One of the main obstacles in using mixed integer linear programming (MILP) formulations for large-scale open pit production scheduling is the size of the problem. The objective of this work is to develop, implement, and verify deterministic MILP formulations for long-term large-scale open pit production scheduling problems. The objective of the model is to maximize the net present value, while meeting grade blending, mining and processing capacities, and the precedence of block extraction constraints. We present four MILP formulations; the first two models are modifications of available models; we also propose, test and validate two new MILP formulations. To reduce the number of binary integer variables in the formulation, we aggregate blocks into larger units referred to as mining-cuts. We compare the performances of the proposed models based on net present value generated, practical mining production constraints, size of the mathematical programming formulations, the number of integer variables required in formulation, and the computational time required for convergence. An iron ore mine case study is represented to illustrate the practicality of the models as well.

The mining industry often uses shotcrete for ground stabilization. However, cracking within shotcrete is commonly observed, which delays production schedules and increases maintenance costs. A possible crack reduction method is using expansive shotcrete mixture consisting of calcium sulfoaluminate cement (CSA), ordinary Portland cement (OPC), and calcium sulfate (CS) to reduce shrinkage. Furthermore, fibers can be added to the mixture to restrain expansion and impede cracking. The objective of this paper is to study the effects of nylon fiber, glass fiber, and steel fiber on an expansive shotcrete mixture that can better resist cracking. In this study, parameters such as density, water absorption, volume of permeable voids, unconfined compressive strength (UCS), splitting tensile strength (STS), and volume change of fiber-added expansive mixtures were determined at different time periods (i.e. the strengths on the 28th day, and the volume changes on the 1st, 7th, 14th, 21st, and 28th days). The results show that addition of fibers can improve mixture durability, in the form of decreased water absorption and reduced permeable pore space content. Moreover, the expansion of the CSA-OPC-CS mixture was restrained up to 50% by glass fiber, up to 43% by nylon fiber, and up to 28% by steel fiber. The results show that the STS was improved by 57% with glass fiber addition, 43% with steel fiber addition, and 38% with nylon fiber addition. The UCS was also increased by 31% after steel fiber addition, 26% after nylon fiber addition, and 16% after glass fiber addition. These results suggest that fiber additions to the expansive shotcrete mixtures can improve durability and strengths while controlling expansion.