Production Scheduling and Optimisation
Pit optimisation using Whittle 4X
Jeff Whittle brought pit optimisation of age with the first fully implemented LerchsGrossmann algorithm. The graph-maximisation approach has a number of advantages over the LP formulation illustrated above. The primary advantage is that the pit optimisation problem can be coded in any language, such as Fortran in the case of early Whittle products. As such, it is not dependent on LP solution algorithms which can vary dramatically in solution speed given their implementation and application. No doubt, Whittle’s early implementations were far faster than solving the LP equivalent using the available Simplex algorithms. Currently, 4X is one of several competing pit optimisation products on the market but is the most widely used and recognised. The following sections are not designed as a Whittle tutorial. Rather, we introduce 4X as an excellent example of the methodology of pushback generation as a means of illustrating the optimisation process for a very large example. While we could expand upon the LP-based example of the previous section, doing so would require a full version of AMPL/Cplex and far more depth in programming than is required to understand the topic. 4X follows the same basic approach as with the LP implementation: pushback generation using a series of price increments. This is supplemented by comprehensive reporting and graphing of results coupled with scheduling algorithms aimed at providing guidance in the selection of pushbacks from among the set of pits generated by applying the price factors. It should be noted that a certain amount of educated trial-and-error is required in using 4X and that the scheduling algorithms are not provably optimal but are heuristic which in some cases provide very good, if not optimal, solutions. Still, as we will see, there is no direct approach to selecting a set of optimised pit limits as pushbacks and the direct optimisation of a life-ofmine production schedule is no trivial task even when using the cleverest implementation of the fastest optimisation algorithms on the biggest computer.
Preparation—Before using 4X
When designing an open pit metalliferous mine, the object is to define the final pit outline, and determine the pit outlines or pushbacks between the final pit and the first pit and when they should be achieved. The most common program used to do this at present is Whittle 4X. Before anything can be done with 4X, the first step is to import a block model. The Whittle format is a text file with the properties of one block listed over one or more records. General mining software (GMS) packages have the ability to convert a block model from their own format into a Whittle block model.
Files There are two files required by 4X, a model file with the extension .mod and a parameters file with the extension .par. The model file contains information about each individual block in
the block model and is imported into 4X from a GMS. The parameters file contains information about the overall block model such as dimensions and costs. The exact information contained within each different file can be seen in Figure 2.1. For this example the following files are provided: Tutorial.mod Generally, the data given in the original block model from the GMS don’t contain all the fields necessary for importing into 4X. With the exception of two fields, MCAF and PCAF, it is possible to derive the extra necessary fields from the fields that will already be present. The only fields necessary for 4X are: Block Tonnes Parcel Tonnes MCAF PCAF total amount of each element present.
Block Tonnes—This field represents the total tonnage of the block, including ore and waste. Ore is defined as one or more rock types, and waste can either be defined as a rock type or left undefined. Parcel Tonnes—Parcels can be used to represent different rock types within a block. Up to 99...