Choosing Between Two Kind of Sampling Patterns Using Geostatistical Simulation: Regularly Spaced or at High Uncertainty Locations?

We suggest a new approach to calculating a project's net present value, termed the displaced equity method. Based on a straightforward formula, it analyzes a project partially financed with debt from the perspective that every year the amount of outstanding debt displaces an equivalent amount of equity that otherwise would be tied up in the project. Although they represent distinct shareholders' perspectives, the displaced equity method and the equity residual method yield identical net present values and internal rates of return. Every year, the project's value calculated with the displaced equity method is equal to the sum of the project's debt and equity values. In practice, when the schedule of expected outstanding debt amounts is known, using the displaced equity method is an easy way to estimate the project's net present value.

Industrial projects are plagued by uncertainties, often resulting in both time and cost overruns. This research introduces an innovative approach, employing Reinforcement Learning (RL), to address three distinct project management challenges within a setting of uncertain activity durations. The primary objective is to identify stable baseline schedules. The first challenge encompasses the multimode lean project management problem, wherein the goal is to maximize a project’s value function while adhering to both due date and budget chance constraints. The second challenge involves the chance-constrained critical chain buffer management problem in a multimode context. Here, the aim is to minimize the project delivery date while considering resource constraints and duration-chance constraints. The third challenge revolves around striking a balance between the project value and its net present value (NPV) within a resource-constrained multimode environment. To tackle these three challenges, we devised mathematical programming models, some of which were solved optimally. Additionally, we developed competitive RL-based algorithms and verified their performance against established benchmarks. Our RL algorithms consistently generated schedules that compared favorably with the benchmarks, leading to higher project values and NPVs and shorter schedules while staying within the stakeholders’ risk thresholds. The potential beneficiaries of this research are project managers and decision-makers who can use this approach to generate an efficient frontier of optimal project plans.

A method and a system for equalizing one or more loudspeaker(s), e.g. a hi-fi system, positioned in a room in order to compensate sound reproduction from the loudspeaker for an influence of the room. The method includes measuring a listening position transfer function (L) from electrical input of the loudspeaker (L1) to a sound pressure at a listening position (LP) in the room. A global transfer function (G) representing a spatial average of sound pressure level in the room generated by the loudspeaker (L1) is determined. This global transfer function (G) can either be determined as an average of two or more transfer functions measured in field points scattered across the room or it can be calculated based on an acoustic power output measured from the loudspeaker (L1) together with data regarding sound absorption properties of the room. An upper gain limit (UGL) as a function of frequency is then determined based on an inverse of the global transfer function (G). An equalizing filter (F) is then determined based on an inverse of the listening position transfer function (L), but with its gain being limited to a maximum gain in accordance with the upper gain limit (UGL). Finally, the loudspeaker (L1) is equalized with the equalizing filter (F), the filter (F) being implemented such as a minimum phase approximation by an FIR or an HR filter. Preferably, a lower gain limit (LGL) as a function of frequency is also determined as an inverse of the global transfer function (G), wherein a gain of the equalizing filter (F) is limited to a minimum gain in accordance with the lower gain limit (LGL). By use of the upper and lower gain limits (UGL, LGL) it is possible to implement a system capable of automatically designing the equalizing filter (F) with only simple tasks to perform for an operator of the system.

Over recent years, new methods have been developed to integrate uncertainty into the optimisation of life-of-mine production planning. One of these methods is based on scheduling with a simulated annealing (SA) algorithm and equally probable realisations of a given mineral deposit. The latter realisations are used to generate production schedules that minimise the possibility of deviating from production targets, and result in schedules with a substantial improvement in the net present value (NPV), shown to be in the order of 25% when compared to conventional scheduling within the conventionally optimal pit limits. To facilitate the utilisation of this method, a sensitivity analysis is presented in this study. The study documents the case of a copper deposit where 10 simulated realisations are sufficient to provide stable life-of-mine optimisation results. In addition, the study shows that the selected true optimal pit limits are larger than those derived through conventional optimisation. Stochastically optimised pit limits are found to be ∼17% larger, in terms of total tonnage, than the conventional (deterministic) optimal pit limits. The difference adds one year of mining and ∼10% of additional NPV when compared to the NPV of conventional optimal pit limits and a production schedule generated stochastically with the same simulated annealing algorithm.

Application of risk assessment to improve sustainability in bauxite mining

ABSTRACTGeostatistical modelling of grades in mineral deposits often requires the simulation of multiple related variables that have sum and fraction constraints. Sum constraints occur when the sum of some variables may not exceed or must equal a given constant. Fraction constraints occur when a variable may not exceed another variable. In this case, the geostatistical simulations should reproduce the histograms, variograms, multivariate relationships and honour the constraints. We present a methodology for the geostatistical simulation of multiple related variables that considers sum and fraction constraints. The methodology is illustrated in a case study. The data were obtained from a bauxite deposit. First, the original variables were re-expressed as ratios. Second, the variables were transformed using the Projection Pursuit Multivariate Transform (PPMT). Then the PPMT transformed variables were simulated independently using sequential Gaussian simulation and back-transformed. The simulations reproduced the histograms, variograms and bivariate relationships and honoured the sum and fraction constraints.

Equivalence ratio fluctuations are known to be one of the key factors controlling thermoacoustic stability in lean premixed gas turbine combustors. The mixing and thus the spatio-temporal evolution of these perturbations in the combustor flow is, however, difficult to account for in present low-order modeling approaches. To investigate this mechanism, experiments in an atmospheric combustion test rig are conducted. To assess the importance of equivalence ratio fluctuations in the present case, flame transfer functions for different injection positions are measured. By adding known perturbations in the fuel flow using a solenoid valve, the influence of equivalence ratio oscillations on the heat release rate is investigated. The spatially and temporally resolved equivalence ratio fluctuations in the reaction zone are measured using two optical chemiluminescence signals, captured with an intensified camera. A steady calibration measurement allows for the quantitative assessment of the equivalence ratio fluctuations in the flame. This information is used to obtain a mixing transfer function, which relates fluctuations in the fuel flow to corresponding fluctuations in the equivalence ratio of the flame. The current study focuses on the measurement of the global, spatially integrated, transfer function for equivalence ratio fluctuations and the corresponding modeling. In addition, the spatially resolved mixing transfer function is shown and discussed. The global mixing transfer function reveals that despite the good spatial mixing quality of the investigated generic burner, the ability to damp temporal fluctuations at low frequencies is rather poor. It is shown that the equivalence ratio fluctuations are the governing heat release rate oscillation response mechanism for this burner in the low-frequency regime. The global transfer function for equivalence ratio fluctuations derived from the measurements is characterized by a pronounced low-pass characteristic, which is in good agreement with the presented convection–diffusion mixing model.

Pharmaceutical enterprises operate in an environment characterised by high uncertainty, long innovation cycles, and significant regulatory and technological volatility. These conditions intensify the complexity of investment decision-making and necessitate adaptive approaches to strategizing enterprise investment behaviour. Traditional financial evaluation methods, particularly the Net Present Value (NPV) model based on the Weighted Average Cost of Capital (WACC), inadequately reflect the dynamic nature of risk and fail to capture the behavioural adaptability of projects under uncertainty. In response to these challenges, this study develops an integrated model for risk assessment that combines the classical WACC-based NPV, the Certainty-Equivalent NPV approach, and a discrete integral metric of deviation between baseline and risk-adjusted cash flows. The methodological framework includes system and comparative analysis, expert-based risk identification, economic–mathematical modelling, and case study analysis of three pharmaceutical investment projects. Certainty-equivalent coefficients (αₜ) are derived through structured expert evaluation, enabling dynamic adjustment of future cash flows to reflect changing risk profiles. The integral deviation metric (IA) quantifies cumulative uncertainty by summing absolute differences between baseline and risk-adjusted cash flows over time, thus capturing the behavioural stability of investment decisions. The empirical results demonstrate significant heterogeneity in the risk exposure of the three analysed projects. One project exhibits high behavioural stability and minimal deviation between WACC and CEQ trajectories, whereas the other two display substantial uncertainty, especially at later implementation stages. These findings highlight the necessity of tailoring investment strategies to project-specific risk dynamics and emphasise the relevance of adaptive, risk-oriented strategizing for enterprises operating in volatile sectors. The proposed model enhances the methodological foundations of strategic investment behaviour by enabling a more nuanced assessment of project robustness under uncertainty. It provides a practical analytical tool for prioritising pharmaceutical investment initiatives, designing adaptive risk mitigation strategies, and improving decision-making resilience in conditions of global and sectoral instability.

Geostatistical simulation comprises a variety of techniques which can help on the decision-making process for uncertainties. They allow the uncertainty assessment of function responses (which depend on the simulated inputs) commonly through a non-linear relationship (net present value, interest tax return, geometallurgical ore recovery...). However, one of their limitations is that running the simulation can take considerable processing time to be executed in large deposits or large grids. Herein is presented an attempt to solve this problem in short-term modeling cases, via the use of Multiple Random Walk Simulation. This algorithm combines kriging with the simulation of independent random walks in order to generate simulated scenarios much faster than via traditional simulation algorithms. A case study is presented to illustrate the application of the method in an iron mine. The Multiple Random Walk Simulation models were properly built, respecting the reproduction of both histogram and variograms. Also, the speed-up was compared with standard methods of geostatistical simulation and there was a considerable speed gain with Multiple Random Walk Simulation (3.39 to 5.65 times faster than the others).

Green roofs are considered to be one of the optimal tools for saving energy and protecting the environment in developed countries. In this paper, an analysis of the possible application of green roofs on existing residential buildings with flat roofs is presented. In the economic analysis, models of existing buildings in Belgrade, with two different types of green roofs, are studied. A key indicator of investment profitability in this investigation is the net present value (NPV) of the green roof project. Besides the private economic impact, other aspects of green roof applications, significant for sustainable development, have been highlighted. The values of the reductions in the annual energy needed for heating and cooling are compared for different scenarios. A maximum energy saving of 22% in the heating season is determined in the building energy simulation program for the model with an intensive green roof. Life cycle profit analysis was based on the probabilistic approach. The corresponding variance-based sensitivity analysis determined the impact of various parameters on the final result. In all models, the first order sensitivity index, which measures the impact of the number of residential units on the NPV, ranges from 12.2% to 63.6%. Sensitivity analysis showed that the benefit of property value increase has the highest influence on the calculated NPV in scenarios that account for this benefit. The obtained results in those scenarios indicate that the most probable NPV at the end of the life cycle is EUR 43/m2 and EUR 82/m2 for extensive and intensive green roofs, respectively.

Mineral resources are estimated to establish potential orebody with acceptable quality (grade) and quantity (tonnage) to validate investment. Estimating mineral resources is associated with uncertainty from sampling, geological heterogeneity, shortage of knowledge and application of mathematical models at sampled and unsampled locations. The uncertainty causes overestimation or underestimation of mineral deposit quality and/or quantity, affecting the anticipated value of a mining project. Therefore, uncertainty is assessed to avoid any likely risks, establish areas more prone to uncertainty and allocate resources to scale down potential consequences. Kriging, probabilistic, geostatistical simulation and machine learning methods are used to estimate mineral resources and assess uncertainty, and their applicability depends on deposit characteristics, amount of data available and expertise of technical personnel. These methods are scattered in the literature making them challenging to access when needed for uncertainty quantification. Therefore, this review aims to compile information about uncertainties in mineral resource estimation scatted in the literature and develop a knowledge base of methodologies for uncertainty quantification. In addition, mineral resource estimation comprises different interdependent steps, in and through which uncertainty accumulates and propagates toward the final estimate. Hence, this review demonstrates stepwise uncertainty propagation and assessment through various phases of the estimation process. This can broaden knowledge about mineral resource estimation and uncertainty assessment in each step and increase the accuracy of mineral resource estimates and mining project viability.

SummaryThe exploration and production (E&P) industry is facing a net-present-value (NPV) paradox. Despite the fact that the NPV method is widely criticized by practitioners and academics alike, the NPV method remains the cornerstone of E&P project valuation. We posit that this contradiction, which we labeled the NPV paradox, is likely to be caused by a combination of limitations of the method, a lack of theoretical understanding, and ambiguity regarding the implementation of the NPV method.Even though the NPV method has been described in numerous papers and textbooks, rigorous and succinct guidance on how to determine risk premiums for systematic risk is not available. We demonstrate that risk-adjusted discount rates are very sensitive to the choice of the length of the periods over which returns are determined (daily, weekly, or monthly), length of the time horizons considered (such as 10 or 25 years), and start date (such as 1965 or 1990). We discuss the fundamental implications and rationale of choices and their effects on the variables that underpin the risk-adjusted discount rate: risk-free rate, company β, market-risk premium, and the cost of debt.Although not entirely satisfactory, we argue for a moderate downward revision of discount rates for projects with timelines exceeding 20 years. This recommendation is dependent on recent advancements in public finance and the reality that the exposure to systematic risk in the long run is significantly less in many real-life E&P projects than the capital-assessment-pricing model (CAPM) implies. The inflated discount rate that is currently used, combined with the extended investment horizons that are common in the upstream sector, will for example result in an underweighting of decommissioning and future legacy costs.In addition to a set of widely recognized shortcomings of the NPV model, there are also lesser well-known issues. For example, the failure of CAPM to capture bankruptcy risk has a bearing on the project-risk premium. Also, the application of the NPV model implies a set of probabilistic assumptions around market risks that are likely to be invalidated when evaluating a set of market scenarios or using a series of probability-weighted market scenarios.

Hydrocarbon field (re-)development projects require the evaluation of a large number of development options under uncertainty. Furthermore, information of data gathering programs might result in narrowing parameter ranges and change the choice of the preferred development option. The large number of development options (and decisions accordingly) which have to be taken under uncertainty leads to the necessity to determine the impact of the decisions on the (re-)development project objective. Knowing the sensitivity of the decisions on the project objective (e.g. NPV) allows for resource and data acquisition planning. The impact of decisions on the project value can be determined by performing a Generalized Sensitivity Analysis. This analysis does not replace Value of Information but facilitates planning and allows focusing on important decisions. To further improve Decision Analysis and focus on important parameters, a Generalized Sensitivity Analysis of uncertain parameters on decisions can be performed. The advantage of such an investigation over sensitivity analysis on Oil Originally in Place (OOIP) or Net Present Value (NPV) is that it includes parameter interactions. Furthermore, it covers the impact of a parameter on the decisions directly rather than indirectly when OOIP or NPV sensitivity is used. The analysis is shown at an example project in a Decision Analysis framework. The use of decision impact evaluation and parameter assessment on decisions might lead to more focused and faster hydrocarbon field (re-)development project execution.

Project value is highly correlated with decisions made during concept comparison and selection. Decisions as such are made amid uncertainty, putting value at risk. This study details a methodology for determining the loss in project value when inaccurate estimates are used during concept comparison and selection. The difference between net present values (NPVs) based on inaccurate estimates and those based on an alternate hypothesis that is assumed to represent the truth determines the magnitude of loss. The value of the information required to reduce uncertainty can then be obtained.

Climbers on Everest are said to take ‘calculated risks’. They reduce the chance of failure by rigorous training. They use the best equipment, plan their expeditions to a fine degree, attempt only viable, if dangerous, routes on the mountain and climb only in acceptable weather conditions. When they have reduced risk to an acceptable level, they proceed with their venture. Most of us prefer the lower slopes; the satisfaction is not so great, but neither is the risk. Although the relationship between reward and risk was introduced in Chapters 1 and 2, when we considered investment appraisal in Chapter 3 we unrealistically assumed that future cash flows are known with certainty. Now this may be so with a fixed-interest government security, but it certainly will not be the case with a speculative goldmining operation. Investors should therefore consider not only the net present value (NPV) of a project, but also the risk that its NPV could vary according to the economic conditions prevailing at the time of the operations. People who subject their capital to high risk will expect high rewards.