A Mean-Variance robust model to minimize operational risk and supply chain cost under aleatory uncertainty: A real-life case application in petroleum supply chain
Introduction
Modern supply chains (SC) are challenged by ever-growing competition and highly unstable business environment. Under such circumstances, the objective of making an efficient SC at the cost of effectiveness exposes the organizations to risk. The risks in SC lead to serious repercussions like inferior product quality, loss of property and machinery, loss of firm’s reputation, delivery delays, conflict among various shareholders and sharp decline in firm’s share price (Rahimi et al., 2019, Tarei et al., 2018).
Though supply chain risk management (SCRM) has emerged as a popular research domain in the recent years, the consideration of risk and uncertainty in the supply chain network design problem are typically rare (Govindan et al., 2017, Choi et al., 2017). Conventional Supply chain network design typically involves decision making regarding determination of optimal location and capacity of facilities to satisfy the market demand at the lowest cost under a static (or stable) environment. Stochastic programming models (Dantzig, 1955, Beale, 1955) developed to consider uncertainty by virtue of probabilistic information, have undergone many theoretical expansions. Although stochastic programming models have been used extensively for past few decades, the primary limitation of stochastic optimization is its inability to handle decision maker’s risk preference (or risk aversion behavior).
The supply chain network design (SCND) problem typically involves various short-term and long-term planning decisions, such as vehicle routing and facility location, respectively. The goal of strategic planning is to maximize the long-term economic performance of a SC by configuring its various decision variables. Given the configuration of a SC, the future condition of the decision parameters can not be known with certainty. This class of problem is typically called decision-making under uncertainty Uncertainty is primarily classified as aleatory and epistemic uncertainty. Aleatory uncertainty is caused by the presence of natural randomness within the system. Whereas epistemic uncertainty is arisen due to the lack of scientific knowledge or information about the process (Helton et al., 2010). The current research work considers the former type of uncertainty, which can be modelled by considering substantial numbers of scenarios, whose probability of occurrence are well known in advance. Govindan et al. (2017) have performed an extensive review of articles pertaining to supply chain network design under uncertainty, and emphasized on the consideration of SC risk in process industries such as biofuel and petroleum in future research works. Their review article also indicates a call for robust SC network design using weighted mean-risk approach.
Petroleum industries play a crucial role in the world economy because they supply the commodities to sustain the global energy supply. The petroleum supply chain (PSC) is one of the complex supply chains, which covers operational activities staring from geoseismic data analysis, exploration of crude, preprocessing, refining, storage, and distribution of petroleum products to the end consumers (Ghaithan et al., 2017).
Like any other SC, risk in PSC can be divided into two broad categories, operational risk and disruption risk (Sabouhi et al, 2018). Operational risks originate from the inherent uncertainties that inevitably exist in supply chains due to lack of coordination between multiple entities (Sreedevi & Saranga, 2017). For instance, slow demand of petroleum products by BRICS (Brazil, Russia, India, China, And South Africa) economies (Planche et al., 2016), trade restrictions (sanction) on Iran, Russia and Venezuala (Brown, 2020), crude oil price drop, transfer price, international taxation, diplomatic relations between oil importing, exporting countries, etc., are considered operational risks (Seshasayee, 2019). Disruption risks, on the other hand, are inadvertent events which restrict the flow/movement of material/information/capital in SC caused by natural, man-made or technological threats (Shekarian et al., 2020). For instance, oil spill in the Gulf of Mexico (Tabuchi & Migliozzi, 2021). Hurricane Katrina destroyed two major pipelines of the USA which lead to an unprecedented crises of oil for several months (Pan & Karp, 2005). A recent terrorist attack in the trans-regional pipeline connecting from Egypt to Jordan, Syria, and Lebanon had caused fifty percent power plants to shut down in Syria (TOI, 2021). Though it seems that disruption risks have pose more impact as compared to operational risk, the findings of Tarei et al. (2018) indicates that operational risks are pertinent in case of Indian PSC over a long-term. Though there has been extensive research on the oil industry optimization and oil supply chain under uncertainty, there are few studies considering supply chain risk management (Azarakhsh et al., 2021, Zhai and Yu, 2019).
Responding to the research issues and limitations mentioned in the previous paragraphs, we have limited the scope of the current work to operational risk only which is primarily caused by aleatory type uncertainty (Interest readers are suggested to refer to Aldrighetti et al., 2021, Xu et al., 2020, Shekarian et al., 2020, DuHadway et al., 2019; and Paul et al., 2019 for disruption risk). The proposed risk averse SC network model (focusing on aleatory type uncertainty) is articulated as a Mean-Variance Robust (MVR) optimization model, which was initially proposed by Markowitz to find out the efficient frontier of financial assets to maximize the expected return at a given level of risk (Markowitz, 1952, Chiu and Choi, 2016). We have validated the mathematical model by considering petroleum SC as an empirical case study in India. We have discussed and compared the results from different risk attitude behavioral perspective, i.e., risk seeking and risk averse.
This research contributes to the literature of PSC mainly in four ways. First, we develop a MVR optimization model focusing on the SC operational risk caused by aleatory uncertainty. Second, we explore and validate the model using a real-life case of PSC in the Indian context. Third, we analyze the results from the behavioral perspective of the decision-maker(s) (i.e., risk seeking, risk neutral, and risk averse attitude). Fourth, we provide multiple feasible solutions to balance the trade-off between SC operational cost and SC risk. By developing MVR model under aleatory uncertainties in PSC network, this study complements the extant literature of PSC that highlights the need to study uncertainties in PSC network (Azarakhsh et al., 2021, Govindan et al., 2017, Mohammadi et al., 2020) and underlines importance of operational risks in PSC (Tarei et al., 2018). As real-life situations are more uncertain and riskier, this study adds value to the literature that considers deterministic measures of PSC (Attia et al., 2019, Leiras et al., 2013; Lima et al., 2021b; Azadeh et al., 2017). We further add value to the PSC literature by bringing behavioral aspects under aleatory uncertainties in PSC in India. India which is one of the fastest emerging economies is the third-largest consumer of crude oil and petroleum products, with 4.7 percent of the global oil consumption in 2018.
The remainder of the paper is structured as follows. Section 2 provides a brief review of literature review, pertaining to the management of uncertainty focusing on petroleum industries. Section 3 mentions the theoretical foundation of MVR optimization model. Section 4 contains the assumption and the problem definition, objective function and constraints of the petroleum SC related to the case country. Section 5 presents a brief introduction of the case study and data collection procedure. Results and implications derived from the study are discussed in section 6. Finally, the paper ends with conclusions, limitations and future research directions in section 7.
Section snippets
Review of literature
In this section, we present the review of literature that motivated to conduct this research work. Since the literature, pertaining to mathematical modelling and optimization under risk and uncertainty is too broad (interested readers are suggested to refer the review paper of Govindan et al., 2017, Choi et al., 2017); we hereby limit the discussion of this section to petroleum and oil specific domain only.
Petroleum or oil SC can be broadly categorized into three segments, viz. upstream,
Mean-Variance robust optimization formulation
In this section, the proposed MVR model is explained in the light of Indian PSC.
Case introduction
To demonstrate the efficacy of the proposed MVR model, we consider a realistic case of the PSC in the eastern region of India. The oil and gas sector in India is among the country's six core industries, which contributes about 15 percent to the overall GDP of the country (Department of Industrial Policy and Promotion, Ministry of Petroleum and Natural Gas, 2017). Toward the start of 2015, India had 635 million metric tons (MMT) of demonstrated oil saves. With close to half of the country's
Results and discussions
In this section, we present the numerical results of the illustrated case study to evaluate the efficacy of the MVR model. The MVR model is coded in GAMS (General Algebraic Modeling System) and executed by CPLEX solver to find global optimality using the parallel computing platform of NEOS (Network Enabled Optimization Solution) server (Czyzyk & Moré, 1998) hosted at www.neos-server.org/neos. The proposed model is reasonably complex in terms of number of variables, number of constraints, and
Conclusion
The growing concern for risk in SC has received a global research attention. In this regard, this research work develops a MVR robust optimization framework to minimize operational risk, which is primarily caused by aleatory type of uncertainty. A real-life case study of Indian petroleum SC is conducted to validate the MVR framework, with the requisite constraints. Five uncertain scenarios are constructed based on the domestic case country’s possible (future) economic conditions. The risk
CRediT authorship contribution statement
Pradeep Kumar Tarei: Conceptualization, Methodology, Writing – original draft. Gopal Kumar: Conceptualization. M. Ramkumar: Conceptualization.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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