Equipment Selection for Mining: With Case Studies

The viability of todays mining industry is very highly dependent on careful planning and management strategies that minimise operating costs. An important and challenging problem is that of selecting and allocating a fleet of trucks and loaders for use in extracting and moving ore and waste throughout the life of the mining operation. This fundamental problem is important as the cost of the truck and loader fleet is estimated to account for up to 55% of the total cost of the operation. The difficulty of the problem is due to many factors including: the scale of the mining operation which involves multiple sites, multiple pits and a mine plan that extends over many periods; the complexity of the mining operation which requires a number of restrictions and operational constraints to be met; and multiple objective criteria that needs to be addressed. In this chapter, we define the equipment selection and allocation problem in the context of surface mining. We provide context by describing the background for the problem and define the scope of equipment selection in this book with respect to equipment and mining types. We also describe and define factors that can have an impact on equipment selection, such as equipment availability and utilisation, planning horizons and operating cost over time.

This chapter presents the basic concepts that are needed to develop mathematical models for the equipment selection problem in mining. These concepts include truck cycle time and a number of productivity measures for both trucks and loaders. The match factor, which is defined as the ratio of truck arrival rate to loader service time, is an important productivity indicator for trucks and loaders. The objective of the truck-loader optimisation problem is to minimise cost. So an important task in modelling is to establish an effective cost model. Equipment cost is dependent on many factors including purchase and salvage costs, maintenance costs and operating costs. In addition to providing some necessary background to equipment selection in mining, this chapter also provides a brief introduction to Linear and Integer Programming. Mixed Integer Linear Programming models provide the best option to accurately model and address the difficult equipment selection problems.

In this chapter, we present a detailed literature review of the equipment selection problem in surface mining as well as the closely related equipment selection problem in the construction industry. We review the modelling and solution methods that have emerged in both the mining and operations research literature. We also consider a number of closely related problems such as shovel-truck productivity, mining method selection, scheduling, dispatching and allocation problems. Our review considers a broad range of modelling and solution approaches that can or have been used for these related problems.

The match factor is defined as the ratio of truck arrival rate to loader service time. For the mining industry, this ratio is an important performance indicator with a dual purpose: during the equipment selection phase, it can be used to determine an appropriate fleet size such that the truck fleet productivity matches that of the loader fleet; during the operational phase, the match factor can be used to estimate the relative efficiency of the selected fleet. Prior to our work the match factor ratio has been restricted to homogeneous fleets. However, heterogeneous fleets are very common in large scale mines. In this chapter, we present a detailed account of the match factor ratio in mining and develop several extensions to the match factor ratio to allow for heterogeneous fleets.

Our aim is to develop effective computational models for determining the optimal truck-loader selection and allocation strategy for use in large and complex mining operations. To achieve this it is important to have real case studies that reflect the true nature of the problems to be addressed. In this chapter, we provide the data and background for two real case studies, one is a simple senario with one mining location and 9 periods each having a 1-year duration, the other is a more complex senario with multiple locations and 13 periods each having a 1-year duration. Our first case study, though small and simple has interesting variation in truck cycle times. It represents a mine in the planning stage with pre-existing equipment. Our second case study, is from an ongoing mining operation and has pre-existing equipment and includes stockpiles. This data was provided by an in-house equipment selection expert from an industry partner.

In a simple surface mining scenario we can consider the mine to have one mining location and one dump-site connected by a single truck route. Our objective is to determine a purchase and salvage policy for trucks and loaders such that the cost of materials handling is minimized over a multiple period schedule. This problem quickly becomes large scale when we consider large sets of possible trucks and loaders, and long schedules. The inclusion of pre-existing equipment leads to the possibility of heterogeneous fleets, and the non-uniform behaviour of different equipment types (with respect to operating cost, availability and productivity) coupled with compatibility issues adds to the complexity of the problem. In this chapter, we present an integer linear program model for equipment selection that incorporates heterogeneous fleets and pre-existing equipment while optimising over multiple periods. We introduce a specialized linear constraint set to ensure satisfaction of production requirements while accounting for equipment compatibility. We also test the model on a truck and loader case study for surface mines. The resulting model is a robust equipment selection tool that obtains optimal solutions quickly for large sets of equipment and long schedules. Many aspects of the presented model, such as the consideration of multiple periods and pre-existing equipment, are novel for the mining industry and ensure that the model is both a new and advanced equipment selection tool.

In this chapter we consider a multi-location mining operation. An important characteristic for multi-location (multi-location and multi-dumpsite) mines is that the underlying problem is a multi-commodity flow problem. The problem is therefore at least as difficult as the fixed-charge, capacitated multi-commodity flow problem. For long-term schedules it is useful to consider both the purchase and salvage of the equipment, since equipment may be superseded, and there is the possibility of used pre-existing equipment. This may also lead to heterogeneous fleets and arising compatibility considerations. In this chapter, we consider two case studies provided by our industry partner. We develop a large-scale mixed-integer linear programming model for heterogeneous equipment selection in a surface mine with multiple locations and a multiple period schedule. Encoded in the solution is an allocation scheme in addition to a purchase and salvage policy. We develop a solution approach, including variable preprocessing, to tackle this large-scale problem. We illustrate the computational effectiveness of the resulting model on the two case studies for large sets of equipment and long-term schedule scenarios.

When performing equipment selection, we can best account for the operating cost by considering the utilised hours of the equipment. In a surface mine, equipment is often not utilised to full capacity and not accounting for this difference may lead to inferior solutions. In operations such as this, the cost of operating equipment depends on the age of the equipment while the utilisation of equipment is usually based on the equipment cost. The co-dependency of the age of the equipment and the utilisation has provided a barrier to tractable equipment selection models. That is, equipment is rarely utilised in a uniform way, causing the ageing of the equipment (when considering the total hours utilised) to be non-uniform. In our bid to address this issue, we consider a single-location multiple-period mine. We present a mixed-integer linear program that achieves optimal equipment selection and accounts for the equipment utilisation. This model considers pre-existing equipment and allows for heterogeneous fleets. We illustrate our approach on a case study.

When performing equipment selection, we can best account for the operating cost by considering the number of hours that the equipment has been utilised. In a surface mine, equipment is often not utilised to full capacity and not accounting for this difference may lead to inferior solutions. Generally, the cost of operating equipment depends on the age of that equipment, while the decision to use a piece of equipment or not is based on the cost. This co-dependency of the age and utilisation of the equipment has so far provided a barrier to tractable equipment selection models. In the mining industry, it is a common practice to discretise both the age of the equipment and the current time into discrete blocks. However, since the running cost of a piece of equipment depends on its age, an undesirable side-effect of this discretisation is that the cost of operating a piece of equipment over a given time period must be determined by its age at the start of that period. It would be more accurate to account for changes in the age of the equipment as time passes within the period. In this chapter, we present a way in which we can capture the effect of these changes, using linear constraints and adjustments to the objective function. These constraints and adjustments are intended to be added to a mixed-integer linear program for equipment selection, which accounts for equipment utilisation, pre-existing equipment and heterogeneous fleets. However, with these additions this mixed-integer programming model increases in complexity and requires further work to achieve tractability in large-scale case studies.

In this book we have presented a comprehensive account of the mathematical based computational models that have been developed for determining the optimal truck-loader selection strategy for use in large and complex mining operations. We have reviewed the methodology developed over the past 50 years from the early ad hoc spreadsheet approaches to the current highly sophisticated and accurate mathematical based computational models. Our approach has been motivated and illustrated by real case studies provided by our industry collaborators. This final chapter discusses a number of open problems that provide important challenges to the research community.