1 Introduction

Metals and minerals are essential components in practically every aspect of life; they enable energy and water supply, healthcare, farming, communications, space technology, transport, and the construction of our cities. They allow the manufacture of current green technologies, such as electric cars, solar panels, wind turbines, and the development of new technologies to meet the urgency of climate change. Significantly, mined resources promote long-term economic growth and develop resilient and inclusive communities. As transitions to cleaner forms of energy gain momentum, there will be a rapid increase in demand for these minerals [1]. Technology developments will continue to call for a wide variety of different mineral resources. Battery performance, lifetime, and energy density directly correlate to the amount of lithium, nickel, cobalt, and manganese in today’s batteries. Permanent magnets, considered essential for electrical vehicle (EV) motors and wind turbines, are made using rare earth elements. Copper is a crucial component of all energy-related technologies. Hence, enormous amounts of it must be used in constructing power networks along with aluminium. According to an International Energy Agency (IEA) report [2], over the course of the next 20 years, the global transition to cleaner forms of energy will have far-reaching effects on the demand for minerals. The total mineral requirement from renewable energy resources is expected to double by 2040 under the Stated Policies Scenario (STEPS). In contrast, under the Sustainable Development Scenario (SDS), it is expected to quadruple (Fig.1).

Fig. 1
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Total demand for selected minerals [2]

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The growth of the metals and minerals supply is important for making the switch to clean energy, and it also has the potential to help some of the poorest people in the world escape poverty. Mineral wealth can improve the ability of governments to provide services and help many people make a living if the correct settings are in place for its development, extraction, and eventual closure. However, mineral development has several potential drawbacks if the planning and scheduling are not correctly handled, including:

  1. (i)

    Energy-intensive mining and processing emit significant amounts of greenhouse gas (GHG)

  2. (ii)

    Negative effects on the environment, such as the extinction of species and the disruption of social systems due to changes in land use, water usage and pollution, waste management, and air pollution

  3. (iii)

    Social consequences of corruption and misuse of government resources include worker and public deaths and injuries, human rights violations such as child labour, and disproportionate repercussions on women and girls

In recent years, heightened public awareness of environmental, social, and governance (ESG) risks has been influenced by several factors in the mining sector. These include the failure of the Brumadinho tailings dam in Brazil [3], the devastation of the Jukken Gorge cave in Western Australia [4], and increased concern regarding the sector’s contribution to climate change via greenhouse gas emissions [5] [6].

ESG is an investment phrase that refers to the environmental, social, and governance considerations that investors and consumers consider when determining whether to purchase a product or invest in a firm. Some claim that ESG provides opportunities for cost reductions, revenue generation, and risk mitigation. ESG is now linked to the longer-term performance of many investment offerings.

ESG encompasses a wide variety of aspects, as follows:

  1. (i)

    Environment: alterations to the climate, loss of biodiversity, improper management of waste, water resources, and pollution

  2. (ii)

    Social: safety, human rights, working conditions, health, diversity, and community

  3. (iii)

    Governance: ethics, attitude to taxation, corporate governance, executive pay, compliance, diversity, lobbying, and other related topics

This standard has been the focus of effort for many stakeholders for well over a decade. Since compliance with ESG standards is frequently linked to financing success, it is currently extremely relevant to the mining and resources industry. According to the British multinational professional services networks Ernst & Young (EY), this year’s (2023) ranking of the top 10 mining and metals risks and opportunities shows that ESG aspects remain at the forefront of concerns for high-level leadership of resources firms. Based on the EY survey of approximately 200 global mining executives, the results in Fig. 2 show that geopolitics is second, followed by climate change at three, licence to operate at four, and costs and productivity at five [7,8,9].

Fig. 2
figure 2

EY top 10 business risks and opportunities for mining and metals, 2023 [7]

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This will significantly affect how new projects are developed, greatly influencing commodities supply and price. ESG disclosures are becoming more and more necessary throughout the supply chain. This is especially important in mining, which significantly affects the environment and nearby communities [10]. There is now much more attention on the industry than ever, and investors and financiers are increasingly reluctant to support projects that are seen as bad for the environment [11]. Because of this, companies and governments need to deal with the harmful effects that mining can have on society and the environment.

In the mining industry, a project will generally follow a sequential order of stages, sometimes referred to as “phases”, as seen in Fig. 3.

Fig. 3
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Mining project pipeline development [12]

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During the pre-feasibility phase of development, more in-depth engineering and socio-environmental investigations are conducted on the preferred configurations/options. In Literature from 1977 to 2023, various objective functions are considered in conducting strategic mine production scheduling for sublevel stoping mining operations, as shown in Table 1:

Table 1 Previous research for different objectives in sublevel stoping production scheduling [13]
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It is evident from Table 1 that most research on mine planning optimisation in sublevel stoping deals with a single objective, which is to maximise profit or NPV. A few researchers have also carried out limited multi-objective optimisation in underground and open-pit mining operations. Moreover, little published research has been completed that simultaneously considers environmental impacts together with economic benefits. In recent years, multi-objective optimisation techniques have tended to be most suitable in solving a wide variety of real-world problems due to their potentiality. Within this context, this review article aims to provide a concise overview of underground mining production scheduling with a particular focus on sublevel stoping operations while also incorporating ESG aspects. The authors aspire to direct future research efforts toward employing multi-objective optimisation in this area to generate mine plans and schedules to evaluate the trade-off between often conflicting economic and ESG intentions.

This paper is divided into the following sections: Underground mining is covered in Section 2, which is divided into three subsections that explain sublevel stoping operations, long-term production planning, and short-term production planning. The topics covered in Section 3’s two subsections elaborate on single and multiple objective optimisations, including mathematical programming and production scheduling optimisation. ESG aspects in mining are covered in Section 4. Applying ESG directly to sublevel stoping operations is discussed in Section 5. The plan for future work is shown in Section 6, and finally, the study’s conclusion is provided in Section 7.

2 Underground Mining

Mining that takes place below the surface of the earth to extract valuable minerals is referred to as underground mining. On the basis of the strength of the rock formation, underground mining methods can be broadly divided into two categories: supported methods and unsupported methods, as shown in Fig. 4. Supported methods are also classified into naturally supported methods and artificially supported methods. In naturally supported mining methods, the stability of the mined-out spaces primarily relies on the inherent strength and stability of the geological formations, rock mass, and surrounding strata. The natural properties of the ore body and surrounding rocks are sufficient to maintain the integrity of the openings, requiring minimal artificial support. In artificially supported mining methods, the excavated spaces’ stability and safety are actively maintained by installing engineered support systems. These methods are employed in geological conditions where the natural rock mass alone cannot ensure safe excavations. Artificial support systems are strategically designed and installed to supplement the inherent strength of the rock [32].

Fig. 4
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Classification of underground mining methods [32].

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This research focuses on the optimal production scheduling of sublevel stoping operations, which is classified as a naturally supported mining method.

2.1 Sublevel Stoping Operation

Sublevel stoping (SLS), also known as long-hole stoping or blast-hole stoping, is a versatile and productive underground mining method which can be implemented for mining mineral deposits with:

  1. (1)

    Vertical or steeply dipping orebodies with regular ore boundaries

  2. (2)

    Competent orebodies surrounded by competent host rocks

  3. (3)

    The dip of the footwall is greater than the angle of repose of the blasted ore

The orebody is first developed by a series of sublevels by drifts linked by ore passages. After developing drives through the orebody so that stopes can be mined at various sublevels, the orebody is often split into primary and secondary stopes, which are square or rectangular [13], [27]. Primary stopes are firstly excavated, while secondary stopes are left as pillars to provide geotechnical support. Once the primary stopes’ extraction, backfilling, and consolidation have been completed, secondary stopes may be extracted. The ore obtained through drilling and blasting activities within sublevels is typically mucked out using load haul dump (LHD) units. Before reaching a surface processing facility, the fractured ore from the blasting process may be directed to a central crusher facility through an ore pass network. The empty stope’s walls and roof are supported by backfilling the void. The fresh fillmass often needs some time to dry out and compact thoroughly. Fig. 5 gives an overview of the architecture of the approach, as well as an illustration of the development of a typical stope.

Fig. 5
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A stope layout for the sublevel stoping method [20]

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The three constraints affecting the production schedule of sublevel stope mines were highlighted by Little et al. [33]. Firstly, once production commences on a stope, it should be rapidly drawn down and backfilled without interruption. This will decrease the risk of failure, which could propagate to surrounding stopes and infrastructure. Secondly, all simultaneous adjacent stope production must be avoided to prevent excessively large unsupported voids. Thirdly, once a stope has completed production and is being backfilled to create a fillmass, production from the remaining adjacent stopes must not expose more than a single side of the fillmass. This offers some protection to the fillmass due to its general lack of strength and inability to transfer stresses.

Sublevel stoping is widely recognised as one of the most established and extensively employed methods for underground mining on a global scale [34]. It has been a prominent mining practice in Canada, Australia, and Scandinavia throughout the 1970s due to its superior productivity. Despite the growing popularity of mass mining techniques such as sublevel caving and block caving, sublevel stoping continues to be the most prevalent mining technique for precious and base metal extraction in Australia [35]. The sublevel stoping method is also responsible for more than 60% of the underground mining sector in North America [36]. However, an initial sizeable financial investment is required to establish underground infrastructure, which includes the development of production levels. This mining approach can potentially dilute irregular deposits, particularly in scenarios where the host rock has a lower competency. Even though the approach’s primary advantages are its high production and efficiency, cheaper costs, and generally good recovery, it is nevertheless conceivable, under unfavourable conditions, for significant dilution to occur [13].

Production scheduling is typically carried out across long, medium, and short-term horizons. The short term seeks to meet the day-to-day challenges of running a complex and dynamic operation while adhering to the long term strategic mine plan. All scheduling horizons should seek optimal ore extraction, resource management, safety, and environmental responsibility while maximising business profitability and long-term stability [37].

2.2 Long-term Production Scheduling

When planning and designing a sublevel stoping operation, one of the most significant steps is the creation of a long-term production schedule. This is a complex optimisation process that involves vast data sets, various hard and soft restrictions, and uncertainty in the input parameters. The scale of the task is unprecedented. During each scheduling period, the goal of the model is typically to maximise the NPV of the cash flows that will result from the mining project while simultaneously satisfying all of the operational restrictions. These constraints typically include mining capacity, ore production capacity, and a mill feed grade blend. Long-term production scheduling is essential for strategic mine planning, determining the optimal sequence of sublevel stoping to maximise ore extraction over the mine’s life cycle. It allocates resources effectively, plans investments, and ensures sustainable operations over the mine’s life, considering financial, environmental, and social aspects. It should allow for the integration of sustainability goals and ESG principles into long-term mining plans, aligning with the company’s vision for responsible and sustainable mining practices. Long-term plans serve as the foundation for both the medium and short-term production schedule in addition to determining the cash flow generated over the mine’s existence. When there is not an effective strategy for long-term planning, thinking only in the short term might result in poor utilisation of mineral resources, decreased production rates, and business operations that are less profitable and efficient.

In order to plan the long-term production schedule of a sublevel stoping operation at Mount Isa, Australia, Trout [17] made the first attempt at employing a mathematical model based on mixed-integer programming (MIP). The objective was to maximise the NPV while simultaneously considering the limitations imposed by stope sequencing, stope extraction and backfill quantities, equipment capacity, and production quality. The author integrated seven variables into the model, five of which were binary variables linked to stope production stages and two integer variables tied to ore tonnage and backfilling amounts to maximise the NPV. The demonstration of optimality could not be carried out as planned since it was disrupted by a shortage of computer processing capacity. Due to additional improvements, the model was not implemented at the mine [19], [38], [39].

Nehring [40] extends Trout’s [17] work by articulating a new constraint for limiting multiple fillmass exposures while not violating any other operational requirements. There was a total of 774 binary variables and 315 integer variables within the model. In addition, the author’s study also demonstrated that using MIP to create production plans is preferable to the commonly used practice of choosing output based on the next highest available cash flow stope. This demonstrated the fact that MIP is more efficient than manual scheduling.

Little et al. [19] created an optimal production schedule using a classic MIP model for sublevel stoping operations. This model was able to significantly improve the effectiveness of the models that had been previously discussed. The authors did this by applying two different theories, natural sequence, and natural commencement, which led to reducing these five sets of binary variables to a single set of binary variables. It notably cut down on the amount of time needed to find a solution while maintaining the integrity of all constraints and improved prior mathematical models for long-term scheduling by integrating additional primary operations, including external and internal development.

Basiri [25] developed a novel strategy to address some of the shortcomings of Nehring’s [41] model for the design and scheduling of sublevel stoping operations. Basiri’s approach aimed to improve the efficiency of the mining process. This was done to bring attention to the significance of levels in the methodologies used in underground mining. The author addressed level-based and field-based optimisation using a method based on binary integer programming. Within the parameters of the level-based technique, the author’s objective was to derive the greatest possible economic and NPV. The field-based approach began by applying the same goal function over the whole orebody before moving on to the level assignment step.

For the combined optimisation of stope and development network designs as well as underground mine production scheduling for sublevel open stoping mining operations, Faria et al. [30] developed a two-stage stochastic integer programme. The objectives of this study are to maximise discounted revenues, minimise development expenses, and manage the risk of not meeting production targets, all while satisfying geotechnical constraints. The outcome demonstrates that the suggested approach offers a physically distinct design and production schedule with an 11% higher NPV and a 2-year shorter life of mine.

In their study, Appianing et al. [31] introduce a mathematical programming framework that utilises a mixed-integer linear programming (MILP) formulation. This framework addresses the challenges of integrated open stope development and production scheduling, specifically combining backfilling, operational level control, and stope extraction duration control. The findings indicate that a total of 2.48 million metric tonnes (Mt) of material was extracted and processed from a mineralised material amounting to 2.88 Mt. This extraction and processing resulted in the NPV of $244.7 million for a gold project with a projected mine life of 25 years.

2.3 Short-term Production Scheduling

Short-term scheduling ensures operational efficiency by planning immediate production volumes from available locations, optimising ore extraction, and managing day-to-day activities for maximum productivity. It enables quick adaptation to change conditions, ensuring safety and efficient mining operations by adjusting plans based on ground conditions and other factors. It helps allocate resources efficiently for each sublevel, ensuring that equipment, such as load haul dump (LHD) units and trucks, workforce, and materials, is used optimally for the best extraction results. Short-term scheduling executes the schedule generated as part of the strategic mine planning process. The objective is to minimise deviation from specified feed grade and metal production targets and, consequently, to maintain a constant mill feed rate. The goal of maximising the NPV of the project should be a long-term objective implemented as part of the short-term plan. While the literature provides a substantial depth and breadth of development relating to strategic (long-term) production scheduling, a relatively small number of authors address the issue of operational (short-term) production scheduling issues.

The work done by Ribeiro [15] was the first time that dynamic programming (DP) was used for short-term scheduling to achieve grade control in sublevel open stoping. The author used it to solve a straightforward issue that occurred in two dimensions and had two sub-levels. In 1987, 5 years later, Dowd and Elvan (1987) revised an earlier version of the DP model to solve some of the model’s shortcomings. This was able to be accomplished by reducing the variability of a large number of other important factors that were linked with the orebody [13].

Nehring et al. [42] suggested a short-term scheduling model for production scheduling in sublevel stoping and assigning equipment items like trucks and load–haul dumps (LHDs) in the conceptual Kelvin subterranean operations. The goal was to achieve as minimal deviation as possible from the planned amount of metal production. The purpose of the model was to schedule the movement of trucks and LHDs, and mixed integer linear programming (MILP) was applied to determine the best possible outcomes. In response to a shift in the subsurface operating circumstances, the shift-based schedule could be optimised, and trucks and LHDs could be promptly reallocated. When a conceptual dataset was tested, optimal findings could be generated in a matter of minutes.

A short-term production scheduling optimisation model was put forth by Campeau and Gamache [43] that takes into account all phases of development and production as well as particular restrictions on personnel and equipment. Optimal planning was produced using a pre-emptive MIP. To validate the model, a mine plan was developed using data from a currently operating gold mine in Canada. The goal was to maximise the amount of ore that could be extracted as quickly as possible while simultaneously reducing the amount required to feed the mill. The model could be solved to optimality, or near optimality in more complex circumstances, in a concise amount of time for examples indicative of various medium-term periods, according to the findings of the application to multiple stages of mine development. The necessity of modelling the problem pre-emptively was proven by comparison with a model that was not pre-emptive. This resulted in more effective and accurate solutions than those produced by the non-preemptive model.

Two distinct methods for constraint programming (CP) models for short-term planning in underground mines were proposed by Aalian et al. [44]. One method involves generating several potential timetables for the issue at hand. The second method consists in adding a confidence constraint to the CP model to define the likelihood that the generated schedule will not underestimate the time required to complete tasks. Real data sets from an underground gold mine in Canada are used to test the methods. The results show that both scenario-based and confidence-constraint methods do a better job of making schedules.

3 Mathematical Programming and Production Schedule Optimisation

Mathematical programming is one of the most powerful tools for making decisions based on generated output data. It has a well-defined structure. The primary objective of mathematical programming is to ascertain the best possible solution while taking into account a number of restrictions. The essential components of a standard mathematical programming model are objective function(s), a number of decision variables, and a set of constraints. Various classifications have been assigned to the mathematical programming models based on the essential components; they include [45]:

  1. (i)

    Linear programming

  2. (ii)

    Nonlinear programming

  3. (iii)

    Network optimisation

  4. (iv)

    Integer programming

  5. (v)

    Mixed integer programming

  6. (vi)

    Multiple criteria optimisation

  7. (vii)

    Dynamic programming

  8. (viii)

    Stochastic programming

Real-world scheduling issues are very difficult, not only due to their combinatorial character but also due to limitations imposed by various production settings. The fact that underground mining techniques are more diverse and sophisticated than surface mining methods demonstrates the importance and complexity of optimisation in these processes. For many years, underground mining technologies have been the subject of optimisation and production planning in the mining industry. However, considerable progress in this area, similar to open-pit mining, has not been made [46].

One of the most common and important issues in both engineering practice and scientific research is optimisation issues. Since the 1960s, optimisation issues have been dealt with in the mining industry using mathematical programming. Williams et al. [47] proposed a linear programming model with continuous variables to minimise deviations from the intended production for sublevel stoping. This marked the beginning of the use of mathematical modelling for the planning of underground mining operations [48]. Other notable early services are acknowledged in Chanda’s basic works from 1990 [49] when the author extended the application to operational issues in a block cave mining operation using simulation and MIP. This is one of the earliest known examples of combining these two approaches. The author devised a production schedule solution for a copper mine in Zambia that would run over a period of six consecutive shifts and have the goal function of minimising the fluctuation of the ore grade. In the years that followed, researchers including Trout [17], Carlyle and Eaves [50], Topal [51], Kuchta et al. [52], and Topal [53] refined the work by enhancing the model framing and solution generation timelines. Nehring et al. [22] and Little et al. [54] give examples of how MIP optimisation can be used to improve segregated and combined medium and short-term underground production schedules and how it compares to other methods.

Progress has been achieved in the production scheduling processes due to the computational limitations and underlying complexity. Various deterministic and stochastic approaches for production scheduling optimisation methods have been proposed. Deterministic scheduling optimisation was carried out by Trout [17], Carlyle and Eaves [50], Smith et al. [55], Kuchta et al. [52], Sarin and West-Hansen [56], Nehring and Topal [18], Topal [51], [57], [53], Nehring et al. [42], Little and Topal [21], Fava et al. [58], O’Sullivan and Newman [59], Brickey [60], King et al. [61], and Zhang et al. [62]. Stochastic scheduling optimisation was carried out by Carpentier et al. [63], Sepúlveda et al. [64], Dirkx et al. [65], Huang et al. [66], Nesbitt et al. [67], and Faria et al. [30]. On the basis of the objective function(s) type, production scheduling optimisation approaches can be classified into two categories: single objective optimisation and multi-objective optimisation.

3.1 Single-Objective Optimisation

Optimisation can be defined as maximising a problem’s advantageous properties while minimising its disadvantageous properties while satisfying all constraints [68]. Optimisation problems can be single-objective or multi-objective, linear or nonlinear, continuous or combinatorial, constrained or unconstrained, and static or dynamic optimisation problems [69]. A single-objective optimisation issue is one that has just one objective function. Most of the time, the single-objective model for production schedule optimisation aims to maximise NPV.

Lietae [14] discussed the use of linear programming in the development of an underground mine. The idea to construct an optimisation model for underground mines originated from the success of two LP models for Centromin-smelting Peru’s refining operations in 1971 and 1972. The strategy aimed to find the ideal mining schedule to maximise the company’s contribution over a specific time horizon. The report comprised mining works and model decision factors. The model was utilised at the Casapalca mine and other company mines.

Mixed integer programming was used by Trout [17] in order to facilitate the creation of the most effective production schedules for underground stoping activities in Mount Isa, Australia. The main goal was to maximise the NPV. In a major underground mine, a case study was provided to show the considerable increase in before-tax NPV over a comparison manual production plan.

Nehring and Topal [18] were provided with a MIP model for a modest conceptual sublevel stoping operation. On an example of nine stops, the results of a schedule made by the MIP production scheduling model and a schedule made by hand are compared. The results show that the MIP production scheduling model has a lot of potential benefits for maximising NPV. Lastly, a new constraint was made to limit the number of times a fill mass could be exposed more than once. This constraint will be incorporated into an existing model for the MIP production scheduling. The application of the formula to the nine-stope example’s central stope was put to the test, and the results demonstrated that it performed as expected without violating any of the other operational requirements. The results showed that MIP modelling might be a good way to figure out the best order of activities because it gave an NPV that was 0.6% higher than the schedule that was made by hand.

Campeau and Gamache [43] established a mathematical model that takes into account all aspects of development and production, as well as unique equipment and personnel limits. The goal function was to maximise extracted tonnes as soon as feasible while keeping ore tonnage to a minimum to feed the mill. To generate optimum planning over a limited time horizon, a mixed integer programme was utilised. Then, a comparison to a non-preemptive model and a case study was provided, with a number of tests conducted with different data sets and circumstances.

3.2 Multi-objective Optimisation

Multi-objective optimisation (MOP), also called multicriteria optimisation, multi-objective programming, Pareto optimisation, vector optimisation, or multi-attribute optimisation, is a field of multiple-criteria decision-making that deals with mathematical optimisation problems with more than one objective function that need to be optimised simultaneously. It shows real needs more correctly, but it also makes the optimal models more complicated. Many scientific domains, including engineering, have used multi-objective optimisation to make judgments when there are trade-offs between two or more potentially conflicting goals [70]. Due to the fact that the optimum goals often conflict with one another, multi-objective optimisations (MOPs) are challenging to solve. Finding an optimum solution that meets all goals from a mathematical standpoint is often challenging.

Let us consider the following multi-objective optimisation problem [71].

$$\mathit{\min}\boldsymbol{f}\left(\boldsymbol{x}\right)$$
$$\textrm{s}.\textrm{t}.\kern0.5em {\boldsymbol{g}}_{\boldsymbol{j}}\left(\boldsymbol{x}\right)\le 0,\kern1em j=1,2,\dots, m$$
(1)

where f(x) ≔ [f1(x), …, fl(x)] stands for a vector of l objective functions and x ∈ ℝn. It is also assumed that the objective functions fi : ℝn → ℝ, i = 1, …, l, and gj : ℝn → ℝ, j = 1, …, m.

The manner in which the solutions to multi-objective optimisation problems are to be defined is a primary concern. From the perspective of theoretical mathematics, there is not a single answer that can be provided for multi-objective problems; rather, there is a collection of answers that can be provided. The solutions of the multi-objective optimisation problem (equation (1)) are called non-dominated solutions or efficient points [72] or Pareto points [73] or Pareto optimal solutions. A solution is referred to as the Pareto optimum when it is not possible to enhance the value of any objective function without compromising the values of other objective functions.

A curve containing the images of these Pareto optimal solutions in the objective space is called the Pareto front. In the context of MOPs, the concept of the Pareto front refers to a group of solutions that do not dominate one another but are superior to the other options in the search space. This shows that no single solution in the Pareto front is the superior to all other options in terms of meeting every goal that is sought after. Therefore, altering the vector of design variables along a Pareto front comprised of these non-dominated solutions cannot concurrently increase all objectives. From a mathematical point of view, each and every one of the Pareto optimal solutions is preferable to each and every other solution of the MOP with regard to all of the objectives. Nevertheless, in our daily life, only one solution out of the whole set of Pareto optimal solutions can be selected. The choice made to select a preferred solution depends on the discretion and current needs of a decision maker. In underground mining, especially in sublevel stoping mining, very limited research has been found for the application of multi-objective optimisation in the production scheduling problem.

Wang et al. [26] proposed a multi-objective optimisation model for the production process in the Huogeqi Copper Mine, which is located in China. This was done so that the mineral resources could be utilised more effectively for sustainable development. This study’s two primary objectives were maximising economic profit and resource efficiency. A fast and elitist non-dominated sorting genetic algorithm (NSGA-II) is utilised to optimise the multi-objective optimisation mode. The findings provide a set of Pareto-optimal solutions that mine decision-makers can use to select from multiple available options to their specific requirements. In addition, compared to the production indicators currently in place, the profit and resource utilisation rate of certain specific optimisation results could be increased by 2.99% and 2.64%, respectively. This research examined the degree to which the Pareto-optimal solutions were affected by the price per unit of copper concentrate. The findings suggest that the Pareto-optimal solutions that result in higher profits are more sensitive to unit copper concentrate price changes than those obtained in regions with lower yields. This is because decreased rates of resource utilisation accompany increased profits.

A multi-objective integer programming (MOIP) model was created by Foroughi et al. [27] for the integrated optimisation of the mine plan and production scheduling process for sublevel stoping mining. This research included two different goal functions: the first was to maximise NPV and the second was to maximise metal recovery. The authors used a multi-objective genetic algorithm known as non-dominated sorting genetic algorithm II (NSGA-II) in order to find a solution to this MOIP. According to the research, adopting NSGA-II results in a more convergent Pareto front and a noticeably shorter solution time from 7–8 days to 6–7 h when compared to the Weighted Sum technique. While metal recovery increased 18.55%, NPV only declined by 0.41%.

Some papers have been written about how multi-objective optimisation can be used in production scheduling for other mining methods. Among them, Sepúlveda et al. [64] formulated a new opportunity for decision-makers to analyse, compare, and select among numerous scenarios in order to achieve an optimal balance of economic and operational objectives in block caving mining. This study concentrates on maximising economic return and minimising the risk associated with geometallurgical variable uncertainty. Results show that a multi-objective approach to production scheduling optimisation can successfully incorporate geometallurgical uncertainty.

Mohtasham et al. [74] proposed a multi-objective mixed-integer linear goal programming model for the open-pit mine shovel scheduling problem. This study aims to maximise production, minimise deviations in head grade, minimise deviations in tonnage to the ore destinations, and minimise fuel consumption of mining trucks. The model’s implementation in a copper mine case study revealed that it is successful and efficient.

Silva-Júnior et al.[75] developed a mixed-integer linear goal programming problem for a work shift for open-pit mines. An optimisation model with four objectives was proposed. The objectives are minimising deviation from the production target rate, minimising deviations from the targets for the control parameters, minimising deviation from the bounds for each control parameter, and minimising the number of trucks used above the lower bound. They tested the model in a case study of an iron ore mine located in the central region of Minas Gerais state, Brazil. The results showed that it is possible to increase the productivity and use of the equipment through the proposed model.

4 ESG in Mining

The mining sector faces both ESG risks and opportunities. Understanding and addressing these factors is becoming increasingly important for mining companies to remain competitive, attract investors, and maintain a positive reputation. ESG is a set of criteria to evaluate a company’s environmental impact, social responsibility, and corporate governance practices. Investors and stakeholders are increasingly interested in companies prioritising sustainable practices and demonstrating good ESG performances.

The failure of mining operations to mitigate ESG risks and enhance ESG opportunities, particularly the environmental and social aspects, can significantly affect a company’s credit rating. It can result in increased financial risks, reduced access to capital, and reputational damage, all of which impact the company’s creditworthiness in the eyes of investors, lenders, and credit rating agencies. Therefore, taking ESG considerations seriously and implementing sustainable practices is crucial for companies to maintain a positive credit rating and secure long-term financial stability [11].

In September 2015, the United States Environmental Protection Agency announced that Volkswagen violated the Clean Air Act by installing illicit software in their diesel vehicles. Following the revelation, regulatory bodies in many nations initiated investigations into the automaker, leading to a significant decline of one-third in the company’s stock price in the immediate aftermath of the announcement [76].

In recent years, the mining industry has been afflicted by various disasters, one of which being the collapse of tailings dams at Samarco and Vale’s Brumadinho mine, both of which are located in Brazil. Destruction of the Juukan Gorge in Western Australia’s Pilbara region in 2020 is another example. Such incidents can tarnish a company’s environmental and social credentials, turn investors away, and take a long time to rebuild trust [77].

Mining companies can focus on minimising their environmental impact through various means, such as implementing cleaner and more energy-efficient technologies, reducing water consumption, managing waste responsibly, and rehabilitating mining sites after extraction. Investing in renewable energy sources for mining operations can also significantly improve a company’s ESG profile. Exploring and identifying new mining sites should be carried out responsibly, taking into account biodiversity conservation and the potential impact on local ecosystems [2].

Engaging with local communities and indigenous peoples is crucial for mining companies. Local communities and indigenous peoples often live near mining operations. If mining companies do not engage in meaningful consultation and establish mutually beneficial relationships, they risk facing opposition, protests, and potential disruptions to their operations. Building strong relationships with local communities and addressing their concerns can lead to better community acceptance and support for mining projects [78].

Mining companies must ensure fair Labour practices, respect human rights, and provide safe working conditions for employees and contractors. Issues related to labour rights, such as child labour or forced labour in the supply chain, can negatively impact a company’s reputation and legal standing. Mining companies need to maintain high standards of corporate governance and ethical practices. Strong governance structures, independent boards, transparent reporting, and anti-corruption measures are crucial for building trust with investors and stakeholders [79].

Embracing technological advancements can lead to improved operational efficiencies, reduced environmental impact, and enhanced safety standards. For example, automation and digitalisation can minimise the need for human presence in hazardous areas and help optimise resource extraction processes [80]. Mining companies can contribute to climate change mitigation efforts by assessing and reducing their carbon footprint. This can involve adopting carbon capture and storage technologies, transitioning to electric vehicles, and offsetting emissions through various means [81].

When making judgments about investments, investors and lenders are placing an increasingly greater emphasis on ESG aspects [82]. This suggests that miners will frequently need to prove their commitment to ESG issues in order to secure financing. Investors who care about ESG issues can get information about companies from a wide range of sources other than what the law and regulations require. Companies are ranked by rating and indexing agencies (such as DJSI, MSCI, FTSE4Good, and Sustainalytics) based on their real or perceived ESG attributes [83]. Several institutional investors have stated that they will consider ESG when making investment decisions, such as the Dutch pension fund ABP, which declared that “responsible investment is central to our investment philosophy” [84]. Another investment management company BlackRock mentioned that “we have integrated ESG considerations across our investment research, portfolio construction, and stewardship processes” [82]. Furthermore, Allianz Global Investors CEO stated, “A more holistic approach to “growth” needs to evolve, looking to capture societal and environmental benefits and costs” [85]. As the world continues to emphasise sustainable practices and responsible resource management, the mining sector’s integration of ESG principles will likely become even more critical. By effectively managing ESG risks and capitalising on opportunities, mining companies can position themselves as responsible and sustainable industry players, attracting long-term investors and ensuring their resilience in an evolving global market focused on environmental and social issues.

Some organisations, such as the World Gold Council, are advocating for insurance companies to play a larger role in the ESG movement, such as making it a requirement for mining firms to adhere to ESG principles in order to receive coverage [85]. The Argentine Securities and Exchange Commission’s Resolution No. 896/2021 approved the Guidelines for the Issuance of Social, Green, and Sustainable Bonds, which are investments that are good for society [86]. The guidelines show how important it is to think about ESG factors when making decisions about allocating capital. This also discusses the significance of integrated reporting, corporate strategy, and the manner in which decisions are arrived at.

ESG is now associated with a Corporate Sustainability Reporting Directive, which will change the reporting requirements that are already in place. In particular, funds whose investment objectives make reference to ESG elements and other funds that apply ESG techniques (ESG-related funds) are advised on how to disclose their practices in relation to ESG considerations by the Canadian Securities Administrators (CSA) [87]. To aid in the spread of best practices of ESG within the mining industry, several voluntary codes of practice and guidelines have been developed. The framework proposed by the International Council on Mining and Metals (ICMM) focuses on the aspects of environmental resilience, social performance, and governance and transparency [88].

The Mining Association of Canada’s (MAC) initiative towards sustainable mining (TSM) has been adopted by the Quebec Mining Association, the Finnish Mining Association, the Cámara Argentina de Empresarios Mineros (Argentina’s national mining association), the Botswana Chamber of Mines, the Chamber of Mines of the Philippines, and the Confederación Nacional de Empresarios de la Mineria y de la Metlaurgia (Spain’s national mining association) as of 2019 [89].

The European Partnership for Responsible Minerals (EPRM) is a multi-stakeholder partnership. It was established to create better social and economic conditions for mine workers and local mining communities. It does this by increasing the number of mines that adopt responsible mining practices in conflict and high-risk areas [90].

Smith and Brooks [91] present one of the first studies that focuses on the inherent opportunities and challenges in the effective integration of social performance issues into long-term strategic planning for mineral assets in South Africa. The authors present the principles that define the Anglo-American “Social Way” framework for regulating social performance.

M Urrets-Zavalia [92] conducts an analysis of the significance of ESG factors within Argentina’s lithium mining sector. The study aimed to look at the rules, commitments, and systems that large lithium mining companies in Argentina have used to control extraction and processing on certain lithium-bearing frontiers. The study gave important information about how multinational mining companies measure and report ESG standards on one of the fastest-growing frontiers for lithium in the world.

For the purpose of developing a low-carbon supply chain in the mining sector, Bustos et al. [93] detail a multi-objective mixed-integer linear programming model. The model’s goals were to reduce economic losses by minimising the total cost of investment and transportation, to reduce environmental losses by minimising carbon dioxide (CO2) emissions from processes and transportation, and to reduce inefficiency losses by minimising deviations in product quality parameters from target values. The results showed that the highest total cost was achieved when CO2 emissions and deviations were kept to a minimum. Conversely, when costs were kept to a minimum, carbon dioxide release was increased.

Li et al. [94] proposed a multi-objective optimisation model for the coordinated development of three different sectors: economy, environment, and resources in three stakeholders: government, coal enterprise, and the residents in China’s coal-based areas Shanxi Province. This study aims to maximise economic growth, minimise pollutant discharge, and minimise coal consumption in the research area. According to the result, the authors recommended paying attention to the government to rationally handle the trend of the coal market and formulate the appropriate tax rate for the coordinated development of the region.

Leon et al. [95] developed a multi-objective mixed-integer nonlinear optimisation problem in designing an integrated water supply system for three mining operations and a neighbouring city in the Atacama Desert in northern Chile. The main intention of this study is to assess the trade-off between economic and environmental aspects of the system. Results show that adding a photovoltaic solar system lowers glasshouse gas pollution, but it also makes the system a little more expensive.

In the realm of environmental economics, Sinha et al. [96] constructed a bi-level multi-objective model between the Finnish mining business and the government in the Kuusamo region. During the 5-year period, the problem was solved using a hybrid bilevel evolutionary multi-objective optimisation algorithm with the goals of maximising tax income and minimising environmental harm. The programme generated a collection of trade-off solutions from which the government may choose the best course of action.

A multi-objective mixed-integer non-linear programming model was presented by Yu et al. [97] for investment decision-making in energy savings and emission reductions in the Chinese coal mine. The three goals of the study were to (1) maximise the mining profit, (2) minimise the energy consumption, and (3) minimise the pollutants. The results showed that, compared to the condition prior to such expenditure, the average energy consumption and pollution level per unit of coal output were reduced by more than 34.8% and 71.6%, respectively.

The Australian mining industry is under increasing pressure to adopt ESG in order to shape the sector’s future over the next decade. Industry 4.0 mining technologies, such as smart mining software and remote sensing tools, are currently defining ESG mining in Australia [98]. These technologies enable mining corporations to determine the most effective methods for extracting resources from their sites. In the USA, the Securities and Exchange Commission is moving forward with climate change and ESG-related disclosures. The European Union is working on a Corporate Sustainability Reporting Directive, which will change the reporting requirements that are already in place [99].

ESG is a key idea that is gradually replacing the conventional understanding of corporate social responsibility as a result of institutional investors’ desire to make effective investments. Since the financial performance and corporate values are today in line with the ESG elements, the false dichotomy between profitable and sustainable investments is no longer relevant. If the mining industry cames to the conclusion that they do not need to address ESG and sustainability properly, it will find it increasingly difficult to secure insurance, funding or a licence to continue their business.

5 Applying ESG in Sublevel Stoping Operation

ESG is a framework to evaluate and integrate sustainability considerations into business and operational strategies. Applying ESG principles in sublevel stoping mining operations involves considering and incorporating sustainability practices in the mining process while optimising production and minimising environmental and social impacts. ESG considerations can lead to selecting mining locations and methods with less environmental impact. This might include using practices with a lower impact on biodiversity or implementing technologies and that reduce pollution, habitat destruction, and land degradation. ESG integration can drive efficient resource allocation and utilisation. By considering environmental and social factors in the optimisation model, mining companies can minimise waste, reduce energy consumption, and optimise the use of natural resources, ultimately leading to cost savings and improved efficiency. Incorporating ESG principles can prioritise safety and health standards for workers. The optimisation model can guide decisions that minimise risks and prioritise employees’ well-being, improving worker satisfaction, reducing accidents, and enhancing the company’s social standing.

By integrating social considerations into the optimisation model, mining companies can actively engage with local communities, seek their input, and address their concerns. This proactive approach can improve relationships, reduce conflicts, and provide community support for mining operations. Adhering to ESG principles ensures compliance with local regulations and international standards, enhancing the company’s reputation and reducing the risk of legal and reputational issues. This, in turn, can attract investors and partners who prioritise responsible and sustainable business practices.

Overall, integrating ESG principles in the optimisation model for sublevel stoping mining operations can drive a holistic approach that maximises economic benefits and prioritises environmental and social responsibility, leading to a more sustainable and resilient mining industry.

6 Proposal for Future Work

There is an enormous quantity of future research required to fully and appropriately incorporate ESG risks and opportunities into the strategic mine planning process. This review article’s goal is to lay the groundwork necessary to improve the ability to apply operations research techniques to solve challenging multi-objective scheduling issues that incorporate ESG in sublevel stope mining together with traditional financial metrics. No prior published work has addressed the integration of ESG risks and opportunities into production scheduling optimisation for sublevel stoping mining operations.

While efforts to develop high-level national and regional frameworks to manage ESG aspects are somewhat advanced, there is a shortfall in how to incorporate ESG aspects at the project/site level. Even less attention has been given to the development of new and robust processes and methodologies that are able to provide decision-makers with the various design/scheduling trade-offs that present as a result of increasing or deducing the weighting associated with the value-driven of one stakeholder group over another. It is only once mine planners are able to appropriately quantify the trade-off between these value drivers (e.g. NPV versus carbon emissions) at the site level that properly informed decisions can be made and whether or not a particular project meets an organisation’s corporate objective as a standalone operation and/or as part of a portfolio of projects.

Future research will be needed to develop new MOP models incorporating ESG opportunities and risks into the strategic mine planning process. As a starting point, the authors propose the development of a new mathematical model specifically aimed to maximise NPV, minimise greenhouse gas emission, and minimise the social impacts of vibration.

7 Conclusion

Mining businesses have a complex and crucial problem to solve when generating a long-term strategic production schedule. This has always been a primary component in calculating value and is frequently followed by a decision point which requires capital commitments in the hundreds of millions of dollars. Mining operations increasingly need to balance economic return with their impact on the environment and communities in which they operate. A formal approach to incorporate these aspects into an optimisation model is required.

Because of the diverse character of the sublevel stoping mining approach, optimisation efforts are sometimes unable to be concentrated on a single objective. Models of multi-objective programming incorporating ESG look for the best possible solution, taking into account a number of different criteria. Although multi-objective optimisation is able to more effectively portray actual needs, it does so at the expense of increasing the complexity of optimum models. It is able to coordinate several objectives by making use of the Pareto equilibrium approach.

It is apparent that throughout the last several years, there have been some excellent review articles published in the literature regarding mining optimisation. Methodologies for advanced planning and scheduling optimisation can assist practitioners in the mining industry in lowering the costs of infrastructure and equipment, increasing production efficiency, and maximising net profits after mining operations have been completed. It is anticipated that a movement towards the development of more sophisticated schedule optimisation approaches incorporating ESG, with the goal that the mining industry will adopt them as a practical and essential toolbox.