(26a) Optimal Scheduling of Copper Concentrate Operations Under Uncertainty
In this work, we address the scheduling of copper concentrate operations using continuous-time formulation, and deal with the uncertainty in elemental composition using both robust optimization and flexibility analysis. Robust optimization  follows the idea of optimizing against adverse realization of the uncertainty while guaranteeing the feasibility of the solution. Li et al.  reviewed methods for scheduling under uncertainty, including several robust optimization approaches. Flexibility analysis  is an uncertainty modeling technique that was originally used for plant design under uncertainty and has been developed in the process systems engineering community for more than thirty years. As shown in a recent paper by Zhang et al., flexibility analysis can have either identical or even better results than robust optimization for linear systems, although it is more time consuming.
To address the scheduling of copper concentrate operations under uncertainty, we use a multi-operation sequencing (MOS) model to formulate the deterministic scheduling problem, and utilize non-overlapping operations to tighten the formulation. Based on the deterministic model, we develop a robust MOS model, within which the robust optimization is embedded into the MOS model to formulate the worst case of the uncertainty, and the flexibility test is used to obtain the values of uncertain parameters in the corresponding worst case. The robust MOS model can be further extended to a multi-objective robust MOS model to allow the violations of quality requirements when a large range of uncertainty is included in the model. The three models are all non-convex Mixed-Integer Nonlinear Programming (MINLP) problems, which can be solved by a tailored two-step MILP-NLP decomposition strategy. An industrial case with 14 concentrates over a 15-day time horizon shows that all three models achieve near global optimal solutions within reasonable time with the decomposition strategy.
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