This paper addresses a key limitation in the real options literature on copper mine valuation, where conventional approaches often rely on geometric Brownian motion (GBM) to model underlying commodity and exchange rate dynamics. Such approaches may overlook discrete jumps and abrupt market shocks that are particularly relevant in emerging markets and commodity-dependent economies. To address this limitation, we first conduct a statistical analysis of copper prices and the Dollar/Rial exchange rate over the period 2013–2025 to identify jump behavior. The empirical evidence supports the presence of significant discontinuous movements in both series. Motivated by these findings, we adopt a Merton Jump–Diffusion (MJD) framework to characterize continuous fluctuations and discrete shocks in the two stochastic variables. Using the estimated jump–diffusion parameters, one-year Monte Carlo simulations of copper prices and exchange rates are generated under the MJD framework. The simulated paths are used to characterize the range of stochastic outcomes and the relevant state-space ranges, rather than being used directly to compute the project value. The Sarcheshmeh copper mine project is then evaluated within a real options framework. The valuation problem is formulated as a two-factor partial differential equation and solved numerically using the Crank–Nicolson finite difference method. To represent the jump component within the valuation PDE, we employ a diffusion-equivalent moment-matching approximation that preserves the first two moments of the jump component. The PDE-based grid solution provides the project-value surface over the relevant state space, which is essential for the subsequent ex-post interpretation of continuation and abandonment regions. This approach is therefore adopted to obtain the complete value surface required for the decision analysis, rather than solely for computational tractability. The approximation does not explicitly capture higher-order distributional characteristics and tail effects associated with extreme jump realizations. A consistent comparison is made between GBM- and MJD-based project valuations, with net present value (NPV) analysis serving as a deterministic benchmark. The results show that incorporating jump risk through the proposed approximation leads to systematically lower project values compared with GBM-based valuation. The analysis examines the effects of jump intensity, jump magnitude, and jump volatility on project value, highlighting the economic significance of discontinuous shocks. The findings indicate that ignoring jump risk may result in the overvaluation of mining projects. The analysis also examines the implications of uncertainty for continuation and abandonment decisions; these operational decisions are inferred ex post from the computed project-value surface rather than modeled as endogenous managerial controls or derived optimal thresholds. Overall, the proposed framework provides a real options approach for evaluating mining investments under commodity price and exchange rate uncertainty, while explicitly recognizing that jump risk in the valuation PDE is represented through a first- and second-moment diffusion-equivalent approximation rather than the full integro-partial differential equation. The Monte Carlo simulations are used to characterize stochastic outcomes and inform the relevant state-space ranges, whereas the PDE solution provides the project-value surface required for the ex-post decision analysis.
We study the existence of equilibrium in dynamic asset markets where agents possess quasi-concave mean-value utility functions. These markets extend the classical Arrow–Debreu framework to the case where consumption sets are unbounded from below and continuous trading occurs over a finite time interval. The dynamic asset market problem is reformulated as a quasi-variational inequality (QVI) with unbounded constraint maps, and sufficient conditions for the existence of solutions to this class of QVI problems are established. The QVI formulation subsequently ensures the existence of equilibrium for the given economic model under a coercivity condition, without relying on traditional no-arbitrage assumptions. Finally, we propose an algorithm for computing an equilibrium of dynamic asset markets by resolving the corresponding quasi-variational inequality into variational inequalities.
This study develops a risk-averse interval bi-level programming framework for sustainable closed-loop production systems operating under dependent uncertainty. Correlated ambiguities in demand, return rates, and operational costs are represented through a structured mean–radius interval formulation with a common dependence factor, while heterogeneous uncertainty attitudes of the leader and follower are incorporated using a preference-based scalarisation approach. The lower-level interval optimisation problem is transformed into a deterministic nonlinear programme via KKT-type optimality conditions, yielding a KKT-based single-level reformulation that is valid under the stated convexity and constraint qualification assumptions. To solve the resulting complementarity-constrained nonlinear model, a hybrid evolutionary–NLP algorithm is proposed that combines global exploration with local refinement. A stylised closed-loop production example is presented to illustrate the applicability of the proposed framework and to examine the influence of uncertainty-width aversion and dependent uncertainty on production, remanufacturing, disposal, and policy decisions. The numerical results indicate that changes in uncertainty attitudes primarily affect the valuation of interval uncertainty, while the system’s operational structure remains comparatively stable across the tested scenarios.
In many practical survey situations, researchers need to estimate several population characteristics simultaneously while operating under limited resources. The motivation of this study arises from the need to obtain efficient estimates for multiple variables in stratified sampling while accounting for differences in measurement costs. In practice, the cost of measuring different variables may vary considerably, but many existing allocation methods do not adequately incorporate these variations, which may result in inefficient sampling designs. To address this issue, this study proposes a new multivariate stratified random sampling technique based on a family of estimators for compromise allocation. The proposed approach aims to improve the accuracy and efficiency of population mean estimation while controlling the overall measurement cost. The problem is formulated as an integer nonlinear multivariate stratified sampling model within a multi-objective mathematical programming framework using the proposed cost functions. The developed procedure is based on integer programming, and the resulting coefficients of variation are compared with those obtained from some existing compromise allocation methods. Numerical illustrations demonstrate that the proposed allocation technique provides improved efficiency. The proposed method is particularly useful in practical survey designs where budget, time, and effort must be carefully balanced with the requirement of achieving reliable statistical estimates.
The optimal location of charging stations for electric vehicles (EV) is a challenging problem which plays an important role in the development of electric mobility for a country. It has been widely studied in the continental context. However, in the case of an island, the specific features of the transport and energy production capacity raise the need for the development of adapted approaches. This research work proposes an optimal location model and a solution approach which takes into account small island features to deploy a green-charging infrastructure for EVs. It focuses on the maximization of the demand captured, over the possible locations and configurations of green charging stations. A customized, exact outer-approximation branch-and-cut algorithm has been developed to solve this optimization problem. This optimal location model is applied to a case study based on Mauritius island which is a well suited example of SIDS’s (Small Islands Developing States) vulnerability to energy and transport problems. A comprehensive analysis has been carried out to explore the viability of green-charging for EVs in Mauritius. Results show that the green strategy developed for the deployment of charging stations is pertinent in an island context whereby a maximum demand capture of 69
This study presents an innovative cloud-based digital twin architecture that enables intelligent supply chain management in dynamic and uncertain conditions by utilizing real-time modeling, fuzzy multi-objective analysis, and a cognitive decision support engine. This architecture provides a live view of the operational status by directly connecting to real and simulated data and has the ability to analyze normal, disruption, and peak load scenarios in an integrated manner. The results show that the developed model is able to generate accurate, stable, and uncertainty-adapted Pareto fronts and adjust decision paths to balance cost, time, quality, and resilience objectives. Performance evaluation in a cloud environment also proves that the proposed architecture is not only industrially deployable, but can also be a foundation for the next generation of intelligent decision support systems in supply chains.
This study introduces column generation via optimization-based sorting (CGOS) for a proportional capital budgeting model with project-specific investment bounds and cardinality-based global limits. The underlying formulation contains an exponential number of investment-pattern constraints, which makes explicit enumeration impractical beyond moderate problem sizes. CGOS embeds an exact sorting-based pricing oracle within the column generation loop: a single sort of the dual-price vector, followed by prefix-sum evaluations, identifies improving upper- and lower-bound patterns for all k in one pass. Computational experiments on randomly generated feasible instances (N = 5–80) and a real-world participatory budgeting benchmark indicate that, in our test setting, CGOS is competitive on small instances and becomes faster than solving the explicit primal LP as N grows; for example, at N = 20 the explicit LP required 14.566 s, whereas CGOS required 0.338 s under the same settings. These results illustrate how exploiting pricing structure can improve the scalability of exact LP solution methods for this problem class. Because CGOS relies on a structured pricing oracle, extending it to formulations with nonlinearities, richer interdependencies, or dynamic constraints remains a topic for future research.
Hurricanes are among the deadliest annual disasters in the United States, posing significant challenges for disaster response and evacuation planning. Forecasts from the National Hurricane Center are essential for guiding evacuation and logistics decisions, but these forecasts are subject to uncertainty, complicating the modeling of evacuation and relief logistics. This paper proposes a data-driven multi-stage stochastic programming (MSSP) model for integrated hurricane relief and logistics evacuation planning under forecast uncertainty, aimed at improving out-of-sample (OOS) performance. The framework captures the Markovian dynamics of hurricane track and intensity by leveraging historical forecast errors and kernel regression for conditional distribution estimation. We formulate a data-driven MSSP model within a distributionally robust optimization framework, incorporating historical forecast errors to improve decision-making under uncertainty. We present an approach for utilizing Markov chain (MC) discretization to reduce computational complexity with a trade-off in asymptotic optimality. Through extensive experiments based on a case study of Hurricane Florence, we demonstrate that the data-driven approach improves OOS performance in worst-case scenarios compared to the MSSP model with the nominal MC. Finally, we provide insights into how the data-driven model’s performance varies with key problem parameters.
Advertising in supply chains commonly includes global advertising, which builds brand awareness, and local advertising, which converts potential customers into actual buyers. Despite their complementary roles, limited research has examined how these instruments should be jointly allocated when manufacturers face budget and production constraints. Motivated by real-world capacity disruptions such as the global chip shortage, this study develops a two-echelon supply chain model formulated as a Stackelberg game in which the manufacturer acts as the leader and retailers are followers. Retailers’ interactions are further characterized through a Generalized Nash game to capture strategic interdependence under shared capacity and cooperative advertising decisions. The manufacturer determines global advertising expenditure, the share of retailers’ local advertising costs, and production allocation, while retailers choose local advertising investments under competitive conditions. Three structures are analyzed: two decentralized settings, one with competitive local advertising and one without, and a fully centralized benchmark. Results show that centralized coordination yields the highest total supply chain profit. Among decentralized settings, eliminating predatory advertising improves overall supply chain performance, although competitive behavior may sometimes benefit retailers individually. The analysis further demonstrates that greater production capacity and higher manufacturer budgets increase participation in local advertising and enhance customer acquisition when advertising remains profitable. Importantly, global advertising alone cannot fully translate market potential into realized demand without sufficient local advertising support. These findings offer practical guidance for capacity-constrained industries, highlighting the importance of coordinated advertising strategies and appropriate participation policies to maximize profitability under resource limitations.
Offshore wind energy is expected to play a central role in the decarbonisation of future power systems, particularly in the North Sea region, where deployment targets are highly ambitious. To support the large-scale integration of offshore wind while maximizing social welfare under long-term uncertainties, this paper proposes a novel stochastic transmission expansion planning framework. The approach relies on a reformulation amenable to Benders decomposition, yielding a scalable and parallelizable algorithm capable of finding exact solutions despite the presence of mixed-integer recourse decisions. The performance of the method is first demonstrated using an illustrative toy example. Subsequently, it is applied to a larger and more realistic representation of the North Sea offshore grid, enabling tractable solution of instances that are computationally challenging for conventional methods. The results reveal clear interconnection patterns, indicating that a highly interconnected offshore grid with multiple cross-border links can provide substantial benefits. Although the resulting topology varies with uncertain demand, the analysis shows that demand uncertainty has relatively limited influence on optimal first-stage investment decisions that are of primary interest.
In decision analysis, the expected value of perfect information (EVPI) is a commonly used evaluation tool. We focus on the concept of maximum possible EVPI (MaxVPI) and demonstrate its relationship with one of the decision analysis criteria, minimax regret. The maximum possible EVPI is easy to evaluate because there is no need to estimate the probabilities of the states of the world. The MaxVPI is an achievable upper bound, meaning that there is a set of probabilities for which EVPI=MaxVPI, and the EVPI for any set of probabilities cannot exceed MaxVPI. We demonstrate this approach on two stochastic facility location models, in the context of both finite and infinite states of the world as well as available options. We also consider a situation in which only partial information about the probabilities is given.
In this work, we consider general probability functions and show how an extension of the spherical radial decomposition of elliptically-symmetrically distributed random vectors can be put to use. In particular we show how the latter may admit explicit formulæ even when the random vector is not elliptically symmetric. We also highlight how earlier obtained results can be leveraged and extended to the situation of mixtures of elliptically symmetric random vectors, that enjoy considerable popularity in the literature. Through two examples, we show how the spherical radial (-like) decomposition can allow for preciser computations of probability function values.
In this paper, we deal with nonsmooth mathematical programs with equilibrium constraints and its dual problems. We obtain Wolfe type dual and Mond Weir type dual in terms of quasidifferential. Further, we establish weak duality and strong duality theorems for considered nonsmooth optimization problems with equilibrium constraints under assumptions of quasidifferential invex function with respect to convex compact set. We also give some examples which verify our results and discuss the comparison between quasidifferential with other differentials.
Due to the long duration of Carbon Capture and Storage projects and the uncertainty of the captured CO_2 amounts, making decisions about the construction of transport infrastructure in the early stages is challenging. The objective of this study is to propose a stochastic programming model to optimize the deployment of infrastructure, specifically pipelines and ships, to transport CO_2 from industrial sources to sequestration sites. The proposed model accounts for uncertainties in the capture (or supply) of CO_2 and is tested using an illustrative case study of the Humber cluster in the UK. The constructed scenario trees incorporate the risk of potential closure and reactivation of the capture facilities, allowing decision makers to make more robust first stage decisions about the type and capacity of transport infrastructure to construct. The experiments in this paper examine changes in optimal investment decision for a range of uncertainties. For example, the trade-off between investment in pipelines and ships is influenced by assumptions about the potential for ships to relocate to other regions if CCS projects close and key policy decisions (e.g. availability of upfront funding for infrastructure investment). For our illustrative case study, pipelines are preferred in cases with lower probabilities of closure in later periods when sufficient budget is available. When a higher probability of project closure is considered or discount rate is increased to typical commercial rates, our model indicates that investment in ships will dominate.
This paper develops optimization models for an omnichannel supply chain to simultaneously determine pricing, delivery time, and service effort decisions across centralized, decentralized, and coordinated structures. Customer demand is modeled as a function of price, delivery time, and product return risk - a key determinant significantly influenced by the retailer’s service effort investment. To coordinate the chain and mitigate the inefficiencies of double marginalization, a novel Double Compensation Profit Sharing (DCPS) contract is proposed. Furthermore, as an extension to the base model, we introduce a Disruption-Responsive DCPS (DR-DCPS) contract to enhance supply chain resilience when facing operational disruptions. Our analyses demonstrate that both contracts successfully coordinate the supply chain, raising the total profit in the decentralized system to the centralized level while ensuring a fair profit-sharing mechanism. Notably, the DR-DCPS contract proves particularly effective in maintaining coordination and equitable profit distribution during disruptions, preventing the member conflict observed in the uncoordinated system. Sensitivity analysis reveals that increased customer loyalty to the offline channel expands the contract’s acceptance range and enhances its efficiency. The study concludes with critical managerial insights derived from analyzing key parameters, highlighting the importance of adaptive contracts in building robust and efficient omnichannel supply chains.
Vietnam is a country with a rapidly developing economy in Asia. Vietnam is increasingly receiving high regard and attention from domestic and foreign investors. The Vietnamese financial system, the economy’s lifeblood, is also garnering close attention. Notably, Vietnamese banks, which mobilize financial resources from various sources through their intermediary role, play a crucial part. In any country, banks always hold a central, critical role in investment, trade, and other economic activities. One of the reasons for banks’ inadequate profitability is insufficient resource management. Consequently, this study evaluates the performance of Vietnamese banks, specifically focusing on identifying potential inefficiencies in resource utilization. Data was collected from 26 banks with carefully selected input and output parameters. The Slack-Based Measure (SBM) model was applied to evaluate the efficiency of Vietnamese banks and identify inefficiencies in resource utilization. Additionally, truncated regression was employed to analyze the key determinants of bank efficiency, examining how factors influence bank efficiency. The DEA analysis reveals that 13 banks have achieved maximum efficiency. The slack analysis highlights inefficient resource utilization, providing a foundation for improving efficiency in underperforming banks. Additionally, the analysis of bank efficiency determinants highlights the importance of scale, capital strength, funding structure, and institutional ownership in explaining variations in bank efficiency. Through the research results, we aim for banks to have suitable resource management strategies and plans to improve their operational efficiency. This, in turn, can further enhance the force of the banking system to ensure the fulfillment of its crucial mission in the national economy.
Natural gas is vital to Europe's energy system, with Norway supplying 30% of European gas demand. Effective management of entry-exit capacity in the Norwegian network can enhance market efficiency and energy security, but is far from trivial due to uncertain demand and prices. This study develops a stochastic programming model to determine optimal capacity allocation under uncertainty, with a focus on scalability. Concerned about network stability, operators tend to be risk averse in deviating from their initial decisions when allocating bookable capacities. We use our model in a case study on Norway's gas pipeline network and find that moderating risk aversion can yield considerable system welfare gains. Additionally, we give insights into the system bottlenecks for policymakers and industry stakeholders and show the value of flexibility in this context. Finally, we provide a comprehensive dataset to advance future research.
Direct disaster housing plays a critical role in mitigating the social costs of displacement and alleviating the suffering of disaster victims. However, effective disaster housing logistics planning remains a significant challenge, as demonstrated by past major disasters. In this paper, we propose a data-driven decision-support framework that integrates disaster housing demand estimation into long-term disaster housing logistics planning through a multi-horizon stochastic programming (MHSP) model. The MHSP model explicitly accounts for both long-term and short-term demand uncertainty. We develop new solution methods tailored for the MHSP model and validate the proposed framework through numerical experiments that demonstrate its advantages over conventional approaches. Our results highlight the value of incorporating short-term uncertainty into long-term logistics planning, providing insights for policymakers to enhance disaster housing preparedness and response.
