Contributed Discussion to "Optimization Techniques for the Open Pit Limit Problem" by L. Caccetta and L. M. Giannini (Bulletin and Proceedings, Vol. 291, December, 1986).

The authors have succeeded in providing additional rigour and clarity to the formulation and execution of the dynamic programming algorithm for optimum open pit limit determination. The inclusion of the blocks on the J + 1 column in the search for Pmax, and constraining this search with blocks assigned a value of negative infinity, ensures an optimal solution within the defmed blocks. The effect of the negative infmity blocks is to preclude mining along the diagonal blocks from the first row that they occur in. Figure 1 graphically illustrates the effects of this on the calculation of P. A practical application for constraining mining with negative infmity blocks is the case where the pit outline is defined by lease boundaries and not by the value of blocks to be removed. Any legal, social or physical constraint could be accounted for in the same way.The danger in applying this technique is that the negative infinity blocks will override any other more profitable solutions that may exist. This is in fact what has happened in the example that the authors use. If a further column is added to the left hand side (column -1) and the calculation is carried out again, a more optimal x-section can be found. (If the negative infinity values are removed the same result is obtained.) This gives a pit value of 112 as against the 108 of the authors' optimal pit. This calculation is shown in Figure 2. Lerchs-Grossman optimization is reliable only if there are sufficient columns available to allow "mining" to optimum depth of the ore body and still allow the pit to break out at the surface within the confines of the columns.This author's approach is to create enough columns each side of the lateral limits of the ore to allow the pit to intersect the surface while still within the confines of the block model. Implementing the methods discussed by the authors helps to reduce the number of columns required to achieve this.