tracked compounds can be set based on what chemical constituents are important to the clients. In the examples in this paper, we only consider P2O5 and MgO for simplicity. Client parameters are recorded in Table 3. Table 3 – Client parameters. Parameter Client 1 Client 2 Client 3 Client 4 Client 5 Client 6 Price ($/tonne) 200 180 160 140 120 100 Demand (tonnes) 200 200 200 200 200 200 Minimum P2O5 (%) 34 33 32 31 30 29 Maximum MgO (%) 0.5 0.6 0.7 0.8 0.9 1.0 Blending and routing are conceptualized to take place simultaneously. Flows from one node to another have a tonnage and chemical composition associated with it. Multiple flows into a node represent blending of the feedstock from multiple sources. Mines, piles, and processes can have compatible piles, processes, and clients, respectively, which dictate what material is allowed to be sent where. Restricting what flows can be sent between which nodes can effectively allow the network to represent blending being “unavailable” at certain stages. In addition to the default case where blending is permissible at any point in the network, the compatible node feature provides the flexibility to represent scenarios where blending is permitted before processing but not after, and vice versa. The network model does not incorporate logistics, which is beyond the scope of this paper. Representative values for all input parameters are informed by the literature (Azzamouri & Hovelaque, 2024; Azzamouri, Hovelaque, & Giard 2024) and data from the OCP Group. These values are not taken directly from real operations, but rather, are meant to represent realistic scenarios. 3.2 Optimization Benchmark For the benchmark optimization approach, we employed a greedy mixed-integer linear programming (MILP) approach that uses mean values to deterministically find the optimal flow assignments on each day. This approach is in line with recent literature and is a state-of-the-art deterministic optimization approach currently employed in a wide range of industry settings. Many mining operations that perform feedstock blending still use simple Excel-based blending formulas, so MILP serves as a gold standard benchmark for comparison. All optimization approaches seek to maximize profit (revenue from clients minus operating costs) as the main performance metric. 3.3 Optimization-under-Uncertainty Formulation Feedstock blending and routing can be viewed as a sequential decision-making under uncertainty problem, and so can be formulated as Markov Decision Process (MDP). Flow assignments must be made sequentially at fixed time intervals (for the simulations in this work, we let that time interval be a day) under uncertainty from two key sources: feedstock variability and process complexity. The uncertainties from these sources are represented as stochastic
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