Dynamic Constraints Modelling

The objective of this article is to introduce the concepts behind Dynamic Constraints Modelling and illustrate how it can be used as a simple but powerful desktop decision support tool for management and executives in the mining industry. Dynamic Constraints Models can provide insight in areas such as capital optimisation, short and medium term planning, budgeting, prioritising productivity initiatives, and as a key input to management reporting at all levels.


A senior executive at a mining major, addressing his executive team at an annual planning session, made the observation that “as far as complexity goes, we have one of the easiest jobs in the world – dig it out of the ground and ship it to our customers.” That simplicity conceals the significant day-to-day challenges faced by mining bosses everywhere – from the strategic – including fluctuating commodity prices in a highly cyclical industry, to tactical - dealing with operational and logistical issues mining in inhospitable and remote locations. Managing the latter, i.e. the “Resource to market value chain”, is the daily challenge for a majority of managers and executives in the industry. While the industry is increasingly moving towards automation, it is still comparatively a laggard in adopting new technology. For decision-making, executives still rely on basic tools such as spreadsheets, and are unable to holistically model the impact of different scenarios. There is a need for effective, user-friendly decision support tools to support operational and strategic decision-making. Dynamic Constraints Models offer an effective option to address this gap.

Key Challenges

Most mining executives will face a common set of conflicting priorities and constraints that need to be resolved optimally. These include:

  • What is the optimal mix of products to satisfy market demand, resource availability, logistical challenges as well as operational constraints such as load and haul capacity, processing capacity, and cost?

  • Where are the key constraints across the value chain that need to be unlocked to maximise value?

  • For large firms with multiple operations, what is the optimal strategy to maximise value to the business?

  • How should capital be allocated to debottleneck the value chain?

  • What productivity initiatives should be prioritised? How can they be quantified?

Dynamic Constraints Modelling

The Resources industry is no stranger to optimisation models. Commonly used tools, however, tend to be either overly simplistic, such as single-constraint based Value Driver Trees (VDT), or complex, sophisticated planning systems that require extensive data integration with SCADA or operational systems.

Figure 1. Holistic view of the value chain

Both approaches tend to fail for a number of common reasons. Simple VDT or Excel models cannot handle the modelling complexity or data requirements of large, integrated value chains and sophisticated tools are expensive, complex to configure and depend heavily on the integrity of operational data, which is not always dependable. In addition, single-constraint based approaches are only useful to analyse incremental performance gains and often produce erroneous results in more complex environments.

Figure 2. Conventional silo-based approach to optimisation, with focus on a single constraint

As the name suggests, dynamic constraints models are not built around a static operational constraint – they are designed to dynamically determine the position of the constraint within the value chain and calculate true system throughput and buffer or stockpile creation at each stage. Dynamic Constraints Modelling (DCM) is a modelling approach designed to realistically model large, complex value chains with multiple entities and products and moving operational constraints. The modelling approach is based upon VDT's, chosen, as they are familiar to analysts within the industry. This allows the DCM to be easily maintained without expensive external support.

Figure 3. Illustrative value chain driver tree logic

The DCM incorporates process design capacities, steady-state achievable targets and historical performance. It also includes cost and revenue drivers, providing the ability to analyse the cost and EBIT impact of performance changes within the value chain.

DCM Analytics

As a decision support tool, Dynamic Constraints Models provide powerful analytical capabilities such as constraints, scenario analysis sensitivity and source of variance analysis. It can be further integrated with powerful risk modelling extensions to provide enterprise class risk analysis.

Constraints analysis

The DCM is built upon a sophisticated constraints analysis algorithm that identifies the process constraints across the value chain and adjusts throughput through each to compensate. The algorithm accounts for stockpile and in-process inventory changes and calculates operational buffers at each process stage.

Figure 4. Constraints analysis

Output from the constraints analysis is visualised by histograms plotting process capacities, operational buffers, and design capacities at each process stage.Constraints analysis is key to understanding the location of a bottleneck where in-process inventories obscure the true capacity of the value chain. Overlaid with realistic performance targets (such as stretch operational targets), it becomes a useful tool to identify focus areas for productivity initiatives and capital prioritisation.

Scenario analysis

The DCM has powerful scenario analysis capabilities that enable planners to create virtually unlimited independent scenarios for planning or what-if analysis

Figure 5. Comparisons between different scenarios

By selectively modifying input drivers (both cost and performance), new scenarios can be created and analysed to quantify the throughput, cost and revenue impacts of the changes. Scenarios can then be compared against each other to understand how the changes impact the value chain.

Sensitivity analysis

A key feature of a DCM is the ability to draw detailed sensitivity reports on,any part or, the whole of the value chain. Outputs include 'tornado' graphs to display sensitivity of outputs to changes to input drivers.

Figure 6. Sensitivity Analysis “tornado” graphs

Source of variance analysis

A common challenge faced by operational managers is understanding the underlying drivers of variance in output in an environment with multiple changing inputs. For example, if load and haul performance in a given month at 8% lower than the last, then what were the key input drivers that changed, and by how much, to result in that variance?

Figure 7. Source of variance waterfall

Source of variance analysis is built upon sensitivity analysis algorithms and quantifies the individual impact of changes in input drivers between two periods on any output measure (for example actuals vs. budget or January vs. February performance).

Variability analysis

Any constrained system is impacted by variability in performance at each process stage. Theory of constraints advocates the use of in-process inventory or stockpiles to reduce the impact of variability on process throughput. Inventory however, is expensive to carry and must be carefully managed to manage cost. The variability analysis module helps quantify the impact of variability within a process on total throughput through the system. The variability analysis algorithms determine the inventory requirements at each process stage based in input performance parameters (rate, availability, utilisation and delays) to deliver the desired output.


Dynamic Constraints Models offer a powerful desktop decision support tool for operational managers and mining executives in environments ranging from single operations to complex multi-site value chains. The familiar design approach and easy integration with operational and financial systems ensures that once rolled out, a DCM can be easily and sustainably integrated into any operation’s operating philosophy.

Nikhil Datta

Managing Partner, DB & Associates

DBA has helped some of the largest open-pit and underground mining firms build Dynamic Constraints Models to optimise their resource-to-market value chains. Contact us for additional information.


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