Cooperation and competition in an oligopolistic and mature industry: A case study on the cationic reagent industry based on an optimization model

Kang, Joohang; Choi, Byoungil; Lim, Chaehong; Eun, Joonyup Article Cooperation and competition in an oligopolistic and mature industry: A case study on the cationic reagent industry based on an optimization model Operations Research Perspectives Provided in Cooperation with: Elsevier Suggested Citation: Kang, Joohang; Choi, Byoungil; Lim, Chaehong; Eun, Joonyup (2025) : Cooperation and competition in an oligopolistic and mature industry: A case study on the cationic reagent industry based on an optimization model, Operations Research Perspectives, ISSN 2214-7160, Elsevier, Amsterdam, Vol. 14, pp. 1-15, https://doi.org/10.1016/j.orp.2025.100325 This Version is available at: https://hdl.handle.net/10419/325802 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-nc-nd/4.0/ Contents lists available at ScienceDirect Operations Research Perspectives journal homepage: www.elsevier.com/locate/orp Cooperation and competition in an oligopolistic and mature industry: A case study on the cationic reagent industry based on an optimization model Joohang Kang , Byoungil Choi , Chaehong Lim, Joonyup Eun ∗ Graduate School of Management of Technology, Korea University, Seoul 02841, South Korea ARTICLE INFO Keywords: Supply chain management Supply chain optimization model Cationic reagent Mature industry Oligopolistic market ABSTRACT A cationic reagent is an essential raw material in printing paper production. The market environment of the cationic reagent industry is influenced by the printing paper industry. Owing to the COVID-19 pandemic, the global expansion of remote work and home education has decreased the demand for printing papers. Consequently, competition among market players (i.e., suppliers and buyers) in the cationic reagent industry is intensifying. This study focuses on cooperation between market players in the cationic reagent industry, representing a typical oligopolistic and mature industry. It proposes a supply chain optimization model that minimizes the costs of the entire supply chain, incorporating buyers’ risk hedge tendency to address market uncertainty. The model is empirically tested using accessible and reliable data to assess its business applicability. Numerical experiments are conducted to explore scenarios that can occur in real market environment, such as levels of risk hedging, trade disputes, decreases in demand, and changes in production capacity. The experimental results provide managerial implications. As buyers maximize the degree to which they diversify their purchase quantities across multiple suppliers to reduce risks, differential costs of the entire supply chain increase by 19%, which are costs that cannot be reduced by suppliers’ capabilities and inevitably arise due to differences between suppliers (e.g., geography, politics, and government policies). However, in unfavorable market conditions, such as trade disputes and decreases in demand, less competitive suppliers can survive. This study shows that when market demand in the cationic reagent industry decreases, two suppliers may potentially experience operational outages. In reality, these two suppliers deteriorated under the challenging market conditions during the COVID-19 pandemic. 1. Introduction The cationic reagent industry operates in the business-to-business sector, where suppliers manufacture cationic reagents for buyers. The industry is characterized as oligopolistic and mature. Oligopolistic markets are typically dominated by a small number of companies, often between two and ten. Several companies control a substantial market share, and thus have significant pricing power and influence [1]. The cationic reagent industry has an oligopolistic nature due to the limited number of suppliers and buyers. Additionally, the industry corresponds to the maturity stage of the product life cycle, which consists of introduction, growth, maturity, and decline stages [2]. The mature nature of the cationic reagent industry is evidenced by the long history of the industry. The cationic reagent industry traces its origins back to the early 20th century with the development of quaternary ammonium compounds [3]. In the 1970s, chemical companies such as Dow and Degussa developed the most common cationic reagent 3-chloro2-hydroxypropyl trimethylammonium chloride. Most of the demand ∗Corresponding author. E-mail address: [email protected] (J. Eun). for this cationic reagent is consumed for the production of cationic starch. Cationic starch enhances the bonding strength between microlayers of paper by ionizing pulp fiber, which enhances the bonding strength between the micro-layers of paper by ionizing pulp fibers. Additionally, it improves overall strength and printability of papers by evenly distributing fillers. As an essential raw material in the production of printing papers, the market environment of the cationic reagent industry are closely tied to those of the printing paper industry. The printing paper industry is currently experiencing an unprecedented crisis due to the COVID-19 pandemic. While the demand for printed materials such as office paper, magazines, and books had been declining even before the pandemic. The expansion of remote work and home education, driven by the pandemic, has further accelerated the contraction of the printing paper market. RISI, Inc., a consulting firm specializing in the paper industry, has focused the potential collapse of the printing paper market owing to the COVID-19 pandemic [4]. https://doi.org/10.1016/j.orp.2025.100325 Received 22 August 2024; Received in revised form 23 December 2024; Accepted 14 January 2025 Operations Research Perspectives 14 (2025) 100325 Available online 22 January 2025 2214-7160/© 2025 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/bync-nd/4.0/ ). J. Kang et al. Moody’s, a global credit rating agency, has forecasted decreased operating profits for paper companies primarily selling printing papers [5]. In 2020, 16 printing paper factories in North America either permanently closed or switched their main product to other product focus due to the lack of demand. The situation in the European paper industry is similar to that of North America [6]. Oligopolistic markets can contribute to economic stability by maintaining price levels and reducing volatility. However, excessive market dominance or collusion may lead to market distortions and hinder overall economic efficiency [7,8]. According to Porter [9] companies in mature industries tend to lower their product prices to secure a larger market share, intensifying competition with other companies. In fact, market players (i.e., suppliers and buyers) in the cationic reagent industry, an oligopolistic and mature industry, experience reduced profits due to excessive competition. Additionally, the COVID-19 pandemic has created an unfavorable market environment for the printing paper industry. Oligopolistic companies wield significant market power, enabling them to influence prices and market outcomes to their advantage. However, this can lead to inefficiencies and inequality within the market, as smaller competitors struggle to compete [10]. This study aims to explore the strategic decisions that market players can make for the public good in an oligopolistic industry (i.e., the cationic reagent industry), which is characterized by strategic interactions [11]. One potential strategy to establish a competitive and robust supply chain in the oligopolistic and mature industry is cooperation between suppliers and buyers. In this regard, there is the concept of competitive cooperation (i.e., co-opetition). Co-opetition is a business strategy that uses insights gained from the game theory to understand when it is better for competitors to work together [12]. The value net model, which consists of customers, complementors, suppliers, and competitors, centered on the co-opetition, emphasized cooperation among competitors [13]. Inspired by this concept, cooperation among competitors (i.e., between suppliers or between buyers) is also highlighted in this study. In this study, we propose a supply chain optimization model that minimizes costs to improve the competitiveness of the entire industry; The term entire industry refers to all business and organizations engaged in a particular product or service. The buyers’ risk hedge tendency is incorporated into the proposed model to examine market uncertainty. The model subsequently analyzes the effects on supply chains based on fluctuations in the buyers’ risk hedge tendency. The proposed model is empirically tested using accessible and reliable data. Managerial implications are derived through numerical experiments under various market environments. The results align with practical events observed during the study. Moreover, based on the experimental results, we present the reasons why reaching an agreement among market players for an ideal equilibrium, where cooperation among market players is achieved, is difficult. Notably, the experimental results, which show that two suppliers are unable to continue their businesses, align with what actually occurred during this study. The contributions of this study are structured into theoretical, managerial, and methodological aspects and presented as follows. (i) From the theoretical perspective, this study proposes a simple yet versatile supply chain optimization model for an oligopolistic and mature industry. This methodology is effective and solid because the model considers only differential costs that inevitably arise due to differences between suppliers. Given the minimal technological and quality differences between suppliers in a mature industry, the optimization model is designed to be effectively tractable by excluding non-differential costs (i.e., convergent costs) affected by technological and quality differences. (ii) From the managerial perspective, by analyzing supply chains of the controlled environment of an oligopolistic and mature industry under various scenarios, the importance of cooperation strategy is highlighted. (iii) From the methodological perspective, the optimization model is designed as an MILP (mixed integer linear program). The proposed model is applicable as a practical methodology for making decisions of market players in various industrial sectors (e.g., raw materials, petrochemical, and rare earths industry) that operate in similar business environment (e.g., an oligopolistic and mature industry). By manipulating parameters that reflect changes in market environment (e.g., trade disputes, changes in demand, changes in supply), players’ status can be analyzed by observing the changes in decision variables (e.g., see Jeon et al. [14] and Cha et al. [15]). In this context, the business environment and market environment refer to the characteristics of an industry and the situations or conditions in which market players operate, respectively. To obtain clear managerial insights from the experimental results, several research questions are raised here and answered in Section 4.7: 1. How does cooperation among market players affect the competitiveness of the entire industry? 2. How do costs of the entire supply chain increase or decrease in response to different levels of risk hedging? 3. How do trade disputes affect sales quantities of suppliers and costs of the entire supply chain? 4. How do decreases in demand cause changes in costs of the entire supply chain? 5. How does increase or decrease in production capacity of suppliers affects costs of the entire supply chain? The remainder of this paper is organized as follows: Section 2 describes the related literature. Section 3introduces a supply chain optimization model that reflects characteristics of an oligopolistic and mature industry. In Section 4, we empirically test the proposed model, analyzing the experiment results to derive managerial implications. Section 5concludes this study. 2. Related literature Companies maintain a competitive advantage by connecting or integrating components of their supply chains [16]. Selecting the most suitable suppliers is crucial because it significantly influences the supply chains components [17]. Accordingly, various industrial sectors, including manufacturing, processing, and logistics, have explored supply chain optimization based on mathematical programming. This section examines previous studies from two perspectives: first, whether the studies focused on maximizing individual companies’ profits or the entire industry’s profitability, as well as on the type of competitive strategy (i.e., either competition or cooperation); second, whether market uncertainty is incorporated into a model. Market uncertainty refers to fluctuations in market environment, including freight costs, raw material prices, labor costs, electricity rates, and import tariffs, driven by sudden events such as the COVID-19 pandemic or trade disputes. Table 1illustrates the characteristics of previous studies and the proposed model in this study. 2.1. Supply chain perspective and competitive strategy Jayaraman et al. [17] proposed a supplier selection model that enables buyers to minimize fixed and variable costs when choosing suppliers. The model pursued the profit of a single buyer and assumed a competitive situation among multiple suppliers and buyers. Sakawa et al. [18] proposed a supply chain model that minimizes production and transportation costs, given suppliers’ production capacities and market demand. They presented a scheme for profits and cost allocation among game participants from the perspective of cooperative game theory, employing fuzzy logic to ensure stable production and transportation in an uncertain environment. Papageorgiou et al. [19] suggested a model for the pharmaceutical industry, which is an oligopolistic and mature industry, incorporating the characteristics of an oligopolistic and mature industry and the global trade structure. The model allowed a company to decide business strategies in the market environment. Vidal and Goetschalckx [20] presented a model that maximizes the after-tax profit of a multinational company. Operations Research Perspectives 14 (2025) 100325 2 J. Kang et al. The model included transfer prices and the allocation of transportation costs as explicit decision variables. They developed an algorithm that employed successive linear programming based on relaxation, yielding acceptable-quality solutions. Thanh et al. [21] proposed an optimization model for a production-distribution system that supports decision-making processes such as supplier selection and flows along the supply chain, considering multi-echelon and multi-commodity factors. In other words, the model helps companies make strategic and tactical decisions. Companies pursue a cooperation strategy in that suppliers offer purchase cost discounts when buyers purchase multiple items in supplier selection. Chang et al. [22] proposed a model that considered multiple buyers and a single supplier while enhancing cooperative relationships across the industry. They found that a policy of shipping small volumes of various items rather than large volumes of a few items could reduce integrated costs, enhancing profits for both buyers and suppliers. Jakhar et al. [23] developed a partner selection and flow allocation model, proposing sustainable supply chain performance measures. They considered the profit of the entire industry and approached competitive strategy through cooperation. Alikhani et al. [24] proposed a model that considers factors such as sustainability and risk at the same time. The proposed model uses interval type-2 fuzzy sets to quantify the decision maker’s input and combines with DEA to efficiently select a supplier. Guo et al. [25] presented a mixed integer linear program and a distributed approximation approach for a sustainable supply chain network design. This model structured the supply chain to consist of suppliers, transformers, distributors, and customers to target the entire industry. Their experimental results indicated the importance of connectivity and collaboration among market players. Gao and You [26] developed a two-stage game-theory-based stochastic mixed linear program. They examined how multiple stakeholders’ independent profit-seeking behaviors affect supply chain performance in non-cooperative environments. Vafaeenezhad et al. [27] proposed a multi-objective linear program for a multi-echelon and multi-product supply chain management. The model was characterized by simultaneously considering environmental, economic, and social impacts. This research was applied to a wood and paper industry case. Experimental results demonstrated that decision-makers could plan a supply chain that best aligned with the characteristics they considered important (i.e., economy, environment, and society). Gholizadeh et al. [28] developed an optimization model and heuristic algorithm to maximize the total profit and minimize environmental effects for a closed-loop supply chain. This study evaluated the model’s performance using data from Saleh Industrial Dairy Group, a well-known dairy product producer in Iran. The optimality gaps obtained by the heuristic algorithm for all experiments demonstrated an acceptable range (less than 5%). Fathollahi-Fard et al. [29] proposed a fuzzy mixed integer linear program to handle uncertain parameters in supply chain networks. This model incorporates a dual-channel (online and offline) and multiproduct approach to account for recent consumer purchasing behavior (i.e., Online to Offline). Through experiments, they demonstrated that for the successful implementation of an O2O policy, appropriate pricing for both online and offline channels must be established. Otherwise, it could lead to negative effects on the entire supply chain. Chowdhury et al. [30] presented a mixed-integer program for a vaccine supply chain that ensures the entire network’s economic performance. They applied the model to the COVID-19 vaccine distribution systems of a densely populated city in Bangladesh and verified that the supply chain network is efficient and well-designed. Mosallanezhad et al. [31] proposed an optimization model in the medical supply chain to ensure the reliable distribution of personal protective equipment for medical personnel in situations like a global epidemic. The objective function of the model is to simultaneously minimize the total costs and the amount of unsatisfied demand for participants such as manufacturers, distributors, and hospitals. 2.2. Market uncertainty Sakawa et al. [18] addressed a real problem regarding the production and transportation of a housing material manufacturer. In the real world, market demand and production capacity were determined based on expert judgment, so they were not always precise values. To tackle this issue, this study incorporated fuzzy goals and fuzzy constraints into a mixed zero–one program. Liu and Nagurney [32] studied the impact of foreign exchange uncertainty and competition intensity on a supplier engaged in overseas outsourcing. They highlighted that companies’ decisions regarding pricing, procurement, outsourcing, transportation, and production can be influenced by foreign exchange uncertainty and competition. Gao and You [26] incorporated various uncertainties into their two-stage game-theory-based stochastic mixed linear program for supply chain networks involving multiple stakeholders. In a case study on shale gas supply chain, they considered the productivity uncertainty of shale gas producers and the operational uncertainty of shale gas processors. Stakeholders showed a tendency to choose more conservative options when market uncertainty, including the uncertainties of other stakeholders, was present. Yılmaz et al. [33] proposed a scenarios-based two-stage stochastic optimization model for reverse supply chain design. They considered the ripple effect that results from sudden disruptions at one or more points in the supply chain and affects the entire network as a form of uncertainty. Experimental results showed that the ripple effect can increase the emission level and total cost by up to 40%. Focusing on uncertainties from the ripple effect, Yılmaz et al. [34] developed a two-stage stochastic optimization model for medical supply chain resilience by employing lean tools and considering the ripple effect, emphasizing preparedness strategies to mitigate pandemic-related risks. Similarly, Özçelik et al. [35] also considered the ripple effect. They developed a robust optimization model for reverse supply chain networks aligned with green principles. Gholizadeh et al. [28] proposed a mixed integer linear program for a sustainable closed-loop supply chain in the dairy industry. The demand, shipping and operating costs, facility capacity, and product return rates are considered as uncertain parameters. For the uncertain parameters, they generated pessimistic, optimistic, and worst-case scenarios and evaluated the model performance. FathollahiFard et al. [29] tackled the uncertainty parameters using a fuzzy model. They considered all parameters related to prices and the rate of waste production as uncertain. Chowdhury et al. [30] considered inventory holding costs, unit assembly costs of packaged vaccines, unit prices of raw materials, supplier capacity, and transportation costs as uncertain parameters in the vaccine supply chain. These parameters were defined as probabilistic with a uniform probability distribution. Naturally, through experiments, it was confirmed that these uncertain parameters impact profitability. 3. Problem definition This section describes a supply chain optimization model that incorporates the characteristics of the target industry (i.e., oligopolistic and mature industry). The objective function of the proposed model is to minimize the total differential costs (TDCs) of the supply chains in the industry through cooperation among market players. Sections 3.1 and 3.2 define the terminologies and assumptions for the model, respectively. The proposed model is formulated as a mixed integer linear program (MILP) and presented in Section 3.3. 3.1. Terminologies •Differential costs refer to the costs that inevitably arise due to differences between suppliers. These costs are influenced by factors such as geography, politics, and government policies, which cannot be reduced by suppliers’ capabilities. In the proposed model, logistics, electricity, labor, raw material costs, and import tariffs are considered differential costs. Operations Research Perspectives 14 (2025) 100325 3 J. Kang et al. Table 1 Related papers and their considerations †. Authors Methodology ‡Perspective Competitive strategy Consideration of market uncertainty Individual company Entire industry Competition Cooperation Jayaraman et al. [17] MILP ✓ ✓ Sakawa et al. [18] MBIP ✓ ✓ ✓ Papageorgiou et al. [19] MILP ✓ ✓ Vidal and Goetschalckx [20] MILP ✓ Thanh et al. [21] MILP ✓ ✓ Chang et al. [22] MILP ✓ ✓ Liu and Nagurney [32] LP ✓ ✓ ✓ Jakhar et al. [23] MILP ✓ ✓ ✓ Guo et al. [25] MILP ✓ ✓ Alikhani et al. [24] LP ✓ ✓ ✓ Gao and You [26] SMIP ✓ ✓ ✓ Vafaeenezhad et al. [27] LP ✓ Yılmaz et al. [33] SMIP ✓ ✓ Özçelik et al. [35] ROM ✓ ✓ Gholizadeh et al. [28] MILP ✓ ✓ Fathollahi-Fard et al. [29] FMIP ✓ ✓ ✓ Mosallanezhad et al. [31] DOM ✓ ✓ Chowdhury et al. [30] MIP ✓ ✓ Sawik [36] SMIP ✓ ✓ Yılmaz et al. [34] SOM ✓ ✓ This study MILP ✓ ✓ ✓ †Note that any characteristics (i.e., perspective, competitive strategy, market uncertainty) that are not explicitly described or cannot be reasonably inferred in a paper have been left blank. ‡LP: linear program, MIP: mixed integer program, MILP: mixed integer linear program, FMIP: fuzzy mixed integer linear program, SMIP: stochastic mixed integer program, MBIP: mixed binary integer program, ROM: robust optimization model, SOM: stochastic optimization model, DOM: deterministic optimization model. •Convergent costs are the varied costs that can be reduced by suppliers’ capabilities and efforts. •Direct material costs are the costs of direct and raw materials identified in the production of products. •Direct labor costs are those for explicitly identifiable labor used to produce products. •Manufacturing overhead costs are the costs that are challenging to identify, encompassing all costs required to produce products except direct material costs and direct labor costs. •Cost and freight (CFR) is a delivery condition that includes freight costs and import tariffs. Under this condition, a supplier covers all costs from their loading location to the buyers’ designated port. •Free on board (FOB) is a delivery condition that excludes freight costs and import tariffs. Under this condition, a supplier is responsible for covering the related costs and procedures until the products are loaded onto a ship at the port of export. However, once the ship departs, the buyer is responsible for the transportation costs and risks. •Buyers’ risk hedge tendency is the degree to which a buyer’s purchase quantities are distributed across multiple suppliers. From a buyers’ point of view, instability caused by monopolistic supply from a few suppliers, price fluctuations, unresponsiveness to a buyer’ order, and uncertainty in lead times are risks associated with suppliers. Diversifying suppliers is a way to mitigate these risks. To quantitatively consider the risk in a supply chain [37], the proposed model suggests a parameter called buyers’ risk hedge tendency, which controls the maximum amount of demand that is able to be assigned to a supplier. 3.2. Assumptions •The target industry is oligopolistic and mature with multiple suppliers and buyers; The growth of supply and demand in a mature industry is slow, with few technological and quality differences among suppliers. Although technology continues to evolve, reducing costs in the industry is challenging. Due to the characteristics of the mature industry, all buyers have an equal level of buyer risk hedge tendency. Due to the high price elasticity of demand and characteristics of oligopolistic industries (i.e., interdependence between companies, high similarity of products, buyer’s budget constraint, supplier’s price-driven strategy, buyer’s expectation) [38,39], all buyers execute price-oriented purchasing decisions. Price-oriented competition is overheating, and the possibility of supply chain restructuring (e.g., withdrawal from the business due to low profitability) exists [2]. •Product costs are divided into differential and convergent costs; In manufacturing companies, three general types of product costs are direct material, direct labor, and manufacturing overhead costs [40]. In the proposed model, these product costs are redefined as uncontrollable differential and controllable convergent costs. Due to the minimal technological and quality differences between suppliers in a mature industry, convergent costs are ignored in the mathematical formulation of Section 3.3. •CFR and FOB are adopted based on International Commercial Terms (INCOTERMS); INCOTERMS are standards for product delivery, cost allocation, risk transfer, transportation, and liability between parties in a trade transaction. If a supplier and a buyer agree to accept INCOTERMS, they are bound by the conditions of the trade contract. •Freight costs are considered inter-country freight rates; In an oligopolistic market where buyers must follow price-oriented purchasing from a few suppliers, transportation is usually conducted by container ships at sea. Small-volume products can be transported by less-than-container load (LCL) shipments. The intercountry freight rate per unit weight for products transported by LCL is assumed to be the same as that charged for container ships. When a supplier within a country transports products to the same country, freight costs are not charged. In Europe, land transportation between countries is conducted by truck or railroad, incurring significantly low freight costs. •The number of workers for each supplier is calculated using the full-time equivalent (FTE) concept; FTE is the total hours worked divided by the maximum number of compensable hours in a full-time schedule. Based on FTE [41], the number of workers required to complete a task within a given period is calculated as a real number, not an integer. Operations Research Perspectives 14 (2025) 100325 4 J. Kang et al. Table 2 Notations used in the proposed model. Sets 𝑆Set of suppliers 𝐵Set of buyers Parameters 𝑦𝑖Capacity of supplier 𝑖(MT) 𝑑𝑗Demand of buyer 𝑗(MT) 𝑓𝑖,𝑗 Freight costs of route per unit of product from supplier 𝑖to buyer 𝑗(USD/MT) 𝑟𝑖Raw material costs per unit of product for supplier 𝑖(USD/MT) 𝑒𝑖Electricity costs per unit of product for supplier 𝑖(USD/MT) 𝑏𝑗FOB price per unit of product for buyer 𝑗(USD/MT) 𝑢𝑖USD sales per employee of supplier 𝑖 𝑤𝑖Annual average wage for supplier 𝑖 𝑥𝑖,𝑗 Import tariff rate per unit of product from supplier 𝑖to buyer 𝑗 𝑚Number of supplier 𝛾Buyers’ risk hedge tendency (0≤𝛾 <1 −1 𝑚) Variables 𝑡𝑖,𝑗 Quantity transported from supplier 𝑖to buyer 𝑗(MT) •Metric ton (MT) is used as the material unit. Moreover, 1 MT is equivalent to 1 ton (2204,6 lb). 3.3. Mathematical formulation Table 2illustrates a summary of parameters and variables. 𝑆and 𝐵are the sets of suppliers and buyers, respectively. 𝑦𝑖represents the manufacturing capacity of supplier 𝑖, and 𝑑𝑗denotes the demand of buyer 𝑗.𝑓𝑖,𝑗 refers to freight costs per unit of product from supplier 𝑖 to buyer 𝑗.𝑟𝑖and 𝑒𝑖indicate raw material costs per unit of product and electricity costs per unit of product for supplier 𝑖, respectively. 𝑏𝑗indicates a product price (i.e., FOB price) per unit of product for buyer 𝑗.𝑢𝑖is USD sales per employee of supplier 𝑖and 𝑤𝑖is annual average wage for supplier 𝑖.𝑥𝑖,𝑗 refers to import tariff rate per unit of product from supplier 𝑖to buyer 𝑗.𝛾indicates buyers’ risk hedge tendency and acts as a constraint on the quantity of product purchased from a supplier. The proposed model aims to find the transported quantities that minimize the TDCs of the target industry to improve its overall competitiveness (i.e., the equilibrium). The objective function is formulated as follows: 𝑀 𝑖𝑛𝑖𝑚𝑖𝑧𝑒 ∑ 𝑖∈𝑆[∑ 𝑗∈𝐵 𝑓𝑖,𝑗 𝑡𝑖,𝑗 +𝑟𝑖∑ 𝑗∈𝐵 𝑡𝑖,𝑗 +𝑒𝑖∑ 𝑗∈𝐵 𝑡𝑖,𝑗 +∑𝑗∈𝐵(𝑏𝑗+𝑓𝑖,𝑗 )𝑡𝑖,𝑗 𝑤𝑖 𝑢𝑖 +∑ 𝑗∈𝐵(𝑏𝑗+𝑓𝑖,𝑗 )𝑡𝑖,𝑗 𝑥𝑖,𝑗 ](1) TDCs are the summation of differential costs from all suppliers. The differential costs for supplier i are categorized into five components: total freight, total raw material, total electricity, total labor costs, and total import tariffs. Total freight costs of supplier i is expressed as ∑𝑗∈𝐵𝑓𝑖,𝑗 𝑡𝑖,𝑗 , total raw material costs of supplier 𝑖as 𝑟𝑖∑𝑗∈𝐵𝑡𝑖,𝑗 , total electricity costs of supplier 𝑖as 𝑒𝑖∑𝑗∈𝐵𝑡𝑖,𝑗 , total labor costs of supplier 𝑖as ∑𝑗∈𝐵 (𝑏𝑗+𝑓𝑖,𝑗 )𝑡𝑖,𝑗 𝑤𝑖 𝑢𝑖 , and total import tariffs of supplier 𝑖as ∑𝑗∈𝐵(𝑏𝑗+𝑓𝑖,𝑗 )𝑡𝑖,𝑗 𝑥𝑖,𝑗 , respectively. ∑ 𝑗∈𝐵 𝑡𝑖,𝑗 ≤𝑦𝑖,∀𝑖∈𝑆(2) ∑ 𝑖∈𝑆 𝑡𝑖,𝑗 ≥𝑑𝑗,∀𝑗∈𝐵(3) 𝑡𝑖,𝑗 ≤(1 −𝛾)𝑑𝑗,∀𝑖∈𝑆 ,∀𝑗∈𝐵(4) Eq. (2) ensures that the total sales quantity of a supplier cannot exceed the supplier’s production capacity 𝑦𝑖. Eq. (3) guarantees that the total purchase quantity of a buyer satisfies the buyer’s demand 𝑑𝑗. Eq. (4) forces the quantity transported from supplier 𝑖to buyer 𝑗is less than or equal to the buyer’s demand considering 𝛾. Fig. 1illustrates how the supply chain works in the proposed model. In this example, we assume that there are only two suppliers and two buyers in the supply chain. The USD sales per employee of suppliers A and C are $1,000,000 each. Products from suppliers A and C arrive at each export port via land routes, with delivery conditions specified as FOB. Large quantities of products are transported by container ships and small quantities are transported by LCLs from export ports to the buyers’ designated ports. At this stage, the delivery conditions are specified as CFR. To explain the TDCs calculation in detail, using the freight volume in Fig. 1and the data from Section 4.2, an example to calculate TDCs is presented as follows. 𝐷 𝑖𝑓 𝑓 𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 𝑐 𝑜𝑠𝑡𝑠 𝑜𝑓 𝑆 𝑢𝑝𝑝𝑙 𝑖𝑒𝑟 𝐴 =4146 20 × 20 +1166 20 × 8 + 456 × 28 + 69 × 28 +((1140 +4146 20 )× 20 × 63093)+((1056 +1166 20 )× 8 × 63093) 1000000 +((1140 +4146 20 )× 20 × 0 +(1056 +1166 20 )× 8 × 0.039) = 21922.6 𝐷 𝑖𝑓 𝑓 𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 𝑐 𝑜𝑠𝑡𝑠 𝑜𝑓 𝑆 𝑢𝑝𝑝𝑙 𝑖𝑒𝑟 𝐶 =3053 20 × 2 +315 20 × 40 + 867 × 42 + 98 × 42 +((1140 +3053 20 )× 2 × 39472)+((1056 +315 20 )× 40 × 39472) 1000000 +((1140 +3053 20 )× 2 × 0 +(1056 +315 20 )× 40 × 0.039) = 44931.44 𝑇 𝐷 𝐶 𝑠=𝐷 𝑖𝑓 𝑓 𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 𝑐 𝑜𝑠𝑡𝑠 𝑜𝑓 𝑆 𝑢𝑝𝑝𝑙 𝑖𝑒𝑟 𝐴 +𝐷 𝑖𝑓 𝑓 𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 𝑐 𝑜𝑠𝑡𝑠 𝑜𝑓 𝑆 𝑢𝑝𝑝𝑙 𝑖𝑒𝑟 𝐶 = 66854.04 (𝑈 𝑆 𝐷) 4. Case study: Cationic reagent industry 4.1. Background A cationic reagent is considered as a mature product. The cationic reagent industry is oligopolistic with only seven suppliers spread across Operations Research Perspectives 14 (2025) 100325 5 J. Kang et al. Fig. 1. A schematic example of the supply chain in this study. Fig. 2. Capacity utilization and sales quantity in the ideal equilibrium. five countries. In 2019, the total production capacity of these suppliers was 170,000 tons, while the total demand from all buyers was 127,654 tons. In other words, the market is experiencing an oversupply of cationic reagents, leading to intense competition among suppliers. Cationic reagents are typically traded in 230-kg drums, 1,100-kg intermediate bulk containers, and 20,500-kg flex bags, and are usually transported in 20-foot dry containers with a capacity of 20 tons. 4.2. Data This case study uses publicly available and accessible data from the cationic reagent industry [42]. The global supply chain for cationic reagents includes seven suppliers and twenty-six buyers. Table 3and Table 4illustrate the data for the suppliers and buyers, respectively. The primary raw material for cationic reagents is propylene [43]. The raw material price (i.e., the price of propylene) illustrated in Table 3is based on the second week of October 2020 [44]. It requires 0.2 MT of propylene to synthesize 1 MT of cationic reagents. The annual labor costs for each supplier are referenced from the data of their respective countries, published by the OECD in 2020 [45]. To standardize the unit of annual labor costs into U.S. dollars (USD), we use the exchange rate from 2019. While reliable data on the labor productivity of suppliers A, B, D, E, F, and G are lacking, we do have reliable data for supplier C. Given the mature nature of the industry, with minimal technological and quality differences among suppliers, supplier C’s labor productivity is assumed to be representative of the other suppliers (𝑢𝐶=𝑢𝑖, where 𝑖∈𝑆). Industrial electricity prices are obtained from the data of each supplier’s country [46]. For reference, this case study sets the electricity requirement for producing one unit of cationic reagents at 250 kWh. Freight costs from suppliers to buyers are collected from relevant online sources [47,48]. The import tariff rate for each country is based on the HS-CODE 2923.90 for cationic reagents. The HS-CODE is an internationally standardized system for classifying traded products and facilitating global customs processes and trade regulations [49]. 4.3. Ideal equilibrium and purpose of market players The ideal equilibrium, achieved through cooperation among market players, is obtained by solving the MILP described in Section 3.3 with 𝛾set to zero. The results, which minimize TDCs in the cationic reagent industry, are presented in Table 5and Fig. 2. Suppliers B, C, E, F, and G achieve full utilization, while suppliers A and D show low utilization. If market players make multilateral concessions and cooperate, TDCs in the cationic reagent industry can be reduced, thereby increasing the competitiveness of the entire industry. However, achieving the ideal equilibrium is challenging due to market players pursuing their individual interests. To test this hypothesis, experiments are conducted to maximize the profits of market players. Given that the target industry is oligopolistic and competitors are wellinformed about each other, the objective functions are set to maximize the overall sales of suppliers and minimize the overall costs of buyers. First, an experiment is conducted to maximizes suppliers’ sales (i.e., FOB sales) reflecting suppliers’ interests. In this experiment, Eq. (5) Operations Research Perspectives 14 (2025) 100325 6 J. Kang et al. Table 3 Data on suppliers. Supplier 𝑖Location Capacity (MT/Year) Raw material price (USD/MT) Labor costs (USD/Year) Industrial electricity price (USD/MWH) A North America 30,000 456 63,093 69 B North America 25,000 456 63,093 96 C North East Asia 25,000 867 39,472 98 D Western Europe 20,000 920 54,262 86 E Western Europe 20,000 920 44,111 74 F North east Asia 30,000 899 10,941 40 G North East Asia 20,000 899 10,941 40 Table 4 Data on buyers. Buyer 𝑗Location Demand (MT/Year) Sale price (USD) Freight costs (USD/20 ft container) when purchasing from supplier 𝑖 Import tariffs (%) when purchasing from supplier 𝑖 A B C D E F G A B C D E F G A’ USA 29,960 1,140 0 0 3,539 2,058 2,503 3,406 3,406 0 0 0 6.2 6.2 6.2 6.2 B’ Canada 4,674 1,140 4,146 4,613 3,053 2,495 2,695 2,949 2,949 0 0 0 0 0 0 0 C’ Brazil 2,133 1,208 796 2,190 3,650 420 834 3,650 3,650 2 2 2 2 2 2 2 D’ Mexico 1,823 1,208 1,095 2,929 3,815 1,780 1,835 3,815 3,815 0 0 0 0 0 0 0 E’ Rest of Latin America 3,182 1,208 685 1,882 3,650 420 834 3,650 3,650 0 0 0 0 0 0 0 F’ Germany 5,674 1,163 491 993 892 7 8 839 839 6.5 6.5 0 0 0 6.5 6.5 G’ Italy 4,355 1,163 622 1,755 950 14 34 950 950 6.5 6.5 0 0 0 6.5 6.5 H’ France 2,879 1,163 472 811 867 4 12 839 839 6.5 6.5 0 0 0 6.5 6.5 I’ UK 4,625 1,163 491 940 1,307 4 11 1,339 1,339 6.5 6.5 0 0 0 6.5 6.5 J’ Spain 2,305 1,163 682 1,046 1,265 9 28 1,097 1,097 6.5 6.5 0 0 0 6.5 6.5 K’ Benelux 2,622 1,163 497 993 867 0 10 839 839 6.5 6.5 0 0 0 6.5 6.5 L’ Russia 5,136 1,163 1,319 1,852 1,485 516 N/A 1,427 1,427 3 3 3 3 3 3 3 M’ Rest of Europe 3,225 1,163 472 993 867 3 17 839 839 6.5 6.5 0 0 0 6.5 6.5 N’ India 7,452 1,091 1,309 1,652 1,075 923 1,939 1,075 1,075 10 10 0 10 10 10 10 O’ ASEAN 9,655 1,091 1,077 1,177 65 950 1,123 125 125 0 0 0 0 0 0 0 P’ Rest of South Asia 5,272 1,091 1,010 1,170 410 1,027 1,198 260 260 5 5 0 5 5 0 0 Q’ China 14,046 1,056 877 890 120 800 1,048 0 0 10 10 0 6.5 6.5 0 0 R’ Japan 5,623 1,056 1,166 1,166 315 1,060 1,298 300 300 3.9 3.9 3.9 0 0 3.9 3.9 S’ South Korea 5,210 1,056 777 1,002 0 800 1,048 300 300 0 0 0 0 0 2.6 2.6 T’ Australia 2,065 1,116 1,661 1,661 1,145 958 958 1,345 1,345 0 0 0 0 0 0 0 U’ New Zealand 556 1,116 1,661 1,661 1,145 958 958 1,345 1,345 0 0 0 0 0 0 0 V’ GCC 2,340 1,228 1,048 1,336 586 689 1,089 855 855 5 5 5 5 5 5 5 W’ Turkey 396 1,228 972 1,209 1,325 595 1,161 1,325 1,325 6.5 6.5 0 0 0 6.5 6.5 X’ North Africa 865 1,228 1,272 1,256 1,682 686 1,320 1,714 1,714 2 2 2 0 0 2 2 Y’ South Africa 940 1,228 1,880 2,363 1,069 N/A N/A 1,620 1,620 0 0 0 0 0 0 0 Z’ Rest of Middle East 641 1,228 1,201 1,299 882 739 1,064 1,024 1,024 5 5 5 5 5 5 5 Table 5 Experimental results of the ideal equilibrium (units: million USD). Costs Supplier A B C D E F G Total Differential costs 7.13 35.94 26.35 3.98 23.04 14.58 9.66 120.69 Freight costs 0 0 0.74 0.06 0.02 0.02 0.94 3.31 Import tariff 0 0 0.24 0.05 0 0 0.19 0.72 Raw material costs 0.45 2.28 4.34 0.50 3.68 3.68 3.60 20.24 Electricity costs 0.09 0.43 0.61 0.06 0.37 0.37 0.20 2.06 Labor costs 6.59 33.22 20.43 3.32 18.97 18.97 4.74 94.36 replaces Eq. (1) as the objective function, as described in Section 3.3. 6illustrates that maximizing supplier sales diminishes the competitiveness of the entire industry. Specifically, maximizing FOB sales increases TDCs by $11.06 million compared to the ideal equilibrium. Additionally, Table 6indicates a significant rise in import tariffs for suppliers B, E, F, and G, who have low levels of FTAs. Furthermore, supplier D’s labor costs significantly increase, reducing its cost competitiveness. 𝑀 𝑖𝑛𝑖𝑚𝑖𝑧𝑒 ∑ 𝑖∈𝑆∑ 𝑗∈𝐵 𝑏𝑗𝑡𝑖,𝑗 (5) Second, similar to previous studies [17,18,22], an experiment is conducted to minimize the costs for buyers (i.e., CFR sales) reflecting buyers’ interests. In this experiment, Eq. (6) replaces Eq. (1) as the objective function, as described in Section 3.3. CFR sales encompass the sum of FOB sales, freight costs, and import tariffs paid by buyers representing the actual purchase costs. Table 7illustrates that minimizing buyers’ actual purchase costs results in a $20.83 million increase Table 6 Experimental result of maximizing sales of suppliers (unit: million USD). Costs Supplier A B C D E F G Total Increase † Differential costs 0 21.72 25.00 27.83 28.28 17.33 11.58 131.75 11.06 Freight costs 0 0.90 0.28 0.50 2.30 2.49 1.83 8.30 4.99 Import tariff 0 0.59 0.24 0 1.44 1.90 0.88 5.05 4.33 Raw material costs 0 1.16 4.32 3.68 3.68 5.39 3.60 21.84 1.60 Electricity costs 0 0.22 0.61 0.43 0.37 0.30 0.20 2.13 0.07 Labor costs 6 18.85 19.55 23.22 20.49 7.25 5.07 94.43 0.07 †Increase refers to the rise in each type of costs compared to what is seen in the ideal equilibrium. in TDCs compared to the ideal equilibrium. This increase is primarily due to a significant rise in labor costs for suppliers A and D, making them less cost-competitive. The competitiveness of the cationic reagent Operations Research Perspectives 14 (2025) 100325 7 J. Kang et al. Table 7 Experimental result of minimizing buyers’ actual purchase costs (units: million USD). Costs Supplier A B C D E F G Total Increase † Differential costs 43.95 6.94 26.46 29.36 23.07 11.72 0 141.51 20.83 Freight costs 0.20 0 0.66 0.81 0.006 0.17 0 1.90 −1.41 Import tariff 0 0 0.19 0.24 0 0.23 0 0.66 −0.07 Raw material costs 2.74 0.44 4.34 3.68 3.68 5.00 0 19.88 −0.36 Electricity costs 0.52 0.08 0.61 0.43 0.37 0.28 0 2.29 0.23 Labor costs 40.49 6.42 20.66 24.21 18.97 6.03 0 116.78 22.42 †Increase refers to the rise in each type of costs compared to what is seen in the ideal equilibrium. industry is therefore adversely affected by market players’ efforts to maximize their individual profits. 𝑀 𝑖𝑛𝑖𝑚𝑖𝑧𝑒 ∑ 𝑖∈𝑆∑ 𝑗∈𝐵 (𝑏𝑗+𝑓𝑖,𝑗 )(1 +𝑥𝑖,𝑗 )𝑡𝑖,𝑗 (6) 4.4. Risk management This subsection investigates supply chain risk management through two experiments. The first examines how TDCs increase or decrease in response to different levels of risk hedging. The second assesses the impact of trade disputes on supply chains and TDCs. The equilibrium is obtained by solving the MILP described in Section 3.3 changing 𝛾. 4.4.1. Impact of risk hedging on TDCs Buyers want to reduce the risk from suppliers failing to deliver products when designing their supply chains. Even if additional costs are needed, concessions and cooperation between market players can lower risks [50]. Apart from concession and market players cooperating, diversifying suppliers is an effective strategy for reducing the risk for buyers. In Section 3.2, it is assumed that buyers have an equivalent level of risk hedge tendency (𝛾) in their purchasing strategies. In this experiment, adjusting 𝛾in Constraint (4) yields changes in TDCs. As 𝛾approaches zero, the quantity that a buyer receives becomes more concentrated on a single supplier. Conversely, as 𝛾approaches 1 −1 𝑚, suppliers become more diversified. For example, if 𝛾is 0.5, a buyer does not purchase more than 50% of the demanded quantity from any single supplier. With 7 suppliers, the minimum percentage required to satisfy more than 100% of the total demand is 15% when considering only integers. However, under this condition, a buyer has to purchase similar amounts close to 15% from each of the 7 suppliers, making it hard to observe changes in sales quantities depending on the market environment. Therefore, the maximum 𝛾is limited to 0.84 in this study. TDCs are lowest when a buyer can purchase the entire demanded quantity from a single supplier (𝛾= 0), as shown in Fig. 3. TDCs and freight costs generally increase when suppliers are diversified. This is because when buyers diversify their suppliers, they eventually purchase the remaining quantities from suppliers located far away. However, despite the increases in TDCs and purchase costs, buyers can ensure supply chain stability by establishing business relationships with various suppliers, making it challenging for the cationic reagent industry to reach the ideal equilibrium. Note that freight costs slightly decrease when 𝛾is 0.4 compared to 0.3. This is because, as the buyer’s purchase limit from a supplier is reduced from 70% to 60%, supplier E, located in Western Europe, diversifies exports to buyers D’ (Mexico), E’ (the rest of Latin America), T’ (Australia), and U’ (New Zealand), where freight costs are higher. (see Fig. 4). 4.4.2. Impact of trade dispute on supply chains When trade disputes arise between countries, trade barriers such as tariffs are often imposed on products and services from the affected counterparts. For example, when a trade dispute between the United States and China erupted in October 2019, both countries imposed retaliatory tariffs on each other’s products [51]. In this subsection, we examine the effects of increased retaliatory tariffs between the United States and China on supply chains. Prior to the dispute, a 10% import tariff was applied to products from US-based suppliers A and B when exported to China, while a 6.2% import tariff was applied to products from Chinese-based suppliers F and G when exported to the US. Following the trade dispute, both countries increased the retaliatory tariff to 30%. Fig. 5illustrates that when 𝛾is zero, the increase in TDCs is negligible because each country has its domestic suppliers, and no trade exists between the two countries. As 𝛾increases, the impact of trade disputes on TDCs increases. This trend intensifies when a hypothetical 100% retaliatory tariff is imposed on both countries. With a 100% retaliatory tariff applied, when 𝛾exceeds 0.6, changes in sales quantities of each supplier before and after the dispute start to occur, as shown in Fig. 6. This means that as 𝛾increases, the trade network between buyers and suppliers becomes significantly complex, and retaliatory tariff rates between two countries owing to the trade dispute also affect other market players. 4.5. Decrease in demand The outbreak of COVID-19 has led a contraction in global economic activity and major downstream sectors of the cationic reagent industry, such as the printing paper industry, have significantly deteriorated. As non-face-to-face social activities were encouraged, remote work and home education spread, decreasing the production of printed promotional materials. Pandemics, such as COVID-19, accelerated the risk of disruptions in production lines, decreasing product demand for all market participants [50]. This subsection examines the effects of a decrease in demand in supply chains. The equilibrium is obtained by solving the MILP described in Section 3.3, changing 𝛾in Eq. (4) and 𝑑𝑗in Eqs. (3) and (4). Sales quantities are observable when demand from all buyers decreases by 15% and 30%, respectively. When 𝛾is zero, a 15% decrease in demand results in sales quantities of suppliers A and D dropping to zero, leading to their operations being halted, as shown in Fig. 7. A 30% decrease in demand results in supplier’s operation (i.e., supplier B) being halted in addition to suppliers A and D. When 𝛾is 0.6, a 15% decrease in demand does not cause any supplier to cease operations. However, a 30% decrease in demand forces suppliers A, B, and D to cease their operations. When 𝛾 is 0.84, no supplier needs to halt operations even in the event of a 30% decrease in demand. Since the total sales quantity decreases with a decrease in demand, the concept of TDCs per unit is used in this subsection to observe the effect of a decrease in demand on TDCs. TDCs per unit are obtained by dividing TDCs by the total sales quantity. As demand decreases, TDCs per unit also decrease, as shown in Fig. 8. This means that decreased demand increases the opportunity to reduce differential costs, including logistics costs, electricity costs, labor costs, raw material costs, and import tariffs. However, as 𝛾increases, TDCs per unit decreases less significantly. This means that the opportunity to reduce differential costs diminishes because buyers are compelled to diversify suppliers. Note that 𝛾at which fluctuations in sales quantities occur increases as demand decreases by 15% or 30%. This is because buyers have to reduce their purchases as demand decreases, while suppliers’ supply remains unchanged, allowing other buyers to purchase more products from cost-competitive suppliers. As shown in Table 8, the products of non-competitive suppliers A, B, and D are no longer purchased by buyers as demand decreases by 30%. Operations Research Perspectives 14 (2025) 100325 8 J. Kang et al. [33] Yilmaz OF, Ozcelik G, Yeni FB. 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