Christina N. Burt

Match factor for heterogeneous truck and loader fleets

The mining and construction industries have used match factor for many decades as an indicator of productivity performance. The term match factor is usually defined as the ratio of truck arrival rate to loader service time. This ratio relies on the assumption that the truck and loader fleets are homogeneous. That is, all the trucks are of the same type, and all the loaders are of the same type. In reality, mixed fleets are common. This paper proposes a method of defining match factor for heterogeneous fleets: in particular, a heterogeneous trucking fleet, a heterogeneous loading fleet, and the case where both truck and loader fleets are heterogeneous.

Equipment Selection for Surface Mining: A Review

One of the challenging problems for surface mining operation optimization is choosing the optimal truck and loader fleet. We refer to this problem as the equipment selection problem ESP. In this paper, we describe the ESP in the context of surface mining and discuss related problems and applications. Within the scope of both the ESP and related problems, we outline modeling and solution approaches. Using operations research literature as a guide, we conclude by pointing to future research directions to improve both the modeling and solution outcomes for practical applications of this problem.

Equipment selection with heterogeneous fleets for multiple-period schedules

In a simple surface mining scenario we consider a mine to have one mining location and dumpsite connected by a truck route. We determine a purchase and salvage policy for trucks and loaders, which minimises the cost of materials handling over a multiple period schedule. This problem becomes large scale when we consider large sets of equipment and long schedules. Pre-existing equipment can lead to heterogeneous fleets; non-uniformity in the operating cost function coupled with compatibility issues also adds to the complexity of the problem. We present an integer programme for this problem, where we introduce a specialised linear constraint set to ensure satisfaction of production requirements while accounting for equipment compatibility. 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.

A Decomposition-Based Heuristic for Collaborative Scheduling in a Network of Open-Pit Mines

We consider the short-term production scheduling problem for a network of multiple open-pit mines and ports. Ore produced at each mine is transported by rail to a set of ports and blended into signature products for shipping. Consistency in the grade and quality of production over time is critical for customer satisfaction, whereas the maximal production of blended products is required to maximise profit. In practice, short-term schedules are formed independently at each mine, tasked with achieving the grade and quality targets outlined in a medium-term plan. However, because of uncertainty in the data available to a medium-term planner and the dynamics of the mining environment, such targets may not be feasible in the short term. We present a decomposition-based heuristic for this short-term scheduling problem in which the grade and quality goals assigned to each mine are collaboratively adapted---ensuring the satisfaction of blending constraints at each port and exploiting opportunities to maximise production in the network that would otherwise be missed.

Exact Models for the k-Connected Minimum Energy Problem

We consider the minimum energy problem for a mobile ad hoc network, where any node in the network may communicate with any other via intermediate nodes. To provide quality of service, the network must be connected, even if one or more nodes drop out. This motivates the notion of k-connectivity. The minimum energy problem aims to optimise the total energy that all nodes spend for transmission. Previous work in the literature includes exact mixed-integer programming formulations for a 1-connected network. We extend these models for when the network is k-connected, and compare the models for various network sizes. As expected, the combinatorial nature of the problem limits the size of the networks that we can solve to optimality in a timely manner. However, these exact models may be used for the future design of mobile ad hoc networks and provide useful benchmarks for heuristics in larger networks.

Models and Algorithms for Intermodal Transportation and Equipment Selection

We study a cement transportation problem with asset-management (equipment selection) for strategic planning scenarios involving multiple forms of transportation and network expansion. A deterministic mixed integer programming approach is difficult due to the underlying capacitated multi-commodity network flow model and the need to consider a time-space network to ensure operational feasibility. Considering uncertain aspects is also difficult but important. In this paper we propose three approaches: solve a deterministic mixed integer program optimally; solve stochastic programs to obtain robust bounds on the solution; and, study alternative solutions to obtain their optimal cost vectors using inverse programming.

Utilisation-Based Equipment Selection

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.

Accurate Costing of Mining Equipment

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.

Methodology: Preliminaries and Background

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.

Match Factor Extensions

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.