Optimizing inventory stockpiles and mine production: An application of separable and goal programming to phosphate mining using AMPL/Cplex

"In the Phosporia formation of SE Idaho, ore quality varies by depth, seam and distance along strike; phosphorus recovery is sensitive to these variations. Plant ore feed can be blended over time to minimize this fluctuation by using a combination of mine production and inventory stockpile scheduling. Mixed-integer and goal programming has been used to optimize short-term mine production, but the seasonal nature of mine haulage requires the use of stockpiles both at the mill and the mine. The contents of the stockpiles can also be optimized as part of the production scheduling problem, but introducing inventory control introduces a nonlinear term into the formulation. A solution using a piecewise linear formulation is modelled and solved using AMPL/Cplex, and solution strategies are discussed for similar large-scale problems. IntroductionIdaho’s minable deposits of phosphate rock are found in the Meade Peak member of the Phosphoria Formation; two separate zones of this formation are mined with a combined thickness of 30 ft to 60 ft. A generalized stratigraphic section of the Phosphoria section is shown in Figure 1, illustrating the degree of complexity encountered when scheduling mine production. Alteration of the formation results in higher grade ore zones near the surface and variable in P2O5 levels between seams and along strike. This variability is seen as well in other quality characteristics critical to the production of acid and elemental phosphorus. Further, plant recovery and nodule quality are sensitive to variations in ore feed; variability in SiO2, carbonates, moisture, organics (carbon), P2O5 and other constituents of the ore can strongly affect plant recovery. Because ore quality characteristics can vary as a function of the alteration zone (or seam) being mined as well as the depth and distance along the strike of the formation, scheduling of mine production can have a highly significant effect on recovery in the plant. As illustrated in Figure 1, there are nine seams containing 20% to 35% P2O5. Phosphoric acid and elemental phosphorus production requires an ore content of 30% and 25% P2O5, respectively. Variability between numerous beds that are mined and quality variation within a seam due to alteration greatly complicates production scheduling with the result that erratic mill feed characteristics greatly decrease recovery."