝛼𝑖+𝛽𝑖= 1. The impact of discrete GERT investment on greenhouse gas emissions mitigation is incorporated as 𝐺𝑖=𝜆𝑖(1 −𝑒−𝜌𝑖𝐸𝑖)=𝜉𝑖𝑒−𝜌𝑖𝐸𝑖, where 𝐸𝑖is GERT investment, and 𝜌𝑖is its efficiency as a scaling parameter. Further, 𝜆𝑖is the savings in emissions due to GERT. It is to be noted that when 𝐸𝑖→∞, then 𝐺𝑖=𝜆𝑖, and when 𝐸𝑖= 0, then 𝐺𝑖= 0. Similar type of investment function has been implemented by Kar et al. [39] for greenhouse gas emissions reduction. A planned backorder strategy is introduced in the system to compensate the shortages originated in the smart integrated system. Fig. 3presents inventory behavior of the sustainable integrated system at manufacturer and retailer. We develop two major case in the proposed model. Case I develops a non-capacitated integrated model before advertisement and emissions control efforts which is solved through a combination of analytical optimization technique and a proposed heuristic approach. Further, Case II presents a capacitated sustainable integrated model with technology investments for advertisement and emissions control which is solved through a metaheuristic approach to identify the optimal advertisement and emission control policy under the flexible production rate. The proposed model cases are validated through numerical experiment and analysis to infer significant managerial insights. 3.1. Notation Below notation are utilized for the proposed model formulation and analysis. Indices 𝑖index for product type (𝑖= 1,2,3...𝑦) 𝑚 index for the vendor/manufacturer 𝑟 index for the retailer Decision Variables 𝑝∗ 𝑖Optimal online selling price of product type-𝑖($ per item) 𝑄∗ 𝑖Optimal batch quantity (items) 𝑞∗ 𝑖Optimal shipment quantity per shipment (items) 𝐵∗ 𝑖Optimal backorder quantity (items) 𝑃∗ 𝑖Production rate for product type-𝑖) (items per year) 𝑊∗ 𝑖,𝑇 𝑒𝑐 ℎOptimal technology investments ($) 𝛼∗ 𝑖Percentage of 𝑊∗ 𝑖,𝑇 𝑒𝑐 ℎallocated to IDT (percentage) Operations Research Perspectives 14 (2025) 100328 7 M. Tayyab et al. 𝛽∗ 𝑖Percentage of 𝑊∗ 𝑖,𝑇 𝑒𝑐 ℎallocated to GERT (percentage) 𝑋[ ]𝑡Decision vector of this paper Parameters 𝐷𝑖Retailer’s estimated demand for product−𝑖(items per year) 𝑇𝑖The cycle time for product type_𝑖(years) 𝑇1𝑖Maximum inventory consumption time (years) 𝑇2𝑖Time for which system faces shortages (years) 𝑇3𝑖Time to compensate the product shortage (years) 𝑇4𝑖Time for inventory fulfillment (years) 𝑡𝑖Time interval among successive deliveries (years) 𝐾𝑖Setup cost per setup ($ per setup) ℎ𝑖Inventory holding cost ($ per item per unit time) 𝑏𝑖Fixed backorder cost ($) 𝑔𝑖Variable backorder cost ($ per item) 𝛿𝑖Batch transportation cost ($ per item) 𝐶𝑖𝑣 Cost of purchasing and processing virgin raw material ($ per item of raw-material) 𝐶𝑖𝑟 Cost of incentive and processing returned material ($ per item of raw-material) 𝜃𝑖Percentage of 𝐷𝑖fulfilled through remanufacturing (percentage) 𝐼𝑖,𝑚𝑎𝑥 Maximum attainable inventory level for product type-𝑖(items) 𝑛𝑖Number of deliveries per cycle for product type_𝑖(number) 𝑑𝑖Initial market size of product type-𝑖(items per year) 𝑢𝑖Scaling parameter for the order processing cost with respect to flexible production rate (number) 𝑣𝑖Shape parameter for the order processing cost with respect to flexible production rate (number) 𝛾𝑖Sale price sensitivity of market demand (number) 𝜓𝑖IDT investment sensitivity (number) 𝜆𝑖Savings in 𝐶 𝑂2emissions through GERT investment (units per item) 𝜉𝑖𝐶 𝑂2emissions per item during processing (units per item) 𝜉𝑖,𝐶 𝑂2Emissions cost per unit of emissions ($ per unit) 𝑧𝑖Storage space required for one item type-𝑖(cubic units) Expressions 𝑇 𝑃𝑖,𝑤𝑜𝑡 Profit function for product type-𝑖in Case-I ($ per unit time) 𝑇 𝑃𝑤𝑡 Profit function for sustainable multi-item in Case-II ($ per unit time) 3.2. Assumptions We use below set of assumptions for the proposed sustainable integrated production delivery model formulation. 1. The proposed study considers a single-manufacturer single-retailer integrated system for production and delivery of multi-items under e-retailing. 2. A dependent product demand that is sensitive to the product price and IDT advertisement investments is considered in this research as 𝐷𝑖=𝛥𝑖−𝛾𝑖𝑝𝑖+𝜓𝑖𝜂𝑖, where 𝛥𝑖is the initial market size of product type-𝑖,𝛾𝑖is the price sensitivity, and 𝜓𝑖is IDT sensitivity [4]. 3. A smart production system is considered where the production rate for each product type-𝑖can be varied within the interval {𝑃𝑖,𝑚𝑖𝑛 −𝑃𝑖,𝑚𝑎𝑥] in response to the fluctuations in online product demand for the retailer [38]. 4. In order to determine an optimal trade-off among inventory holding cost and batch transportation cost, an SSMD policy is implemented in this research where the manufacturer ships the product in smaller batches to the e-retailer’s warehouse [30]. 5. Shortages are allowed in this study and are fully backordered in the proposed sustainable integrated system, where both of the fixed and variable portions of backorder cost are considered. 6. Products are made with virgin and returned material, where pre-defined 𝜃𝑖percentage of the online demand for product type-𝑖is fulfilled using return products as a raw material. 7. Initial delivery of each product type-𝑖(𝑖= (1,2,3,…, 𝑛)) takes place at time 𝑡= 0. 8. The successive production cycles are identical in nature. 4. Mathematical model Analytical derivation of the proposed sustainable integrated model is initiated by determining the size of individual shipment to the e-retailer’s warehouse. The manufacturer produces a quantity 𝑞𝑖=𝑃𝑖𝑡𝑖over the time interval 𝑡𝑖and the retailer receives 𝐷𝑖𝑇𝑖units of demand from the market during this time period. If the warehouse inventory of the retailer is enough, this demand will be met and otherwise the shortage will occur. Hence, given the 𝑛𝑡ℎ 𝑖delivery, the consumed inventory over the last 𝑛𝑖− 1deliveries can be determined as (𝑛𝑖− 1)𝐷𝑖𝑡𝑖. As the batch size is 𝑄𝑖=𝑛𝑖𝑞𝑖, the maximum quantity for the retailer can be obtained from Fig. 3as 𝐼𝑖,𝑚𝑎𝑥 =𝑛𝑖𝑞𝑖− (𝑛𝑖− 1)𝐷𝑖𝑡𝑖−𝐵𝑖, =1 𝑃𝑖[𝐷𝑖𝑞𝑖−𝐵𝑖𝑃𝑖−𝐷𝑖𝑄𝑖+𝑃𝑖𝑄𝑖].(1) Operations Research Perspectives 14 (2025) 100328 8 M. Tayyab et al. Table 2 Input data for numerical experiments. Parameter Value Parameter Value 𝑦3𝑐𝑣𝑖 [50 60 40] \$∕item 𝛥𝑖[1000 1400 800] units∕year 𝑐𝑟𝑖 [40 50 30] \$∕item 𝛾𝑖[5 3 4] units 𝑣𝑖[90 90 90] 𝑃𝑖,𝑚𝑖𝑛 [1500 1800 1200] units∕year 𝑍𝑟1950 units3 𝑃𝑖,𝑚𝑎𝑥 [2200 2500 1800] units∕year 𝑢𝑖[0.02 0.01 0.02] 𝜓𝑖[0.03 0.015 0.02] units 𝑘𝑖[100 150 80] \$∕setup 𝜂0.40 percent 𝜌𝑖[0.012 0.021 0.009] units 𝑔𝑖[45 50 40] \$∕item∕year 𝛿𝑖[10 8 13] \$∕batch ℎ𝑖[20 20 20] \$∕item∕year 𝑧𝑖[4 4 4] units3 𝜃𝑖[0.25 0.30 0.20] percent 𝑊𝑟3000 ($) Table 3 Optimal solution for Case I. Model type Optimal solution Model type Optimal solution 𝑛, 𝑞∉Int. 𝑞∗33.5 𝑛, 𝑞∈Int. 𝑞∗27 𝐵∗10.49 𝐵∗10.60 𝑝∗134.46 𝑝∗134.60 𝑛∗2.31 𝑛∗3 𝑇 𝑃∗ 𝑤𝑜𝑡 20,749.75 𝑇 𝑃∗ 𝑤𝑜𝑡 20,742.60 Fig. 4. Behavior of the objective function under variations in decision variables for Case I. 6.2. Computational outcomes and discussion The proposed model Case I without technology investments for IDT and GERT is solved through hybrid methodology for product type-1 presented in Section 5. Remark 1. A traditional production system with fixed production rate of 𝑃𝑜= 2000 units per year generates a profit of $19,133.8 per unit time with optimal values of the decision variables as 𝑞∗= 36.68 units, 𝑛∗= 1.96 shipments, 𝑝∗= $137.225 per unit, and 𝐵∗= 9.28 units. However, for a smart production system, varying the production rate with appropriate step size within the interval 𝑃∈ {𝑃𝑚𝑖𝑛 −𝑃𝑚𝑎𝑥}generates a superior solution at 𝑃= 1500 units per year. The optimal solution for this smart production system in this case is 𝑞∗= 33.50 units, 𝑛∗= 2.31 shipments, 𝑝∗= $134.46 per unit, 𝐵∗= 10.49 units, and the total profit of $ 20,749.75 per unit time. One can notice a 8.44% improvement in the system profit in this case by transforming a fixed system into a smart production system. Hence, we consider smart production systems with 𝑃∗= 1500 for making further analysis. As indicated earlier, the analytical solution approach for the proposed smart integrated production management model does not guarantee integer solutions for the optimal shipment size (𝑞∗) and number of shipments (𝑛∗). Hence we apply further steps (Step VI −Step XI) of the proposed heuristic to determine integer solution of these variables in order to satisfy 𝑞∗∈𝐼 𝑛𝑡𝑒𝑔 𝑒𝑟𝑠 and 𝑛∗∈𝐼 𝑛𝑡𝑒𝑔 𝑒𝑟𝑠.Table 3presents a comparative analysis of the integer and non-integer solutions. A reduction of $7.15 per unit time in optimal profit of the system is observed to compensate the integer solution requirements in devising optimal shipment size and number of shipments. Fig. 4illustrates the concavity of profit maximization objective presented in Case 1 for different values of the decision variables as proved in Section 5through analytical optimization technique. The proposed multi-item constrained integrated model in Case II is solved through a GA-supported metaheuristic approach presented in Section 5.Table 4presents optimal solution for the proposed model under capacity limitation and technology investments for advertisement (IDT) and emissions control (GERT), and Fig. 5shows an instance of a GA-supported solution algorithm. One can observe that the optimal solution for Case II presented in Table 4develops a wise trade-off among technology investments for information disclosure technology and green emissions reduction technology while satisfying the capacity limitations. Operations Research Perspectives 14 (2025) 100328 15 M. Tayyab et al. Table 4 Optimal solution for Case II under capacity limitation and technology investments. Item type 𝑞∗ 𝑖 (units) 𝐵∗ 𝑖 (units) 𝑃∗ 𝑖 (units per year) 𝑊∗ 𝑖,𝑡𝑒𝑐 ℎ ($) 𝛼∗ 𝑖 (%) 𝛽∗ 𝑖 (%) 𝑝∗ 𝑖 ($ per unit) 𝑛∗ 𝑖 (number) 𝑇 𝑃∗ 𝑤𝑡 ($ per unit time) 1 55.59 63.50 1500 1200.00 0.84 0.16 136.47 5.28 $ 144,757.292 31.04 0.00 1800 156.46 0.00 1.00 280.78 5.13 3 37.07 14.66 1200 156.37 0.00 1.00 126.75 3.06 Fig. 5. Solution algorithm implementation for Case II on MATLAB. Table 5 Optimal solution for Case II under capacity constraint without technology investments. Item type 𝑞∗ 𝑖(units) 𝐵∗ 𝑖(units) 𝑃∗ 𝑖 (units per year) 𝑊∗ 𝑖,𝑡𝑒𝑐 ℎ($) 𝛼∗ 𝑖(%) 𝛽∗ 𝑖(%) 𝑝∗ 𝑖($ per unit) 𝑛∗ 𝑖(number) 𝑇 𝑃∗ 𝑤𝑡 ($ per unit time) 1 20.19 8.33 1500 0 0 0 134.68 3.69 $ 139,375.392 21.59 0 1800 0 0 0 284.55 4.44 3 35.44 0 1200 0 0 0 127.89 1.54 Remark 2. Technology investments IDT and GERT are considered in Case II of the proposed model under capacity constraints. Analysis of the model outcomes under capacity constraints and no technology investments scenario indicates an inferior solution as shown in Table 5. One can observe a decrease of $5,381.90 in case of no investments for technology integration, as the model without technology investments produce a maximum profit of $139,375.39 per unit time. Whereas, the model case with technology investments generates a profit of $144,757.29 per unit of time. This substantiates a constructive account of technology investments for improvements in system profitability. Remark 3. For a non-capacitated scenario under Case II with technology investments for IDT and GERT, the model generates a superior solution in comparison to the capacitated model with and without technology investments. Table 6shows optimal solution for this case, where the model attains maximum profit of $145,507.33. It is evident from the model solution of this case that a trade-off among capacity expansion cost and technology investment efficiency is crucial for economic advancement of the production system. The managers can identify a level of capacity expansion for which the following inequality holds. New revenue after capacity expansion −Capacity expansion cost −Additional technology investment Current revenue with no capacity expansion ≥1,(33) where capacity expansion cost is calculated as units of increment in capacity times per unit increment cost. We utilize Eq. (33) to identify optimal capacity level for Case II the proposed model under technology investment. Fig. 6presents maximum capacity level of the system as 2805 units for which system profit attains maximum value of $145,507.33. Any further incremental capacity under the current parametric information and technology investment budget is surplus for the system. Operations Research Perspectives 14 (2025) 100328 16 M. Tayyab et al. Table 6 Optimal solution for Case II under technology investments and no capacity limitation. Item type 𝑞∗ 𝑖 (units) 𝐵∗ 𝑖 (units) 𝑃∗ 𝑖 (units per year) 𝑊∗ 𝑖,𝑡𝑒𝑐 ℎ ($) 𝛼∗ 𝑖 (%) 𝛽∗ 𝑖 (%) 𝑝∗ 𝑖 ($ per unit) 𝑛∗ 𝑖 (number) 𝑇 𝑃∗ 𝑤𝑡 ($ per unit time) 1 55.59 63.5 1500 1200 0.84 0.16 136.47 5.28 $ 145,507.332 44.71 43.34 1800 1200 0.86 0.14 283.89 8.56 3 37.06 14.66 1200 156.37 0 1 126.75 3.06 Fig. 6. Maximum capacity level for Case II under technology investment. Fig. 7. Comparison of the proposed study with existing research in the literature. 6.3. Comparison with existing studies in the literature In this section, we compare the numerical results of proposed model with the existing studies in the literature. If IDT and GERT investments, smart production system, multi-item production delivery mechanism, and green emissions reduction efforts-dependent demand are ignored, then our study reduces to Sadeghi et al. [8]. Our proposed model further reduces to Sarkar et al. [58] if multi-shipment policy and manufacturer–retailer collaborative decision making are also ignored. Sadeghi et al. [8] proposed a mathematical model to optimize total cost of a single-manufacturer single-retailer supply chain by considering multi-shipment policy. However, they ignored technology investments to reduce environmental impact of the supply chain and improve product demand. Further, they considered traditional production system with constant production rate to produce a single-type of product with constant market demand. Their numerical results provided by their proposed model generated a minimum cost of $4321.91. Our model provides a minim cost of $4039.26 with the similar data set and considering IDT and GERT investments for emissions reduction to fulfill the environmental awarenessbased consumer demand. This provides a 6.54% cost savings, which illustrates the superiority of the proposed model. Moreover, Sarkar et al. [58] presented a single-stage production model with random defective rate by considering fully backordered shortages. However, they ignored the environmental impact and multi-shipment policy in their model. The numerical experiment of their model presented a minimum cost of $3078.10 where the random defective rate follows a beta distribution. Our model provides a minimum cost of $2820.16 for the similar parametric information and the consideration of green technology integration for emissions reduction. This demonstrates a cost saving of 8.37% in comparison to the production model provided by Sarkar et al. [58]. Fig. 7illustrates the superiority of the proposed model in comparison to the existing studies in the literature. 6.4. Impact of technology investment for advertisement and emissions control Case II of the proposed integrated production model considers technology investment for IDT and GERT. Fig. 8shows the impact of allocated technology investment budget on overall profitability of the system following diminishing return on investment. We observe the variation in distribution of the technology investment budget among IDT and GERT by varying 𝛼𝑖, and among different product types by varying 𝜂𝑖within the interval [0,1] for Case II. Fig. 9presents an interplay between 𝛼,𝛽, and expected profit of the system and Fig. 10 illustrates the impact of variation in 𝜂𝑖on total profit of the system. One can observe that the variation in maximum allowed proportion (𝜂𝑖) of technology budget to the product type-𝑖has a direct impact on profitability of the system. As we reduce the limit of distribution of maximum available technology investment budget from 𝜂𝑖= 80% (∀ 𝑖, 𝑖= (1,2,3)), total profit of the system reduces. However, any such limitation above this value (𝜂𝑖≥80%) shows no improvement in the profit above $146,369.13 per unit time. Therefore, the managers should pay close attention to the interplay between allocated investment budget amount and its distribution strategy among different aspects of the production system while focusing on system profitability. Operations Research Perspectives 14 (2025) 100328 17 M. Tayyab et al. Fig. 8. Impact of technology investment budget on system profitability for Case II. Fig. 9. Impact of technology investment budget distribution (𝛼 , 𝛽) on system profitability for Case II. Fig. 10. Impact of technology investment budget distribution (𝜂) on system profitability for Case II. Operations Research Perspectives 14 (2025) 100328 18 M. Tayyab et al. Fig. 11. Impact of price sensitivity and technology investment efficiency for advertisement on system profit for Case II. Table 7 Comparison of model outcomes for SSSD and SSMD policy for Case I. Production delivery policy Optimal solution Production delivery policy Optimal solution SSSD policy 𝑞∗64.64 SSMD policy 𝑞∗27 𝐵∗10.83 𝐵∗10.60 𝑝∗135.00 𝑝∗134.60 𝑛∗1𝑛∗3 𝑇 𝑃∗ 𝑤𝑜𝑡 20,648.58 𝑇 𝑃∗ 𝑤𝑜𝑡 20,742.60 6.5. Impact of advertisement efficiency The level of advertising expenditure relies primarily on how effective a company’s advertising efforts are in terms of reaching and influencing the target audience through the chosen advertising channels. Advertising firms define their target audience and then suggest spending plans for advertising Sarkar and Dey [4]. Therefore, managers of production systems should carefully examine the interaction between the incremental gains obtained from advertising activities across various channels. Managers may strategically choose the most beneficial channel by carefully evaluating the incremental benefits associated with each option and selecting the one with the most incremental benefit. Remark 4. In the proposed model, we consider a pre-determined advertisement channel with advertisement efforts efficiencies of 𝜓𝑖= 0.03, 𝜓2= 0.015, and 𝜓3= 0.02 for product type 1,2, and 3, respectively. Adoption of this advertisement policy as IDT generates a profit of $144,757.29 per unit time, which is higher than the no-advertisement case presented in Remark 2(with a profit of $139,375.39 per unit time). Now we examine the impact of −50% to +50% variation in the advertisement efficiencies of all product types under this channel on expected profit of the proposed multi-item integrated system (see Fig. 11). It is observed that 25%, and 50% reduction in advertisement efficiency tends to reduce the system profit by 3.77% and 11.89%, respectively. However, 25%, and 50% increase in advertisement efficiency improves the profit of the system by 7.41% and 22.65%, respectively. This verifies the importance of putting efforts in improving the advertisement efficiency constants for the system. 6.6. Impact of product selling price sensitivity of consumer market Selling price sensitivity parameter (𝛾𝑖) plays a crucial role in limiting the maximum selling price asked for the product type-𝑖. The interaction between initial market size and the product selling price sensitivity of the consumer market (𝛥𝑖∕𝛾𝑖) puts an upper bound on maximum asking price of the product. Product selling price sensitivities for each product type in the proposed model are initially set at 𝛾1= 5,𝛾2= 3, and 𝛾3= 4; resulting in the per unit time profit of $144,757.29. Making a 25%, and 50% simultaneous reduction in product price sensitivity of all the product types tend to improve the system profit by 36.66% and 64.07%, respectively. Whereas, 25%, and 50% increase in these reduce the profit by 32.72% and 53.44%, respectively (see Fig. 11). 6.7. Comparison with SSSD policy The proposed integrated model suggests SSMD policy to make a trade-off between setup cost, inventory holding cost, and transportation cost. We implement SSSD policy for Case I and Case II by strictly limiting 𝑛𝑖= 1and observe the variation in system profit (see Fig. 12). Tables 7and 8 present a comparative analysis between SSSD and SSMD policy implementation for Case I and Case II, respectively. For a model with SSSD policy implementation, we can observe that the system profit reduces by $94.02 for Case I and $1535.83 per unit time for Case II. This analysis verifies the superiority of SSMD policy adoption over the prior one as supported by the recent research including Sarkar et al. [57], Sadeghi et al. [8], and Umar et al. [7]. Operations Research Perspectives 14 (2025) 100328 19 M. Tayyab et al. Table 8 Comparison of model outcomes for SSSD and SSMD policy for Case II. Production delivery policy Item type 𝑞∗ 𝑖 (units) 𝐵∗ 𝑖 (units) 𝑃∗ 𝑖 (units per year) 𝑊∗ 𝑖,𝑡𝑒𝑐 ℎ ($) 𝛼∗ 𝑖 (%) 𝛽∗ 𝑖 (%) 𝑝∗ 𝑖 ($ per unit) 𝑛∗ 𝑖 (number) 𝑇 𝑃∗ 𝑤𝑡 ($ per unit time) SSSD policy 1 106.95 25.52 1500 154.92 0.00 1.00 133.39 1.00 $ 143,221.462 108.72 0.00 1800 138.33 0.00 1.00 281.99 1.00 3 85.07 13.47 1200 124.36 0.00 1.00 127.58 1.00 SSMD policy 1 55.59 63.50 1500 1200.00 0.84 0.16 136.47 5.28 $ 144,757.292 31.04 0.00 1800 156.46 0.00 1.00 280.78 5.13 3 37.07 14.66 1200 156.37 0.00 1.00 126.75 3.06 Fig. 12. Comparison of model outcomes for SSSD and SSMD policy adoption. Fig. 13. Optimal production delivery policy suggestion for Case I. 6.7.1. Optimal production delivery policy suggestion In this section, we analyze the impact of setup cost variation on the optimal production delivery policy suggestion for Case I. Fig. 13 illustrates the impact of setup cost on optimal policy. It is observed from this analysis that lower setup costs suggest SSSD as an optimal policy for the system. Whereas, a setup cost of $13.08 is a critical point, above which SSMD policy becomes feasible. The step-wise incremental behavior of 𝑛∗−curve in Fig. 13 indicates optimal breakdown of the batch size into specific number of shipments that maximizes the system profit. This analysis is completely in line with the observations of Ben-Daya et al. [29], Sarkar et al. [57], and Sadeghi et al. [8] that lower setup costs tend to reduce the average batch size and associated inventory holding cost of the production system which eradicates the need of SSMD policy. However, as the setup cost of the system increase to the critical point, the batch size and related inventory holding cost increase and the model suggests shifting from SSSD production delivery policy to SSMD policy. Similar type of policy suggestions can be devised for other parameters of the system. 6.8. Sensitivity analysis In this section, we examine the impact of variation in other key model parameters on total profit of the system for Case II. The parameter values are varied from −50% to +50% within equal intervals for each product type and the corresponding changes in total profit per unit time of the system are recorded. Table 9shows percentage change in total profit of the system for corresponding percentage changes in the model parameters. It is observed from the sensitivity analysis that any decrease in setup cost (𝑘𝑖), variable backorder cost (𝑏𝑖), inventory holding cost (ℎ𝑖), carbon emissions cost (𝜉𝑖), and batch shipment cost (𝛿𝑖) improves total profit of the system. Whereas, any decrease in percentage of returned products Operations Research Perspectives 14 (2025) 100328 20 M. Tayyab et al. Table 9 Sensitivity analysis of key model parameters. Parameter(s) Changes in parameter value Changes in system profit Parameter(s) Changes in parameter value Changes in system profit 𝑘𝑖 −50% +0.31% 𝜉𝑖 −50% +0.33% −25% +0.15% −25% +0.13% +25% −0.17% +25% −0.35% +50% −0.35% +50% −0.76% 𝑏𝑖 −50% +0.40% 𝛿𝑖 −50% +0.15% −25% +0.095% −25% +0.087% +25% −0.06% +25% −0.18% +50% −0.11% +50% −0.26% ℎ𝑖 −50% +1.139% 𝜃𝑖 −50% −1.08% −25% +0.56% −25% −0.54% +25% −0.49% +25% +0.54% +50% −0.91% +50% +1.08% Fig. 14. Sensitivity analysis of key model parameters for Case II. (𝜃𝑖) used in manufacturing reduces the total profit. One can see that the system profit is highly sensitive to ℎ𝑖and 𝜃𝑖, where 50% decrease in ℎ𝑖 improves the profit by 1.139% and the similar decrease in 𝜃𝑖reduces the profit by 1.08%. On the other hand, 50% increase in ℎ𝑖reduces the profit by 0.91% and the similar level of increment in 𝜃𝑖improves the profit by 1.08%. Any reduction in 𝑘𝑖and 𝜉𝑖induces similar level of increment in the profit, where 25% decrease in these variables increases the profit by 0.15% and 0.13%, and 50% decrease in these variables increases the profit by 0.31% and 0.33%, respectively. However, any increase in values of these variables show different effects on the profit, where 25% increase in these variables reduce the profit by 0.17% and 0.35%, and 50% increase in these variables reduces the profit by 0.35% and 0.76%, respectively. Fig. 14 presents a graphical representation of the changes in profit for these variations in key model parameters. 6.9. Managerial insights In this section, we devise significant managerial insights from the experimental outcomes and extensive analysis of the proposed integrated model that can support managers and decision makers in determining optimal production delivery policies for profit maximization under collaborative Operations Research Perspectives 14 (2025) 100328 21 M. Tayyab et al. e-retailing to improve consumer service. Research outcomes of the proposed model illustrate that converting a rigid manufacturing system into a smart one, capable of modifying output rates within a defined range, results in a significant 8.44% augmentation in the system’s profitability. Hence, the managers should contemplate using smart production systems, as seen in Case I, where modifying the production rate within the range 𝑃∈ {𝑃𝑚𝑖𝑛 −𝑃𝑚𝑎𝑥}led to a more optimum result. Upon analyzing Case II, it becomes evident that information sharing and technological investments (IDT and GERT) have a significant and favorable effect on the product demand and profitability of the system. The model that incorporates technological investments generates a profit of $144,757.29 per unit of time, whereas the profit without technology integration is $139,375.39. It is advisable for managers to allocate resources towards incorporating technology into their operations, namely for the sake of information disclosure and emissions reduction. This investment will ultimately improve the overall profitability of the system. This study verifies the significance of advertising effectiveness in impacting the profitability of the e-retailing system. A fluctuation in advertisement efficiency ranging from −50% to +50% directly correlates with fluctuations in system profit. Hence Managers should proactively focus on improving the efficiency constants of the advertising system in order to generate favorable effects on profitability. It is crucial to strike a balance between capacity and investment in technology for information disclosure. Analysis of the Case II in the proposed research emphasizes the significance of achieving a suitable equilibrium between capacity growth and technological investment in order to foster economic advancement. The most efficient approach, taking into account both limitations on capacity and expenditures in technology results in a maximum profit of $145,507.33. Managers should thoroughly assess this equilibrium, taking into account the expenses associated with expanding capacity and the effectiveness of investing in technology, in order to attain economic advancement in the production system. The research emphasizes the need of managers strategically distributing the monetary budget for technology investment between Information Disclosure Technology (IDT) and Green Emissions Reduction Technology (GERT). The correlation between the designated investment budget and its distribution across different components of the production system has a substantial impact on the overall profitability. Managers should prioritize increasing profitability by strategically allocating the technology budget among various product categories and technologies. 7. Conclusions A growing trend towards online shopping and environmental awareness is transforming consumer choices as they are now placing a strong emphasis on sustainability and environmentally friendly products they purchase. In order to deal with these environmentally conscious commitments, it is essential for the e-retailing industry to have effective communication with the consumers regarding the green practices of their production and retailing channels. Information technology platforms such as blockchain and social media offer efficient platforms for individualized advertising that can be used to educate the customers about the emissions control efforts put be manufacturers of the said products. However, the effectiveness of this policy heavily relies on a collaboration among the supply chain players. The inventory management strategies like Vendor Managed Inventory (VMI) and single-setup-multi-delivery (SSMD) policy play a crucial part in improving production and delivery efficiency by guaranteeing timely and most economic availability of the product. In the aforementioned context, this research introduces a comprehensive e-retailing model for a collaborative supply chain management between a manufacturers and a retailer. The model takes into account SSMD production delivery policy and technological investments for advertising and controlling greenhouse gas emissions. The manufacturer employs a smart manufacturing system and incorporates a predefined ratio of returned items into the production of new products. He makes technological investments in Green Emissions Reduction Technology (GERT) for the production system, while the retailer invests in Information Disclosure Technology (IDT) on social media to promote the system’s efforts in controlling emissions through information sharing and increase customer demand for the product. Multiple model instances are developed and a hybrid analyticalheuristic method is utilized to derive optimal production delivery policy, investment distribution, and product price. The study examines the strategic allocation of technology budget between IDT and GERT, considering several scenarios of budget and stocking capacity limitations. The sensitivity analysis identifies critical parameters, and key recommendations are provided to enhance the economic viability of the system considering the fluctuations in these parameters. The acquired management insights offer decision-makers the essential focus to implement effective investment and production delivery policies in order to achieve environmental and economic sustainability of the coordinated system. The research outcomes provide significant managerial insights for the decision-makers seeking to maximize profits through joint optimization of sustainable production delivery policies for a manufacturer and e-retailer. Model results verify that the adoption of a smart manufacturing system over a fixed one yields a substantial 8.44% rise in profitability of the system. Furthermore, significant increases in profitability are positively correlated with investments in Green Emissions Reduction Technology (GERT) and Information Disclosure Technology (IDT). This underscores the critical need for managers to allocate resources towards the smooth integration of smart manufacturing technology and information sharing into their production and retailing processes, respectively. Further, the results indicate that advertising efficiency plays a pivotal role in improving economic and environmental sustainability of the system. This insight suggests to take proactive measures in improving the efficiency constants of the advertising channel. Model analysis recognized that accomplishing a balanced approach between expanding production capacity and investing in technology is vital for fostering economic success in the manufacturer–retailer collaborative scheme. The policy suggestion analysis indicates identification and monitoring of critical points of the model parameters should be focused to determine the suitable production delivery policy. While this study makes significant contributions in the literature, a few limitations may affect its practical applicability in certain scenarios. We assume constant cost components for model formulation and evaluation while ignoring inherent uncertainty in the costs. Additionally, we have considered the perfect production process by neglecting the possibility of defective products production due to the production process shifting to an out-of-control state [34] in several real-world situations. Furthermore, the proposed integrated model is limited to a single manufacturer and a single e-retailer, whereas several collaborations may involve multiple suppliers [10] or retailers [9] for enhanced economic and environmental sustainability, and robust optimization [59]. Therefore, to enhance the effectiveness of this study, potential research directions include developing an inspection schema [31], incorporating imperfect product production process [49], exploring integrated decisions with multi-manufacturers and multi-retailers [3], and addressing uncertainty issues in the model cost parameters [60] by implementing deep reinforcement learning [61], and fuzzy optimization [62] approaches. These extensions may contribute to a more comprehensive and adaptive manufacturer–retailer integrated model for online and offline sales. Operations Research Perspectives 14 (2025) 100328 22 M. Tayyab et al. CRediT authorship contribution statement Muhammad Tayyab: Writing – review & editing, Writing – original draft, Software, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. Hira Tahir: Writing – review & editing, Visualization, Software, Data curation. Muhammad Salman Habib: Visualization, Supervision, Resources, Project administration, Methodology, Investigation, Formal analysis. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment This research work is sponsored by the Interdisciplinary Research Center for Finance & Digital Economy (IRC-FDE) at King Fahd University of Petroleum & Minerals (KFUPM) under the Project Number INFE2401 awarded on January 3, 2024. Appendix A 𝛺=𝐵𝑖ℎ𝑖−𝐵2 𝑖𝑔𝑖 2𝑛𝑖𝑞𝑖 −𝐵2 𝑖ℎ𝑖 2𝑛𝑖𝑞𝑖 −ℎ𝑖𝑛𝑖𝑞𝑖 2, 𝜏𝑖= −𝜃𝑖(𝑐𝑣𝑖 −𝑐𝑟𝑖)+𝑐𝑣𝑖 +𝑃𝑖𝑢𝑖+𝑤𝑖 𝑃𝑖 +𝜉𝑖, 𝜎=−𝑏𝑖𝐵𝑖 𝑛𝑖𝑞𝑖 −𝑘𝑖 𝑛𝑖𝑞𝑖 −ℎ𝑖𝑞𝑖 2𝑃𝑖 +ℎ𝑖𝑛𝑖𝑞𝑖 2𝑃𝑖 −𝛥𝑖 𝑞𝑖 −𝜏𝑖, 𝛤=𝐵𝑖𝑔𝑖 2𝑛𝑖 +𝐵𝑖ℎ𝑖 2𝑛𝑖 −𝐵2 𝑖𝑔𝑖 2𝑛𝑖𝑞𝑖 −𝐵2 𝑖ℎ𝑖 2𝑛𝑖𝑞𝑖 −𝑔𝑖𝑞𝑖 8𝑛𝑖 −ℎ𝑖𝑞𝑖 8𝑛𝑖 , =𝛾𝑖𝛤 , 𝜒=𝑃𝑖−𝛥𝑖 =𝛤 𝛥𝑖, =𝛾𝑖+𝛾𝑖,and =−. Appendix B First principle minor |(𝐻11)|at the optimal values is |(𝐻11)|=−2𝑏𝑖𝐵𝑖𝜇𝑖 𝑛𝑖𝑞3 𝑖 −𝐵2 𝑖𝑃𝑖(𝑔𝑖+ℎ𝑖) 𝑛𝑖𝑞3 𝑖(𝑃𝑖−𝜇𝑖)−2𝜇𝑖(𝑘𝑖+𝛿𝑖𝑛𝑖) 𝑛𝑖𝑞3 𝑖 <0. Second principle minor |(𝐻22)|at the optimal values is |(𝐻22)|=1 64𝑛4𝑃2𝑞4(𝑃−𝜇)2 ⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣ 8𝐵2𝑃2(24𝑏2𝜇2(𝑃−𝜇)2+ 2𝑔(4𝜇(𝑃−𝜇)(−2𝑏𝜇 𝑞+ 3𝑘𝑃 + 2𝛿 𝑛𝑃 ) +ℎ𝑞2(3𝜇 𝑃− 2𝑛2(𝑃−𝜇)2) )+8ℎ𝜇(𝑃−𝜇)(−2𝑏𝜇 𝑞+ 3𝑘𝑃 + 2𝛿 𝑛𝑃 ) + 3𝑔2𝜇 𝑃 𝑞2+ℎ2𝑞2(3𝜇 𝑃− 4𝑛2(𝑃−𝜇)2) )−64𝐵3𝜇 𝑃3(𝑔+ℎ)(3𝑏(𝜇−𝑃) +𝑞(𝑔+ℎ)) − 16𝐵 𝜇 𝑃(𝑃−𝜇)(𝑏(𝜇 𝑃(−3 𝑔 𝑞2− 8(𝑃−𝜇)(3𝑘+ 2𝛿 𝑛)) +ℎ𝑞2(4𝑛2(𝑃−𝜇)2− 3𝜇 𝑃) )+8𝜇 𝑃 𝑞(𝑔+ℎ)(𝑘+𝛿 𝑛))+48𝐵4𝑃4(𝑔+ℎ)2 − 2ℎ𝜇 𝑃 𝑞2(𝑔 𝑞2(𝜇 𝑃− 4𝑛2(𝑃−𝜇)2)+ 8𝑘(𝑃−𝜇)(4𝑛2(𝑃−𝜇)2− 3𝜇 𝑃) + 16𝛿 𝜇 𝑛𝑃 (𝜇−𝑃))+𝜇2𝑃2(16𝑘(𝑃−𝜇)(3𝑔 𝑞2+ 16𝛿 𝑛(𝑃−𝜇))−𝑔 𝑞2 (𝑔 𝑞2+ 32𝛿 𝑛(𝜇−𝑃))+ 192𝑘2(𝑃−𝜇)2)−ℎ2𝑞4(𝜇 𝑃− 4𝑛2(𝑃−𝜇)2)2 ⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ <0. Third principle minor |(𝐻33)|at the optimal values is Operations Research Perspectives 14 (2025) 100328 23 M. Tayyab et al. |(𝐻33)|= −1 64𝑛5𝑃 𝑞5𝛺3 ⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣ (𝑔+ℎ) (16𝑃2(4𝐵 𝛤(2𝑏𝛺 −𝑞(𝑔+ℎ))− 4𝐵2𝑃(𝑔+ℎ)+𝛤(𝑞2(𝑔+ℎ)+ 8𝑘𝛺))(2𝑏𝐵 𝛤 𝛺−𝐵2𝑃(𝑔+ℎ)+ 2(𝑘+𝛿 𝑛)𝛤 𝛺) −(−8𝑏𝐵 𝑃 𝛤 𝛺+ 4𝐵2𝑃2(𝑔+ℎ)−𝑃 𝛤(8𝑘𝛺 −𝑔 𝑞2)+ℎ𝑞2(4𝑛2𝛺2+𝑃 𝛤))2)+4(𝛤(𝑞(𝑔+ℎ)− 2𝑏𝛺)+ 2𝐵 𝑃(𝑔+ℎ)) (4𝑃 (𝛤(𝑞(𝑔+ℎ)− 2𝑏𝛺)+ 2𝐵 𝑃(𝑔+ℎ))(2𝑏𝐵 𝛤 𝛺−𝐵2𝑃(𝑔+ℎ)+ 2(𝑘+𝛿 𝑛)𝛤 𝛺)−(𝐵 𝑃(𝑔+ℎ)−𝑏𝛤 𝛺) (8𝑏𝐵 𝑃 𝛤 𝛺− 4𝐵2𝑃2 (𝑔+ℎ)+𝑃 𝛤(8𝑘𝛺 −𝑔 𝑞2)−ℎ𝑞2(4𝑛2𝛺2+𝑃 𝛤) ))−4(𝐵 𝑃(𝑔+ℎ)−𝑏𝛤 𝛺) ( (𝛤(𝑞(𝑔+ℎ)− 2𝑏𝛺)+ 2𝐵 𝑃(𝑔+ℎ)) (8𝑏𝐵 𝑃 𝛤 𝛺− 4𝐵2𝑃2(𝑔+ℎ)+𝑃 𝛤(8𝑘𝛺 −𝑔 𝑞2)−ℎ𝑞2(4𝑛2𝛺2+𝑃 𝛤) )−4𝑃(𝐵 𝑃(𝑔+ℎ)−𝑏𝛤 𝛺) (4𝐵 𝛤(2𝑏𝛺 −𝑞(𝑔+ℎ))− 4𝐵2 𝑃(𝑔+ℎ)+𝛤(𝑞2(𝑔+ℎ)+ 8𝑘𝛺) )) ⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ <0. Fourth principle minor |(𝐻44)|at the optimal values is |(𝐻44)|=𝛾 512𝑛6𝑃2𝑞6𝛺6 ⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣ −𝛾((𝑔+ℎ)(𝑞− 2𝐵)(2𝐵+𝑞)𝑃2 𝛺2− 8(𝑏𝐵 +𝑘+𝑛𝛿)𝑃− 4ℎ(𝑛− 1)𝑛𝑞2) (2(4𝛤 𝛺 𝑏2+ 4ℎ𝑞(−𝛤)𝑏+𝑔2𝑞2+ℎ2𝑞2+ 8𝑔 𝑘𝑃 + 8ℎ𝑘𝑃 + 2𝑔 𝑞(2(−𝛤)𝑏+ℎ𝑞) )𝛤 𝛺((𝑔+ℎ)(4𝐵2−𝑞2)𝑃2+ 4(ℎ(𝑛− 1)𝑛𝑞2+ 2𝑃(𝑏𝐵 +𝑘+𝑛𝛿))𝛺2)−(4(2𝐵(𝑔+ℎ)𝑃 +𝛤((𝑔+ℎ)𝑞− 2𝑏𝛺) ) (𝐵(𝑔+ℎ)𝑃−𝑏𝛤 𝛺)−(𝑔+ℎ) (4𝐵2(𝑔+ℎ)𝑃2−(8𝑘𝛺 −𝑔 𝑞2)𝛤 𝑃− 8𝑏𝐵 𝛤 𝛺 𝑃+ℎ𝑞2(4𝑛2𝛺2+𝑃 𝛤))) ((𝑔+ℎ)𝑃2(𝑞− 2𝐵)2 + 4ℎ𝑛2𝑞2𝛺2+ 8(𝑏𝐵 +𝑘)𝑃 𝛺2)+ 2(2𝑏𝛺2+ 2𝐵(𝑔+ℎ)𝑃−(𝑔+ℎ)𝑃 𝑞) (4𝑃(4(𝑔+ℎ)𝑃 𝐵2 + 4𝛤((𝑔+ℎ)𝑞− 2𝑏𝛺)𝐵−((𝑔+ℎ)𝑞2+ 8𝑘𝛺)𝛤) (𝐵(𝑔+ℎ)𝑃−𝑏𝛤 𝛺)−(2𝐵(𝑔+ℎ)𝑃+𝛤((𝑔+ℎ)𝑞− 2𝑏𝛺)) (4𝐵2(𝑔+ ℎ)𝑃2−(8𝑘𝛺 −𝑔 𝑞2)𝛤 𝑃− 8𝑏𝐵 𝛤 𝛺 𝑃+ℎ𝑞2(4𝑛2𝛺2+𝑃 𝛤) )))𝛺2−(2𝑃(8𝑛𝑞 𝛺3+(𝑔+ℎ)𝑃(𝑞− 2𝐵)2 𝛾) (4(2𝐵(𝑔+ℎ)𝑃 +𝛤((𝑔+ℎ)𝑞− 2𝑏𝛺) ) (𝐵(𝑔+ℎ)𝑃−𝑏𝛤 𝛺)−(𝑔+ℎ) (4𝐵2(𝑔+ℎ)𝑃2−(8𝑘𝛺 −𝑔 𝑞2)𝛤 𝑃− 8𝑏𝐵 𝛤 𝛺 𝑃+ℎ𝑞2(4𝑛2𝛺2+ 𝑃 𝛤)))−𝛾(2(2𝐵(𝑔+ℎ)𝑃+𝛤((𝑔+ℎ)𝑞− 2𝑏𝛺))(2𝑏𝛺2+ 2𝐵(𝑔+ℎ)𝑃−(𝑔+ℎ)𝑃 𝑞)−(𝑔+ℎ) ( (𝑔+ℎ)𝑃2(𝑞− 2𝐵)2 + 4ℎ𝑛2𝑞2𝛺2+ 8(𝑏𝐵 +𝑘)𝑃 𝛺2)) ((𝑔+ℎ)(4𝐵2−𝑞2)𝑃2+ 4(ℎ(𝑛− 1)𝑛𝑞2+ 2𝑃(𝑏𝐵 +𝑘+𝑛𝛿))𝛺2)+ 2𝛾(2𝑏𝛺2+ 2𝐵 (𝑔+ℎ)𝑃−(𝑔+ℎ)𝑃 𝑞)( (4𝐵2(𝑔+ℎ)𝑃2−(8𝑘𝛺 −𝑔 𝑞2)𝛤 𝑃− 8𝑏𝐵 𝛤 𝛺 𝑃+ℎ𝑞2(4𝑛2𝛺2+𝑃 𝛤)) (2𝑏𝛺2+ 2𝐵(𝑔+ℎ)𝑃− (𝑔+ℎ)𝑃 𝑞)−2(𝐵(𝑔+ℎ)𝑃−𝑏𝛤 𝛺)((𝑔+ℎ)𝑃2(𝑞− 2𝐵)2 + 4ℎ𝑛2𝑞2𝛺2+ 8(𝑏𝐵 +𝑘)𝑃 𝛺2) ))(−4𝐵2(𝑔+ℎ)𝑃2+ 8𝑏𝐵 𝛤 𝛺 𝑃+𝛤(8𝑘𝛺 −𝑔 𝑞2)𝑃−ℎ𝑞2(4𝑛2𝛺2+𝑃 𝛤) )+8𝑃(4𝑃(4𝛤 𝛺 𝑏2+ 4ℎ𝑞(−𝛤)𝑏+𝑔2𝑞2+ℎ2𝑞2+ 8𝑔 𝑘𝑃 + 8ℎ𝑘𝑃 + 2𝑔 𝑞(2(−𝛤) 𝑏+ℎ𝑞 ))𝛤 𝛺(8𝑛𝑞 𝛺3+(𝑔+ℎ)𝑃(𝑞− 2𝐵)2 𝛾)−𝛾(2(2𝐵(𝑔+ℎ)𝑃+𝛤((𝑔+ℎ)𝑞− 2𝑏𝛺)) (2𝑏𝛺2+ 2𝐵(𝑔+ℎ)𝑃−(𝑔+ℎ) 𝑃 𝑞)−(𝑔+ℎ)((𝑔+ℎ)𝑃2(𝑞− 2𝐵)2 + 4ℎ𝑛2𝑞2𝛺2+ 8(𝑏𝐵 +𝑘)𝑃 𝛺2) )( (𝑔+ℎ)𝑃2(𝑞− 2𝐵)2 + 4ℎ𝑛2𝑞2𝛺2+ 8(𝑏𝐵 +𝑘) 𝑃 𝛺2)+2𝛾(2𝑏𝛺2+ 2𝐵(𝑔+ℎ)𝑃−(𝑔+ℎ)𝑃 𝑞) (2𝑃(4(𝑔+ℎ)𝑃 𝐵2+ 4𝛤((𝑔+ℎ)𝑞− 2𝑏𝛺)𝐵−((𝑔+ℎ)𝑞2+ 8𝑘𝛺)𝛤) (2𝑏𝛺2 + 2𝐵(𝑔+ℎ)𝑃−(𝑔+ℎ)𝑃 𝑞)−(2𝐵(𝑔+ℎ)𝑃+𝛤((𝑔+ℎ)𝑞− 2𝑏𝛺)) ( (𝑔+ℎ)𝑃2(𝑞− 2𝐵)2 + 4ℎ𝑛2𝑞2𝛺2+ 8(𝑏𝐵 +𝑘)𝑃 𝛺2))) (2𝑏𝛤 𝛺 𝐵−𝐵2(𝑔+ℎ)𝑃+ 2𝛤(𝑘+𝑛𝛿)𝛺)+ 4(𝐵(𝑔+ℎ)𝑃−𝑏𝛤 𝛺) (−2𝑃(8𝑛𝑞 𝛺3+(𝑔+ℎ)𝑃(𝑞− 2𝐵)2 𝛾) (4𝑃(4(𝑔+ ℎ)𝑃 𝐵2+ 4𝛤((𝑔+ℎ)𝑞− 2𝑏𝛺)𝐵−((𝑔+ℎ)𝑞2+ 8𝑘𝛺)𝛤) (𝐵(𝑔+ℎ)𝑃−𝑏𝛤 𝛺)−(2𝐵(𝑔+ℎ)𝑃+𝛤((𝑔+ℎ)𝑞− 2𝑏𝛺)) (4 𝐵2(𝑔+ℎ)𝑃2−(8𝑘𝛺 −𝑔 𝑞2)𝛤 𝑃− 8𝑏𝐵 𝛤 𝛺 𝑃+ℎ𝑞2(4𝑛2𝛺2+𝑃 𝛤) ))+𝛾( (𝑔+ℎ)(4𝐵2−𝑞2)𝑃2+ 4(ℎ(𝑛− 1)𝑛𝑞2+ 2𝑃 (𝑏𝐵 +𝑘+𝑛𝛿) )𝛺2)(2𝑃(4(𝑔+ℎ)𝑃 𝐵2+ 4𝛤((𝑔+ℎ)𝑞− 2𝑏𝛺)𝐵−((𝑔+ℎ)𝑞2+ 8𝑘𝛺)𝛤) (2𝑏𝛺2+ 2𝐵(𝑔+ℎ)𝑃−(𝑔+ℎ) 𝑃 𝑞)−(2𝐵(𝑔+ℎ)𝑃+𝛤((𝑔+ℎ)𝑞− 2𝑏𝛺))((𝑔+ℎ)𝑃2(𝑞− 2𝐵)2 + 4ℎ𝑛2𝑞2𝛺2+ 8(𝑏𝐵 +𝑘)𝑃 𝛺2) )−𝛾( (𝑔+ℎ)𝑃2(𝑞− 2𝐵)2+ 4ℎ𝑛2𝑞2𝛺2+ 8(𝑏𝐵 +𝑘)𝑃 𝛺2)( (4𝐵2(𝑔+ℎ)𝑃2−(8𝑘𝛺 −𝑔 𝑞2)𝛤 𝑃− 8𝑏𝐵 𝛤 𝛺 𝑃+ℎ𝑞2(4𝑛2𝛺2+𝑃 𝛤)) (2𝑏𝛺2+ 2𝐵 (𝑔+ℎ)𝑃−(𝑔+ℎ)𝑃 𝑞)−2(𝐵(𝑔+ℎ)𝑃−𝑏𝛤 𝛺)((𝑔+ℎ)𝑃2(𝑞− 2𝐵)2 + 4ℎ𝑛2𝑞2𝛺2+ 8(𝑏𝐵 +𝑘)𝑃 𝛺2) )) ⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ <0, where 𝛺=(𝑃+𝑝𝛾 −𝛥), 𝛤=(𝑝𝛾 −𝛥). Data availability No data was used for the research described in the article. References [1] Khan Md Al-Amin, Cárdenas-Barrón Leopoldo Eduardo, Treviño-Garza Gerardo, Céspedes-Mota Armando. Strategizing emissions reduction investment for a livestock production farm amid power demand pattern: A path to sustainable growth under the carbon cap environmental regulation. Oper Res Perspect 2024;13:100313. [2] Feng Xiaohang Flora, Liu Xiao, Zhang Shunyuan, Srinivasan Kannan. Sustainability and competition on amazon. In: Xiao and Zhang, Shunyuan and Srinivasan, Kannan, Sustainability and Competition on Amazon (September 16, 2024). 2024. Operations Research Perspectives 14 (2025) 100328 24