Integrated planning for a global pharmaceutical supply chain: an ambidexterity perspective

Yousefi Sarmad, Mahsa; Pishvaee, Mir Saman; Jahani, Hamed; Khaksar, Seyed Mohammad Sadegh; Ivanov, Dmitry Article — Published Version Integrated planning for a global pharmaceutical supply chain: an ambidexterity perspective Annals of Operations Research Provided in Cooperation with: Springer Nature Suggested Citation: Yousefi Sarmad, Mahsa; Pishvaee, Mir Saman; Jahani, Hamed; Khaksar, Seyed Mohammad Sadegh; Ivanov, Dmitry (2023) : Integrated planning for a global pharmaceutical supply chain: an ambidexterity perspective, Annals of Operations Research, ISSN 1572-9338, Springer US, New York, NY, pp. 1-50, https://doi.org/10.1007/s10479-023-05554-5 This Version is available at: https://hdl.handle.net/10419/308119 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/ Annals of Operations Research https://doi.org/10.1007/s10479-023-05554-5 ORIGINAL RESEARCH Integrated planning for a global pharmaceutical supply chain: an ambidexterity perspective Mahsa Yousefi Sarmad1·Mir Saman Pishvaee1·Hamed Jahani2· Seyed Mohammad Sadegh Khaksar3·Dmitry Ivanov4 Received: 15 March 2022 / Accepted: 8 August 2023 © The Author(s) 2023 Abstract Based on the concept of ambidexterity, we develop a multi-objective, multi-product, and multi-period model to integrate planning for research and development (R&D) and production and distribution (P&D) in a global pharmaceutical supply chain (PSC) considering delays in the entire supply chain. We also propose robust possibilistic programming (RPP) approach to deal with the epistemic uncertainty of some critical input parameters. Applying the ambidexterity approach that emphasizes optimizing a balanced framework based on the R&D and P&D planning, our study reconciles the explorative and exploitative supply chain strategies in the context of global PSCs. The proposed integrated model can manage the inherent delays and uncertainties in the R&D processes and P&D systems via a novel, credibility-based, robust possibilistic programming model. We illustrate the application of our model using a real-world case study of one of the largest and most reputable pharmaceutical companies in Iran. The results affirm the credibility and feasibility of the proposed model when juxtaposed with a non-integrated model. Our study suggests the use of ambidexterity approach in resource allocation planning, risk management, and enhancement of performance in sophisticated settings such as global PSCs. BDmitry Ivanov [email protected] Mahsa Yousefi Sarmad [email protected] Mir Saman Pishvaee pishv[email protected] Hamed Jahani [email protected] Seyed Mohammad Sadegh Khaksar [email protected] 1School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran 2School of Accounting, Information Systems and Supply Chain, RMIT University, Melbourne, Australia 3La Trobe Business School, La Trobe University, Melbourne, Australia 4Berlin School of Economics and Law, Global Supply Chain and Operations Management, Berlin, Germany 123 Annals of Operations Research Keywords Pharmaceutical supply chain ·Global supply chain ·Research and development (R&D) ·Production and distribution ·Robust possibilistic programming ·Ambidexterity 1 Introduction The unique characteristics of pharmaceutical products in achieving sustainable community health make global pharmaceutical supply chains (PSCs) dynamic and complex. Disruptions at any stage of a global PSC’s planning and coordination can significantly impact the supply chain efficiency and directly affect human lives at the global level (Lücker & Seifert, 2017). Therefore, PSCs utilize strategies to minimize the risk of investment failures. Such strategies involve planning for research and development (R&D) processes and optimizing production and distribution (P&D) of pharmaceutical products. Planning for R&D processes occurs in the early stages of global PSCs when the chains adopt an explorative supply chain approach to produce new pharmaceutical products. This can be seen in the cumulative R&D expenditure of a pharmaceutical company over the long term. According to Austin and Hayford (2021), investments in R&D processes in the pharmaceutical industry have a success rate of only 12% and may take up to a decade to be commercialized. The industry has experienced increased investments in the R&D activities over the past two decades (Marques et al., 2020). Prior studies proposed complex mathematical models like the random capacity planning model for clinical trials, which used a scenario-based approach (Rotstein et al., 1999), realistic risk-assessment models (Colvin & Maravelias, 2011), multi-stage, multi-period stochastic capacity planning models (Gatica et al., 2003), multi-period models for the development of new products (Jahani et al., 2017; Rogers et al., 2002), and multi-site, multi-period, multi-product capacity-planning models (Levis & Papageorgiou, 2004). In addition, P&D planning allows the pharmaceutical industry to exploit currently developed products, market share, and solutions to responding to unprecedented changes in demand patterns, especially at the times of crisis (Marques et al., 2019; Nasrollahi & Razmi, 2021; Rekabi et al., 2021). Therefore, many companies in the pharmaceutical industry consider the P&D planning as a solution to reducing supply chain costs and risks (Guerrero et al., 2013; Liu et al., 2017). This requires the global PSCs to optimize operating models and speed up the pace of mass production and delivery in a short period of time (Gilani & Sahebi, 2022). Some prior studies, therefore, focused on exploitative strategies that demonstrate allocationdistribution optimization (Laínez et al., 2012;Sousaetal.,2011), multi-product distribution planning (Guerrero et al., 2013; Zandkarimkhani et al., 2020), or multi-period and multiproduct production, distribution and capacity planning models (Kabra et al., 2013; Saracoglu et al., 2014). Some other studies applied fuzzy rule-based systems (Shakouhi et al., 2021; Zandkarimkhani et al., 2020) and possibilistic programming (Savadkoohi et al., 2018). We discerned that many prior studies predominantly focused on one of two areas in global PSCs. They either examined planning for R&D processes, encapsulating the explorative approach, or they concentrated on P&D planning, representing the exploitative approach. This may render suboptimal solutions and increase the risk of failure across the supply chain, as both planning for R&D processes and P&D planning are interlinked and necessary (Marques et al., 2020). To bridge this research gap, the literature suggests the concept of ambidexterity, which refers to an organization’s ability to simultaneously pursue both explorative and exploitative approaches (Junni et al., 2013). 123 Annals of Operations Research The explorative approach is associated with the search, experimentation, and R&D processes. However, it may require vast investment in the early stages of a product’s lifecycle (Rojo et al., 2016). It will develop the long-term supply chain’s objective to improve profitability (Kristal et al., 2010). In contrast, an exploitative approach is related to continuous improvements, innovative execution, and waste reduction through optimal operational costs that enhance supply chain efficiency (Blome et al., 2013). This study aims to propose an integrated planning model for complex R&D processes and P&D systems that can help optimize explorative and exploitative approaches to profitability across a PSC. Indeed, any delays in the commercialization of pharmaceutical products increase risks of investments in planning for R&D activities and reduce public trust and customer satisfaction. This study develops a multi-objective, multi-product, and multi-period model for integrating R&D and P&D planning decisions in a global PSC, considering delays and operational costs in the chain, and proposes a robust possibilistic programming (RPP) approach to deal with the epistemic uncertainty of some critical input parameters (e.g., those in crisis). Integrating R&D and Production and P&D planning decisions in a global pharmaceutical supply chain requires a multi-objective, multi-product, and multi-period model due to the inherently complex and uncertain nature of this industry. This model serves two opposing yet interconnected objectives. First, it aims to maximize ENPV of total profit. The maximization of ENPV is a critical element in any business model, but more so in pharmaceuticals, where significant upfront investment is required in the early stages of a product’s lifecycle, particularly in R&D. The expected payoff from these investments occurs over an extended period, thus emphasizing the need to focus on long-term profitability. Second, the model strives to minimize the maximum unsatisfied demands. In the pharmaceutical industry, unsatisfied demand can have serious health consequences for patients and can harm a company’s reputation. It is essential to minimize such demands, ensuring an adequate and consistent supply of products. The need for such a model is further amplified by the industry’s complexity. With multiple products, each with its own lifecycle and demand patterns, the planning process becomes increasingly sophisticated. In addition, the model accounts for different time periods, recognizing that decisions made today have impacts that unfold over many years. In addition, as the success rate of a patent in this industry is low, generic pharmaceutical products will have a higher chance to enter the market, with lower cost than innovative products. Therefore, we define another objective function to maximize the production of innovative pharmaceutical products to better address the profitability of innovative products. The remainder of this paper is as follows: The next section provides a literature review on the global pharmaceutical supply chain, with an emphasis on planning for R&D processes and planning for P&D. In the following section, we articulate the significant research contributions. We then explore the problem context where we discuss the specific environment and circumstances in which our model was evaluated. The next section describes the formulation of our model and the objective functions, detailing the mathematical representation of the decision-making problem. After the model has been established, the following section discusses the implementation and assessment of the proposed model, including the process of data collection, as well as presenting the results from the Pareto analysis, model validity checks, and sensitivity analysis. The paper culminates with a critical discussion on the results of our study, where we interpret the findings in light of the existing literature and propose the theoretical and practical implications that emerge from our work. 123 Annals of Operations Research 2 Literature review 2.1 Pharmaceutical industry characteristics The global pharmaceutical industry includes (1) innovative pharmaceutical products (an exclusive patent of 10–20 years) that require high R&D expenditures at the early stages of production; and (2) generic pharmaceutical products with limited expiration of the original product’s copyright or license, maintained by manufacturers involved in the process of production (Lücker & Seifert, 2017; Marques et al., 2020). It is noteworthy that governments often set regulations for generic pharmaceutical products that the pharmaceutical industry must comply with (Abraham et al., 2003). Regardless of the product type, the complexity of pharmaceutical product development has significantly increased over the past two decades (Laínez et al., 2012), requiring regulatory agencies to consider more rigorous procedures to protect public health. For example, the Food and Drug Administration (FDA) in the USA and the European Medicines Agency (EMA) in Europe are regulatory authorities that develop and establish policies to ensure the safety, efficacy, and security of residents across the production, marketing, and distribution phases in food, cosmetic, and pharmaceutical products (Marques et al., 2020). These regulatory authorities also support the pharmaceutical industry to accelerate innovation in pharmaceutical products and make them more effective, affordable, and secure (Abraham et al., 2003). Although some developing countries like India or China rely on their own regulatory authorities (e.g., the Drug Controller Generalin India) (Mahajan et al., 2015), due to the rigid framework of the process of new product development in the global pharmaceutical industry, governments in many developing countries pursue the regulations recommended by the FDA in the USA or the European Medicines Agency (EMA) in Europe. The Iran Food and Drug Administration (IFDA) is a regulatory agency that oversees clinical investigations of pharmaceutical products in Iran (Iran Food and Drug Administration, 2021). According to the FDA (2021), the R&D processes of pharmaceutical products consist of five phases (e.g., discovery and development, pre-clinical, clinical, FDA approval, and safety monitoring), followed by the P&D processes (i.e., production, marketing, distribution and delivery in customer zone). These phases are described in Fig. 1. Indeed, the process of new product development, commercialization and distribution in the pharmaceutical industry imposes substantial challenges for decision-makers. Many scholars considered R&D and P&D processes as the two ends of a typical PSC (e.g., see Lücker & Seifert, 2017; Narayana et al., 2014; Shah, 2004). In other words, R&D processes in a PSC are tailored by the post-market safety monitoring phase (i.e., mass production, inventory, distribution and delivery), making a PSC more complex than a typical supply chain. Therefore, the PSC design has been often a challenging topic in production and operations research (Marques et al., 2018). As a result, Laínez et al., (2012, p. 20) stated that “[the] high cost and low rate in product discovery and clinical development” create a paradoxical tension in commercializing pharmaceutical products; therefore, the industry may be too uncertain about investing in the new products and may look for externally developed products instead. From the global perspective, strict regulations for new product development in a country can lead to a situation when P&D processes in other countries increase the burden of inventory management, leading to the loss of product values. Furthermore, the complexity of stakeholder engagement in a global PSC (e.g., R&D teams, manufacturers, distributors, customers, service providers, regulatory agencies, and governments) makes investments in new products too risky (e.g. see Bhakoo & Chan, 2011). In this vein, Marques et al. (2019) 123 Annals of Operations Research Fig. 1 R&D and P&D processes in a PSC recommended that future modeling approaches consider key stakeholders’ roles in new pharmaceutical development and commercialization to leverage efficiency in the entire PSC. Therefore, pharmaceutical companies prefer to invest less in the early stages of new pharmaceutical product development, and this in turn creates many opportunities for developing countries (e.g., India) to take advantage of the capitalized low-cost production nature of the pharmaceutical industry (Mahajan et al., 2015). 2.2 Ambidexterity in the global PSC The concept of ambidexterity refers to situations in which an organization or a network of organizations explore new knowledge while simultaneously exploiting current opportunities (Junni et al., 2013). Ambidexterity enables organizations to achieve a sustainable competitive advantage by utilizing the existing opportunities and getting ready for future challenges (Ardito et al., 2020). In the context of supply chain management, actors must actively coordinate and integrate organizational resources to achieve these two objectives (Aslam et al., 2018). Early conceptualization of ambidexterity in supply chain management is rooted in studies by Kristal et al. (2010) and Blome et al. (2013), which examined the simultaneous influence of exploitative and explorative supply chain approaches. These studies later inspired a body of research on how ambidextrous supply chain approaches can improve supply chain performance (Aslam et al., 2018). Rojo et al. (2016) and Salvador et al. (2014) suggested that ambidexterity in supply chain management enables the chain to become efficient by focusing on existing opportunities and acquiring external knowledge about market demand. Therefore, Aslam et al. (2018) concluded that in the supply chain ambidexterity, organizations could 123 Annals of Operations Research quickly respond to short-term market changes and establish long-term strategies to improve profitability. To better understand the role of ambidexterity in the pharmaceutical industry, we need to articulate the relationships between the explorative and exploitative supply chain approaches and how these two can impact performance. In a meta-analysis on ambidexterity and performance in eight industries (e.g., the pharmaceutical industry), Junni et al. (2013) found that integrating explorative and exploitative approaches can improve organizational profitability. He and Wong (2004) found that organizations may respond differently toward these two approaches (e.g., emphasizing one over the other). Uotila et al. (2009) stated that the balance between the explorative and exploitative supply chain approaches is defined based on the power of internal and external factors. For example, an explorative approach may be appropriate for R&D planning, whereas an exploitative approach may work better in situations where the pharmaceutical products must meet the market demand. Uotila et al. (2009) therefore highlighted that the integration between the two approaches is critical in the R&D-intensive supply chain design (e.g., the pharmaceutical industry). 2.2.1 Planning for R&D processes (the explorative approach) Schmidt and Grossmann (1996) and Jain and Grossmann (1999) proposed optimization models using a mixed-integer linear program (MILP) with resource constraints to reduce the scheduling of testing tasks in phases of discovery and development and preclinical research in R&D planning. Rotstein et al. (1999) presented a random capacity planning model (based on the MILP methodology) for Phase 3 of R&D planning (clinical trials). They also used the model to minimize investments in product development and introduction strategy of pharmaceutical products. Gatica et al. (2003) presented a multi-stage, multi-period stochastic capacity planning model to optimize planning for R&D processes in the clinical trial phase. They proposed the R&D planning as a large-scale, multi-stage, and multi-period stochastic optimization problem that must be resolved through an optimization-based approach. Their methodology reformulated the problem as a multi-scenario MILP model, enabling R&D planning for multiple products to be efficient. This methodological approach was also applied by Maravelias and Grossmann (2001), Rogers et al. (2002) and Levis and Papageorgiou (2004) who proposed a multi-period model for the development of new products, using MILP to maximize the net value of introducing new products to the market. However, these studies applied a heuristic algorithm based on Lagrangean decomposition to propose optimal or near-optimal solutions to the R&D processes. Some other studies have applied a combination of mathematical modeling approaches to resolving the issues of R&D planning in the pharmaceutical industry. For example, Luna and Martínez (2018, p. 1063) proposed a model-based optimization strategy using a probabilistic tendency approach to efficiently improve operating scenarios in new product development. Their mathematical modeling helped mitigate the risk of failure in the early stages of product development. Colvin and Maravelias (2011) proposed a multi-stage stochastic programming framework to (1) optimize the selection and scheduling of R&D activities using the pass/fail uncertainty conditions; (2) optimize the resource planning decisions (e.g., contracts, outsourcing procedures) for multiple products; and (3) provide a framework for formulating value at risk in pharmaceutical companies. Considering the importance of decisions at the early stages of R&D processes, Marques et al. (2018) presented a multi-objective integer programming model to develop the best design strategy for maximizing the productivity of R&D processes. None of these studies, however, has explicitly considered links of R&D and P&D—a distinct and substantial contribution made by our study. 123 Annals of Operations Research 2.2.2 Planning for P&D processes (the exploitative approach) Planning for P&D is as important as R&D in designing a PSC. Although clinical trials (Phase 3 of R&D activities) help gather important information, the true picture of a product’s efficacy and safety evolves over time, especially when it enters the market for consumption (Lücker & Seifert, 2017; Mahajan et al., 2015). Furthermore, after a new pharmaceutical product is prepared for commercialization (Phase 5 of R&D activities), the success of P&D systems is not necessarily guaranteed (FDA, 2021). Accelerating the pharmaceutical product’s P&D systems is, therefore, important for two reasons. First, capturing a large portion of the market share for a new product may require years of marketization and commercialization (Marques et al., 2020). Second, to maximize the pace of P&D systems for the pharmaceutical product while minimizing operational costs (e.g., mass production, storage, transportation), it is important not to focus only on one part of the PSC. Many studies in P&D planning reviewed settings with primary and secondary pharmaceutical production operations (Marques et al., 2020). Primary production (i.e., pharmaceutical substance manufacturing) focuses on transforming primary components into active pharmaceutical ingredients that require a chain of chemical and separation processes. Secondary production (i.e., pharmaceutical product manufacturing) focuses on transforming the active pharmaceutical ingredients into end products that are ready for delivery to customers. This often involves further procedures such as standardizing dosages for different groups, packaging, and developing security against expiration. Therefore, the secondary production must be aligned with distribution networks to ensure the efficiency of the entire PSC (Jahani et al., 2023). Although time and cost are two aligned constraints in the literature of PSC design, some studies focused on these two constraints to provide better strategic decisions for policymakers in both the primary and secondary production operations. According to Rekabi et al. (2021), operating times in the production and delivery of pharmaceutical products in PSCs is vital; therefore, they combined the two multi-objective methods using LP-metric and goal attainment to increase the performance of a real-world production–distribution system. In contrast, Zandkarimkhani et al. (2020) proposed a bi-objective MILP model using fuzzy rule-based systems for perishable pharmaceutical products to minimize the different yet interlinked variables of the network costs and lost demand amount. They note that some lost sales are inevitable; therefore, companies must invest more in distribution facilities to cover a wide variety of hidden demands in the market. The same findings are also observed in the study by Nasrollahi and Razmi (2021), although their model was based on a multi-objective non-dominated ranked genetic algorithm. Sousa et al. (2011) proposed a mathematical model for optimizing the allocation and distribution structure of a PSC in both primary and secondary production operations. The model was aimed at optimizing the allocation of products to different locations and to customers in various age groups to increase demand satisfaction. However, we found that the study by Uthayakumar and Priyan (2013) is one of the early studies that directly applies operations research and optimization in PSCs to decrease the level of unsatisfied demands. They stated that pharmaceutical product shortages, restrictions in production, and storage and distribution matters require high-level coordination in establishing optimal PSC and inventory management policies; therefore, they proposed a two-echelon mathematical procedure for determining optimal solutions to simultaneously reduce the PSC costs and improve the competitive business environment through minimizing unsatisfied demands. In another study by Akbarpour et al. (2020), an integrated pharmaceutical relief network (min–max robust model) under demand uncertainty and perishability of products in times of crisis was developed and 123 Annals of Operations Research tested in a developing country. This study showed that P&D modeling in the pharmaceutical industry could substantially improve the efficiency of PSCs. Sousa et al. (2011) then considered the critical roles of production cost, transportation cost, tax, and insurance rates at various locations, utilizing a profit maximization objective function, and proposed a model based on two decomposition algorithms. The same practical approach was taken into consideration in the study by Susarla and Karimi (2012), which proposed an integrated procurement P&D planning model for a multi-product PSC. In their study, the integrated mixed-integer programming model is formulated in terms of holding inventory and raw material costs and tax differences. AccordingtoSheuandLin(2012), with the rapid maturity of globalization, global supply chains must utilize operational objectives that help reduce the level of uncertainty and cost and improve coordination in P&D channels. They proposed a multi-objective programming model to systematically minimize network configuration cost and unsatisfied demand and maximize operating profit. Their study later inspired some other PSC studies. For example, Liu et al. (2017) developed two distribution planning models (uncertain demand and service time) for pharmaceutical products using a time–space network approach for daily delivery in a hospital. In addition, Zahiri et al. (2017) proposed a new mathematical model to design a distribution network in a PSC in France in times of crisis. They developed a new approach based on meanabsolute deviation and fuzzy possibilistic-stochastic programming to minimize the total cost of pharmaceutical product delivery while increasing the resilience of the PSC with respect to the social responsibilities of France’s pharmaceutical companies. 2.3 Research contributions As evident in Table 1, we found that studies on PSC planning addressed either R&D planning or P&D planning, even if an integration between these two areas could improve profitability and minimize unsatisfied demand. A lack in this integration may render suboptimal solutions. The integrated planning of R&D processes and P&D operations can help the PSC optimize investments in R&D activities as well as increasing profitability and market share by utilizing effective strategies. Furthermore, delays in R&D phases of production and delivery can jeopardize PSC resilience, both individually and collectively; this is also overlooked in prior studies. Indeed, the timely arrival of pharmaceutical products in the market can increase profitability and reduce unsatisfied demands; this is useful for further investments in R&D processes. To summarize, many prior studies did not consider both the long-term and shortterm benefits of integration in supply chain approaches (i.e., ambidexterity in supply chain management) during PSC planning. This study makes the following contributions to the literature to bridge these research gaps. First, we develop a multi-objective, multi-product, and multi-period model for integrating R&D and P&D planning decisions in a global pharmaceutical supply chain considering delays in R&D and P&D phases. Second, we propose an RPP approach to deal with the epistemic uncertainty of some critical input parameters. Third, applying the ambidextrous approach that emphasizes optimizing a balanced framework based on the R&D planning and P&D planning, our study reconciles the explorative and exploitative supply chain strategies in the context of global PSCs through maximizing ENPV of Total Profit; (ii) minimizing the maximum unsatisfied demands; and (iii) maximizing the production of innovative pharmaceutical products. The integration of these three objective functions within a multi-objective model acknowledges the interconnectedness and interdependencies among various aspects of the 123 Annals of Operations Research Fig. 3 HPC supply chain network use P&D planning for both the generic and innovative pharmaceutical products to optimize the PSC planning. To achieve this, we implemented our proposed model in an authentic case study, Hakim Pharmaceutical Company (HPC), one of the largest and most well-known pharmaceutical companies in Iran. HPC can produce a diverse range of medicines such as tablets, coated tablets, hard gelatin capsules, gel capsules, oral drops, syrups, oral suspensions, topical solutions, topical gels, topical creams, and ointments (HPC, 2021). The underlying structure of the HPC supply chain is shown in Fig. 3. The company has a candidate portfolio of generic and innovative pharmaceutical products that flexibly shape the P&D lines based on the rate of profitability and market share. HPC has also outsourced the production of some generic products to other pharmaceutical companies (HPC, 2021). However, the innovative products that require passing the five phases of R&D planning must be undertaken within HPC itself. Delays in pre-clinical and clinical testing and the IFDA review and approval may also impact benefits resulting from early commercialization (e.g., profitability). Therefore, these delays are also taken into consideration in this study. Although HPC has a large portion of the local market of Iran, its pharmaceutical products are exported to other countries, including Iraq, Afghanistan, Pakistan, United Arab Emirates, Qatar, Turkmenistan, Syria, and Armenia (HPC, 2021). Therefore, the integrated planning for R&D and P&D must comply with international regulations, contracts, and agreements (e.g., Free on Board (FOB) and Cost, Insurance, and Freight (CIF)). This requires us to consider the cost of transportation, insurance, and tax rates between the origin and destination countries. The multi-objective multi-period optimization model for the HPC case is formulated by defining the problem’s parameters, decision variables, objectives, and constraints. The decision variables in this model represent adjustable parameters that have a direct impact on the outcomes. 123 Annals of Operations Research 4 Model formulation The following indices, parameters, and variables are used to formulate the integrated R&D planning and P&D planning problem. 4.1 Nomenclature Indices tIndex of time periods, t∈{1,2,...,T}, unit =year, season, or several months fIndex of manufacturing centers, f∈{1,2,...,F}, unit =number dIndex of distribution centers, d∈{1,2,...,D}, unit =number gIndex of customer zones, g∈{1,2,...,G},unit =number iIndex of pharmaceutical products, i∈{1,2,...,I}, unit =number Parameters (R&D planning) dliR&D time for product in, unit =days, months CDNP1iUnit R&D cost of product iin formulation phase, unit =a currency like $ or Rial CDNP2iUnit R&D cost of product inin IFDA approval phase, unit =a currency like $orRial cr1Marginal cost of delay time in formulation phase, unit =a currency like $ or Rial cr2Marginal cost of delay time in FDA approval phase, unit =a currency like $ or Rial lr1iDelay time for product iin formulation phase, unit =days, months lr2iDelay time for product iin FDA approval phase, unit =days, months Parameters (P&D planning) Pl fi Delay times in production center ffor product i, unit =days, months PC fi Storage capacity of production center ffor product io, unit =number CPfi Unit manufacturing cost of product iin production center f, unit =a currency like $ or Rial CI fi Unit storage cost of product iin production center f, unit =a currency like $ or Rial IIfit Initial inventory of product iin production center fat time period t, unit = number DLC ft Unit delay time cost in production center fat time period t, unit =days, months πiWeight of importance for product i, unit =percentage TR t fTax rate of income of production center fat time period t. If production center is losing out, the tax rate is zero, unit =percentage CFfi Storage capacity of production center ffor product in, unit =number Dt gi Demand in customer zone gfor product iat time period t, unit =number Pdi Price of product iin domestic distribution center d, unit =a currency like $ or Rial Pdi Price of product iin external distribution center d,unit =a currency like $ or Rial Lfd Delay times between production center fand distribution center d,unit =days, months 123 Annals of Operations Research Ldg Delay times between distribution center dand customer zone g, unit =days, months CIdi Unit storage cost of product iin distribution center d, unit =a currency like $ or Rial CdStorage capacity of distribution center dfor product io, unit =number IIdit Initial inventory of product iin distribution center dat time period t, unit = number TC1fd Unit transportation cost between production center fand external distribution center ddfin the country of origin, unit =a currency like $ or Rial TC2fd Unit transportation cost between production center fand distribution center ddf in destination country, unit =a currency like $ or Rial TC3dg Unit transportation cost between distribution center ddfand external customer zone g, unit =a currency like $ or Rial TCdg Unit transportation cost between domestic distribution center ddhand domestic customer zone g, unit =a currency like $ or Rial TCfd Unit transportation cost between production center fand domestic distribution center ddh, unit =a currency like $ or Rial INdUnit insurance cost in domestic distribution center ddhvia marine, unit =a currency like $ or Rial INdUnit insurance cost in external distribution center ddfvia marine, unit =a currency like $ or Rial μiPercentage of marketing cost, unit =% rf Rate of inflation, unit =% rt Rate of interest, unit =% ex f iExpiration time of product i, unit =months, years TR t dTax rate of income of distribution center dat time period t. If distribution center is losing out, the tax rate is zero, unit =% DRt di Import duty of product ito the country of distribution center dat time period t, unit =a currency like $ or Rial TRC t fdi Upper bound of CIF transfer price of transshipped product ifrom production center fto external distribution center ddfat time period t, unit =a currency like $ or Rial TRC t fdi _ Lower bound of CIF transfer price of transshipped product ifrom production center fto external distribution center ddfat time period t, unit =a currency like $ or Rial TRF t fdi Upper bound of FOB transfer price of transshipped product ifrom production center fto external distribution center ddfat time period t, unit =a currency like $ or Rial TRF t fdi _ Lower bound of FOB transfer price of transshipped product ifrom production center fto external distribution center ddfat time period t, unit =a currency like $ or Rial PIt fdi Domestic sales price of transshipped product ifrom production center fto distribution center dat time period t, unit =a currency like $ or Rial CDdStorage capacity of distribution center dfor product in, unit =number Other parameters It Marginal cost of delay, unit =a currency like $ or Rial 123 Annals of Operations Research MLarge number (using in the model’s constraints) EXtExchange rate at time period t, unit = Decision variables It fi Inventory level of product iin production center fat the end of time period i, unit =number It di Inventory level of product iin distribution center dat the end of time period i, unit =number yt fd A binary variable equal to 1 if relation between production center fand distribution center din period tis existed, 0 otherwise yt dg A binary variable equal to 1 if the relation between distribution center dand customer zone gin period texists, 0 otherwise St fdi Quantity of product itransshipped from production center fand distribution center dat time period t St dgi Quantity of product itransshipped to distribution center dand customer zone gat time period t Qt fi Quantity of product imanufactured in production center fat time period t Xt fi A binary variable equal to 1 if product inis available for entering the market, 0 otherwise Xt fi A binary variable equal to 1 if product inis researched, and developed by the R&D sector, approved by IFDA, manufactured and commercialized by the company for entering the market at time period t, 0 otherwise Xt iA binary variable equal to 1 if product inis transferred from formulation test to IFDA approval at time period t, 0 otherwise ref fit Quantity of deteriorated product iin all production centers at time period t ref dit Quantity of deteriorated product iin all distribution centers at time period t yft fdi 1 if FOB transshipment term between production center fand distribution center ddffor product tin period tis selected, 0 otherwise yct fdi 1 if CIF transshipment term between production center fand distribution center ddffor product tin period tis selected, 0 otherwise zt+ fProfit before tax deduction from production center fat time period t, unit =a currency like $ or Rial zt− fLosses before tax deduction from production center fat time period t, unit =a currency like $ or Rial zt+ dProfit before tax deduction from distribution center dat time period t, unit =a currency like $ or Rial zt− dLosses before tax deduction from distribution center dat time period t, unit =a currency like $ or Rial tr f t fdi FOB transfer price of transshipped product tfrom production center fto distribution center ddfat time period t, unit =a currency like $ or Rial trct fdi CIF transfer price of transshipped product tfrom production center fto distribution center ddfat time period t, unit =a currency like $ or Rial 4.2 Objective functions The first objective function maximizes the expected net present value (ENPV) of total profit after tax deduction in Eq. (1). Jahani et al. (2019) stated that the ENPV calculation in the 123 Annals of Operations Research supply chain network design could help better illustrate how the supply chain performs in different scenarios. To achieve this in the studied global PSC, the objective function can be formulated as follows: Maxz1= t1+rf 1+rt t−1zt 1+zt 1+zt 1(1) zt 1= f1−TR t fzt+ f−zt− f∀t(2) zt 1= d1−TR t dzt+ d−zt− d∀t(3) zt 1=− i∈nCDNP1 iXt i+CDNP2 iXt fi− f,i∈n DLCftXt fi −Xt+dli fi  − icr1lr1 iXt i+cr2lr2 iXt fi∀t(4) Equations (2)and(3) calculate the after-tax profit at P&D centers, respectively. Equation (4) reflects the penalty cost of delays in different R&D, production, and market entry stages. In addition, zt+ fandzt+ drepresent the profit of the production center fand distribution center dat time period t, respectively. zt− fandzt− drepresent the loss of the manufacturing center fand distribution center dat time period t, respectively. Given tt the tax belongs to the profit in the proposed objective function, only zt+ fandzt+ dare dependent on taxation. Equation (5) represents the profit (or loss) before tax in the production center fin period t. Table 2describes all terms used in this equation accordingly. zt+ f−zt− f= d∈df,i tr f t f,d,iSt fdiyft fdiEXt+ d∈df,i trct fdiSt fdiyct fdiEXt + d∈df,i PIt fdiSt fdi − d∈df,i TC1 fdyft fdiEXt − d∈df,iTC1 fd +TC2 fd +INyct fdiEXt− d∈dhTC fd +INyt fd − i CIfiIt fi − i CPfiQt fi −It d Lfdyt fdEXt∀f,t,(5) zt+ d−zt− d= g,i Pdi St dgi EXt− f,i tr f t fdiSt fdiyft fdiEXt− f,i trct fdiSt fdiyct fdiEXt − fTC2 fd +INyt fdEXt− f TC3 dgyt fdEXt− f,i DRt ditr f t fdiSt fdiyft fdiEXt − f,i DRt diTC2 fd +INyft fdi − f,i DRt ditrct fdiSt fdiyct fdiEXt − d,i CI di It di EXt− g,i μiPdi St dgi EXt−It g Ldgyt dgEXt − g TCdgyt dgEXt∀d∈df,t,(6) Equation (6) calculates the profit (or loss) before tax in the foreign distribution center df at time period t, described in Table 3. It is noteworthy that import duties in many countries are calculated based on the value of CIF goods reported by the importers (Grivani & Pishvaee, 2017). In this study, therefore, the 123 Annals of Operations Research Table 2 Explanation of terms used in Eq. (5) Number Term Description 1d∈df,itr f t f,d,iSt fdiyft fdiEXtRevenues at production centers where pharmaceutical organizations sell products directly to external distribution centers through FOB or CIF contracts and domestic distribution centers using inter-organizational agreements 2d∈df,itrct fdiSt fdiyct fdiEXt 3d∈df,iPIt fdiSt fdi 4d∈df,iTC1 fdyft fdiEXtThe portion of shipping costs when a pharmaceutical product is shipped from a production center to a distribution center that is often paid once when an FOB contract is selected 5d∈df,iTC1 fd +TC2 fd +INyct fdiEXtThe shipping and associated insurance costs from a production center to a distribution center when a CIF contract is agreed upon, which would be paid once, as well 6d∈dhTCfd +INyt fd The transportation and associated insurance costs between a production center and a domestic distribution center 7iCIfiIt fi The cost of preserving pharmaceutical products in all production centers 8iCPfiQt fi The cost of producing generic and innovative pharmaceutical products 9ItdLfdyt fdEXtThe delay transition cost of generic and innovative pharmaceutical products from a production center to a distribution center CIF value is used to calculate the import duties in our model. To convert the value (price) from FOB to CIF, the following formulation is used: Value (price) of CIF goods =Value (price) of FOB goods +Shipping cost between every two ports of P&D centers +insurance cost between every two ports of P&D centers. Equation (7) shows the before-tax profit (or loss) gained from domestic distribution center dhin period t. The expressions used in Eq. (7) are from the sales of pharmaceutical products to consumers, the cost of a purchasing product at an internal price, the cost of storing the product at a distribution center, the cost of transportation from a distribution center to consumers, the marketing cost, and the cost of delays in delivering generic and innovative pharmaceutical products from a distribution center to consumers. zt+ d−zt− d= g,i P di St dgi − f,i PIt fdiSt fdi − i CI di It di − g TCdgyt dg − g,i μiPdi St dgi −It g Ldgyt dg ∀d∈dh,t(7) 123 Annals of Operations Research Table 3 Explanation of terms used in Eq. (6) Number Expression Description 1g,iPdi St dgi EXtRevenues gained by external distribution centers from selling pharmaceutical products to customers 2f,itr f t fdiSt fdiyft fdiEXtThe cost of purchasing pharmaceutical products from manufacturing centers under FOB and CIF contracts 3f,itrct fdiSt fdiyct fdiEXt 4f(TC2 fd +IN)yt fdEXtThe cost of transportation and insurance between the port of production centers and distribution centers 5fTC3 dgyt fdEXtThe cost of transportation between two distribution centers 6f,iDRt ditr f t fdiSt fdiyft fdiEXtThe costs of import duties and taxes when goods are purchased under FOB and CIF contracts, respectively 7f,iDRt di(TC2 fd +IN)yft fdi 8f,iDRt ditrct fdiSt fdiyct fdiEXt 9d,iCI di It di EXtThe cost of storing pharmaceutical products in warehouses of distribution centers 10 g,iμiPdi St dgi EXtThe cost of marketing for pharmaceutical products 11 ItgLdgyt dgEXtThe delay cost related to the shipping of pharmaceutical products from a distribution center to consumers 12 gTCdgyt dgEXtThe cost of shipping from a distribution center to consumers The second objective function in this study intends to minimize the maximum unsatisfied demands. The maximum unsatisfied demands are multiplied by the parameter πiin Eq. (8) to consider the importance of pharmaceutical products. We consider the maximum possible loss here for a worst-case (maximum loss) scenario. Minz2=Maxg,iπiDt gi − d St−Ldg dgi  (8) The coordination of R&D activities and production of innovative pharmaceutical products is critical in the pharmaceutical industry since it ensures the long-term profitability of pharmaceutical companies. In addition, patenting in the pharmaceutical industry is quite dissimilar to other industries, as the patent is the product itself (a new medicine) that has been developed under costly R&D activities and long-term clinical examinations (Masoumi et al., 2012). Therefore, the success rate of a patent in this industry is low, indicating that generic pharmaceutical products will have a higher chance to enter the market, with lower cost than innovative products. This is a threat to the profitability of innovative products. Therefore, we define another objective function formulated in Eq. (9) to maximize the production of innovative pharmaceutical products in our model. Maxz3= t,i∈n Qt fi (9) 123 Annals of Operations Research 4.3 Flow balance constraints The flow balance constraints at each facility of the PSC network are formulated at Constraints (10)–(16). It fi =IIfit +It−1 fi +Qt−Pl fi fi − d St fdi,∀f,i,t,(10) It di =II dit +It−1 di + f St−Lfd fdi − g St dgi,∀d,i,t,(11)  d St−Ldg dgi ≤Dt gi ,∀g,i,t,(12)  f St−Lfd fdi +It−1 di ≥ g St dgi,∀d,i,t,(13) Qt−Pl fi fi +It−1−Pl fi fi ≥ d St fdi,∀f,i,t,(14)  i St fdi ≤Myt fd,∀f,d,t,(15)  i St dgi ≤Myt dg,∀d,g,t,(16) Constraints (10)and(11) indicate the flow and inventory balance at the production center fand the distribution center d, respectively, in each period. Constraint (12) ensures that the products shipped to customer zones should be less than or equal to the demand of the corresponding customer zone. However, Constraints (13)and(14) calculate the imbalance in supply and demand of a product between P&D centers and customer zones. Equation (15) demonstrates the flow of pharmaceutical products from a production center to a distribution center if there is a link between the centers. A similar limitation is also considered in Eq. (16) for the flow of pharmaceutical products from a distribution center to a customer zone. 4.4 Capacity constraints Below, the capacity constraints of P&D centers are formulated: Qt fi ≤PCfi,∀f,i∈o,t,(17)  f,i∈o St fdi ≤Cd,∀d,t,(18) Qt fi ≤CFfiXt−lr2 i fi ,∀f,i∈n,t,(19)  f∗,i∗∈n St f∗di∗≤CD dXt−lr2 i fi ,∀d,i∈n,f,t,(20) Constraints (17)and(18) represent the capacity of generic pharmaceutical products at P&D centers, respectively. Accordingly, Eqs. (19)and(20) indicate the capacity of innovative pharmaceutical products in P&D centers. 123 Annals of Operations Research 4.5 New product allocation We also develop a set of constraints and equations to rationalize the new product allocation in both explorative and exploitative planning. Qt fi ≤MXt fi,∀f,i∈n,t,(21)  t∗≤t Xt∗ fi ≥Xt+dli fi ,∀f,t,i∈n,(22)  i∈n Xt fi =1,∀f,t,(23) Xt fi ≤Xt i,∀f,i∈n,t,(24) Constraint (21) indicates that if an innovative pharmaceutical product is produced, it should have been previously available for market entry at the end of R&D processes. According to Eq. (22), once the innovative pharmaceutical product arrives at time periods less than t,it should have passed from the R&D process at least for a period of tto be able to enter the production line. In this vein, Constraint (23) implies that in each production center, only one innovative pharmaceutical product can be researched and developed and then entered the production line. We also develop Constraint (24) to indicate that a pharmaceutical product must earn IFDA approval once it enters the production line. 4.6 Perishability constraints Perishability may influence supply chain network planning, especially in the exploitative phase. The related restrictions are formulated in Eqs. (25)and(26). t  t=1 Qt fi − min(t+ex fi,T)  t=1 St fdi =ref fit,∀f,d,i,t= T,(25) t  t=1 St fdi − min(t+ex fi,T)  t=1 St dgi =refdit,∀f,d,g,i,t= T,(26) Equation (25) reflects the number of deteriorated pharmaceutical products in production center fat each time period. Equation (26) assigns the number of deteriorated pharmaceutical products in distribution center dat each time period. It is noteworthy that the medicines produced in period t. Are maximally consumable up to t+ex fiaccording to the First In, First Out (FIFO) warehouse management system. 4.7 Shipping contract constraints FOB and CIF are the most common international shipping agreements in transporting goods between a buyer and a seller, which are formalized in Eqs. (27)–(31).  i yct fdi ≥yt fd,∀f,d,t,(27)  i yft fdi ≥yt fd,∀f,d,t,(28) yft fd +yct fd ≤St fdi ≤yft fdi +yct fdiM,∀f,d∈df,t,i,(29) 123 Annals of Operations Research According to constraints (27)and(28), the FOB and CIF contracts are applied between a production center and a distribution center once these two center connected. Constraint (29) ensures that the shipping contract is only agreed upon once the flow of goods between a production center and a distribution center exists. TRC t fdi ≤trct fdi ≤TRC t fdi,∀f,d∈df,t,i,(30) TRF t fdi ≤tr f t fdi ≤TRF t fdi,∀f,d∈df,t,i,(31) Equations (30)and(31) introduce the upper and lower bounds of transfer prices under the CIF and FOB contracts, respectively. 4.8 Non-negativity and binary constraints Equations (32)and(33) are proposed to reinforce the decision variable types. yt fd,yt dg,yft fdi,yct fdi,Xt fi,Xt fi,Xt i∈{0,1},∀f,d,g,i,t,(32) It fi,It di,St fdi,St dgi,Qt fi,zt+ f,zt− f,zt+ d,zt− d,tr f t fdi,trct fdi ≥0,∀f,d,g,i,t.(33) 5 Solution methodology 5.1 Linearization of the proposed model The proposed model is nonlinear due to several terms of the objective functions. One is the minimum–maximum structure formulated in the second objective function (Eq. (8)). The following linearization method is used to transform this objective function into linear. Minz2=θ(34) s.t θ≥πiDt gi − d St−Ldg dgi ,∀g,i,(35) In the first term of Eq. (5), three variables are multiplied, leading to another source of nonlinearity. These three comprise two continuous variables (St fdi,tr f t fdi) and one binary variable (yft fdi). To convert this expression to a linear form, we first define the multiplication of the continuous variable St fdi and the binary variable yft fdi through the development of anewvariablewt fdi =St fdiyft fdi. We apply the technique proposed by Chang and Chang (2000) and include Constraints (36), (37)and(38) to the model. wt fdi ≤St fdi,∀f,d∈df,t,i,(36) wt fdi ≤Myft fdi,∀f,d∈df,t,i,(37) wt fdi ≥St fdi −Myft fdi,∀f,d∈df,t,i,(38) These three constraints suggest that if yft fdi is equal to zero, the auxiliary variable wt fdi will be zero, as well. Otherwise, if yft fdi is equal to one, the variable wt fdi will be equal to 123 Annals of Operations Research Table 4 Demand for each medication Customer medication (g.i)Dt gi ×1000 Customer medication (g.i)Dt gi ×1000 T1−T12 T1−T12 Dt gi (1)Dt gi (2)Dt gi (3)Dt gi (4)Dt gi (1)Dt gi (2)Dt gi (3)Dt gi (4) 1.1 285 300 3.1 330 3.1 161.5 170 178.5 187 1.2 190 200 3.2 220 3.2 95 100 105 110 1.3 38 40 3.3 44 3.3 3.8 4 4.2 4.4 1.4 20.9 22 3.4 24.2 3.4 20.9 22 23.1 24.2 1.5 332.5 350 3.5 385 3.5 332.5 350 367.5 385 1.6 2.85 3 3.6 3.3 3.6 2.85 3 3.15 3.3 2.1 142.5 150 157.5 165 4.1 237.5 250 262.5 275 2.2 66.55 70 73.5 77 4.2 66.5 70 73.5 77 2.3 9.5 10 10.5 11 4.3 85.5 90 94.5 99 2.4 28.5 30 31.5 33 4.4 123.5 130 136.5 143 2.5 285 300 315 330 4.5 142.5 150 157.5 165 2.6 28.5 30 31.5 33 4.6 47.5 50 52.5 55 123 Annals of Operations Research Table 5 The optimal amount of production in different periods Innovative product (f.i)Qt fi ×1000 T t1t2t3t4t5t6t7t8t9t10 t11 t12 1.1 350 350 350 3500 350 350 350 350 350 350 350 350 1.2 350 350 350 3500 350 350 350 350 350 350 350 350 1.3 121.9 0 0 0 47.5 127.3 350 350 350 350 350 350 1.4 0 0 0 0 0 0 3500 3500 3500 3500 3500 3500 1.5 0 0 0 0 0 3500 0 0 0 0 0 0 1.6 0 0 0 0 0 0 0 0 0 0 0 3500 2.1 145 145 145 145 145 145 145 145 145 145 145 145 2.2 145 145 145 145 145 145 145 145 145 145 145 145 2.3 145 83 126.8 127.3 136.8 145 145 145 145 145 145 145 2.4 0 00 0 0 0 000000 2.5 0 0 0 0 0 0 1450 1450 1450 1450 1450 0 2.6 0 0 0 0 0 1450 0 0 0 0 0 1450 3.1 130 130 130 130 130 130 130 130 130 130 130 130 3.2 130 130 130 130 130 130 130 130 130 130 130 130 3.3 0 0 0 0 0 0 0 0 0.38 130 130 130 3.4 0 0 0 0 0 1300 0 0 0 0 0 0 3.5 0 0 0 0 0 1300 1300 1300 1300 1300 1300 0 3.6 0 0 0 0 0 0 0 0 0 0 0 1300 4.1 190 190 190 190 190 190 190 190 190 190 190 190 123 Annals of Operations Research Table 5 (continued) Innovative product (f.i)Qt fi ×1000 T t1t2t3t4t5t6t7t8t9t10 t11 t12 4.2 190 190 190 190 190 190 190 190 190 190 190 190 4.3 0 0 0 0 0 0 85.5 190 190 190 190 190 4.4 0 0 0 0 0 0 0 0 0 0 0 1900 4.5 0 0 0 0 0 1900 0 0 0 0 1900 1900 4.6 0 0 0 0 0 0 1900 1900 1900 1900 0 0 123 Annals of Operations Research in complex and uncertain environments, ensuring optimal results under a variety of possible conditions. 6.3 Pareto solutions The -constraint method as a posteriori (generation) multi-objective solution method is employed in this study to generate various balanced and unbalanced Pareto solutions (Mavrotas, 2007). The main reason to generate the Pareto solutions is to ensure that the main objective functions can be simultaneously improved, although they may even be contradictive in nature (Engau & Sigler, 2020). To ensure that the objective functions proposed in this study contradict each other yet are coexistent and interlinked, we generated the Pareto solutions using the -constraint method. Figure 5displays the pairwise conflicts of the objective functions. The monetary values are reported in MIRR (million Rial, the Iranian accuracy). The results in Fig. 5show that the first objective function (profit maximization) varies in a broader range than the other two objective functions (minimizing maximum dissatisfied demand and maximizing the production of innovative pharmaceuticals). 0 10000 20000 30000 40000 50000 60000 Second Objective Function "Z2" (Kg) First Objective Function"Z1" (MIRR) 0 10000000 20000000 30000000 40000000 50000000 60000000 70000000 Third Objective Function "Z3" (Kg) First Objective Function "Z1"(MIRR) 0 10000000 20000000 30000000 40000000 50000000 60000000 70000000 Third Objective Function "Z3" (Kg) Second Objective Function "Z2" (Kg) Fig. 5 Pareto solutions generated by the ε-constraint method 123 Annals of Operations Research 6.4 Validation of the proposed model In this section, we develop several simulation tests to analyze the performance of the proposed RPP model. To develop these tests, we apply the validation method presented in Pishvaee et al. (2012). Ten simulation tests are randomly taken on non-deterministic parameters. For each uncertain parameter presented by the trapezoidal membership function (for instance, ˜ d=(d1,d2,d3,d4), a random number must be generated uniformly between the most pessimistic and optimistic values (for example, dreal =d1,d2). We then extracted the achieved optimal values of decision variables by solving the RPP model under a nominal value that would later be used in Model (53). The following model is the compact form of the model used to evaluate the solution obtained by the developed robust model. Maxz1=Fx−(Fx +Cy)− I,T  i,t pnδ+ it +δ− it , Minz2=x Maxz3=Nx s.t. Ax =0 Jx ≥0 Sy ≥0 Rx ≤My Lx≥Dreal −δ1+ it +δ1− it, Lx ≤Drealδ2+ it +δ2− it, Ox ≤PCrealδ3+ it +δ3− it, Ox≤PDreal −δ4+ it +δ4− it, Bx ≤CFreal y−δ5+ it +δ5− it, Bx≤CD real y−δ6+ it +δ6− it, Py =1 Dx ≥Qy δ+ it +δ− it = n=6  n=1δn+ it +δn− it δn+ it,δn− it ≥0 y∈{0.1},x≥0 (53) Figure 6shows the average profit value for the deterministic and robust model solutions under simulation tests and based on varied penalty values (i.e., δ∗ ∗∗). Penalty values are used to penalize the violation of constraints under simulation tests. The deterministic stands for the optimization model are developed using Eqs. (1)–(45). It is noteworthy that when the penalty increases, the use of risk aversion models (i.e., the developed RPP model) is more desirable. Indeed, the RPP model can control the risk of constraint violation and create a reasonable balance between risk and operation costs. Therefore, the proposed robust model results in higher profit for the company than the deterministic model. 123 Annals of Operations Research 0 20,000 40,000 60,000 80,000 1,00,000 1,20,000 1,40,000 1,60,000 1,80,000 2000 3000 4000 5000 6000 7000 Averge Profit (ENPV, MIRR ) Penalty Value Deterministic Robust Fig. 6 Average profit with respect to different penalty values for robust and deterministic models 6.4.1 Comparison of the integrated and non-integrated models We conducted a series of comparative analyses to better understand the performance of the developed model (the integrated model) compared to the non-integrated model. Herein, we name the integrated model by using all formulations provided in Sect. 4. The non-integrated model is implemented by creating two separate models: (1) Manufacturing-distribution model in which the objective functions are optimized by excluding R&D parameters (CDNP1 iCDNP2 i) and the related constraints, and (2) R&D model in which the objective functions are optimized by only R&D parameters and the related constraints. We use the results of model (1) for the decision variables as the parameters of this model. Figure 7illustrates the performance of both models through the maximization of ENPV in Eq. (1). The results show that the integrated optimization of R&D planning (the explorative approach) and production distribution planning (the exploitative approach) improves the profit up to 67.45%, compared to attempts to optimize planning for these two approaches separately (non-integrated model). Therefore, it can be argued that our model increases the company’s profitability in its global supply chain. Several analyses help us better position the role of the integrated model in the improved profitability of HPC in its supply chain. For example, Fig. 8exhibits the delay times in producing all innovative products in both the integrated (IN-DLC) and non-integrated (NonIn-DLC) models. The results show the delay times in two stages of the R&D planning (formulation and IFDA approval). Although both the integrated and non-integrated models reduce profitability over the four delay periods (note that zero represents no delay as the first of each stage), the integrated model has less reduced profitability over the four delay periods. In addition, the integrated model reduced profitability with a lower slope than that of the non-integrated model. Similar trends are reported in Fig. 9, where delays are compared by all product centers (Fig. 9a), between all production centers and distribution centers (Fig. 9b), and between all distribution centers and customer zones (Fig. 9c). While all trends report that delays in both the integrated and non-integrated models declined over time, the integrated model helps the company mitigate the risk of more profit loss than in the non-integrated model. This result may be better explained in Fig. 10, which indicates the accumulated delay 123 Annals of Operations Research 0% 20% 40% 60% 80% 100% 120% 140% 0.00E+00 2.00E+10 4.00E+10 6.00E+10 8.00E+10 1.00E+11 1.20E+11 1.40E+11 1.60E+11 1.80E+11 Non-Integrated Model Integrated Model Percentage Improvement PROFIT (ENPV) 67.45% Fig. 7 The integrated planning model versus the non-integrated model Fig. 8 Delay times of all innovative products in the R&D phase times across the supply chain (from R&D to customer zone). As evident in Fig. 10, delays in the non-integrated model caused a significant decline in the entire global supply chain of innovative products, reducing the profitability to 171,168 MIRR (equivalent to 4,048,930 USD) at delay period 4, based on the exchange rate recorded in December 2021. That is, the profit at delay period 4 in the integrated model has been recorded at 54.290 MIRR, which is equal to only 1,284 USD. 6.5 Sensitivity analysis The most important parameter of our model is the R&D cost. Certainly, a change in the cost of R&D has a significant impact on the selection and production of a new pharmaceutical product. In this regard, the cost impact of the R&D phases, which includes the two phases of formulation test and FDA approval, is evident in Fig. 11. The results show that if the R&D cost increases, the company’s profitability will be decreased in both the integrated and non-integrated models. For example, if the R&D cost increases four times, the ENPV of the 123 Annals of Operations Research Fig. 9 Delay times in production centers, distribution centers, and customer zones Fig. 10 Accumulated delay times across the global PSC in both the integrated model (IN) and non-integrated model (NonIN) integrated and non-integrated models’ profits will decrease by 1% and 7.7%, respectively. Therefore, it can be concluded that the integrated model results in more stable solutions than the non-integrated model. If the cost of R&D increases, the superiority of the integrated model over the non-integrated one increases significantly. Using both models, we also analyzed the unit delay cost in producing all innovative products. As evident in Fig. 12, the results of the integrated model suggest less decline in profitability in all cost levels. However, it is reported that changes in cost level impact both models differently. For example, the profitability differences in both models at the cost levels of +25% and +50% are greater than that in −25% and −50%. In other words, the more the company increases the production cost of all innovative products, the better the 123 Annals of Operations Research 65.9% 66.3% 67.5% 68.9% 70.0% 63.0% 64.0% 65.0% 66.0% 67.0% 68.0% 69.0% 70.0% 71.0% 0.00E+00 2.00E+10 4.00E+10 6.00E+10 8.00E+10 1.00E+11 1.20E+11 1.40E+11 1.60E+11 1.80E+11 2.00E+11 0.25 0.5 1 2 4 PROFIT (ENPV) RATIO OF R&D COST Integrated Model Non-Integrated Model Percent Fig. 11 Sensitivity analysis of profit on the integrated and non-integrated models to change the R&D cost parameter Fig. 12 Unit delay cost in producing all innovative products integrated model performs, compared to the non-integrated model. Indeed, the integrated model increases profitability and better manages cost. Other than the unit delay cost, the unit production cost of all innovative products in all production centers indicates that the integrated model performs better than the non-integrated model (See Fig. 13) in all scenarios (i.e., cost levels of −50%, −25%, 0%, 25%, and 50%). Our analyses indicated that the integrated model could significantly reduce transportation cost in the entire supply chain compared to the non-integrated model. As evident in Fig. 14, we identified four areas in which transportation cost will be significantly impacted: (a) transportation cost between all production centers and all external distribution centers within the origin country; (b) transportation cost between all production centers and all external distribution centers while the products are being shipped toward their destination countries; (c) 123 Annals of Operations Research Fig. 13 Unit production cost of all products in all production centers Fig. 14 Transportation cost in different parts of the global supply chain transportation cost between all external distribution centers and all external customer zones; and (d) total transportation cost across the global supply chain. All sub-figures in Fig. 14 indicate that the integrated model suggests a better performance in varying cost levels. 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