(476g) Integration of Planning and Scheduling Using Data-Driven Feasibility Analysis

The economic success of a process industry is largely determined by its supply chain design, planning, and operation decisions. These decisions include the design of a robust supply chain network, and the deployment of supply chain resources to maximize profit while maintaining high customer service level^1,2. Optimal decisions necessitate the use of integrated models, which capture multi-level dynamics³. Although integrated models improve accuracy of solution by leveraging the interconnection between levels, they can become intractable as problem’s dimensions increase⁴.

Operational planning and scheduling are concerned with allocating available resources over time to perform a set of tasks required to complete several customer orders for finished products. Integrating the planning and scheduling model improves the feasibility and optimality of the planning decisions by taking into consideration detailed scheduling constraints². The integration is achieved either using a simultaneous or hierarchical (sequential) approach^3,5. Although the simultaneous approach can reach a coordinated and global solution, the resulting model can quickly become computationally intractable. Sequential approaches, on the other hand, needs to be refined appropriately to avoid infeasible solution. Therefore, additional coordinating constraints should be incorporated in the different decision levels to avoid the infeasibility issue. For the scheduling and planning problem, these coordinating constraints are resource constraints and the production cost constraint³. In the surrogate space, radial basis function (RBF) models have shown to approximate highly nonlinear responses to high accuracy⁶. For high-dimensional problems, the corresponding surrogate models are highly nonlinear expressions. Although the use of surrogate models to express production limits reduces problem’s infeasibility, it complicates the integrated problem⁴.

This work exploits the radial basis function (RBF) kernel of support vector classifier by mapping the input data to randomized feature space and applying existing fast linear methods to this transformed predictor. This is done by approximating the RBF kernel's feature map by Monte Carlo approximation of it’s Fourier transform ^7,8. The basic idea of this approach is to reduce the training time for surrogate generation and build a linear model that is easily adaptable to the integrated model. The feasibility metrics proposed by Wang and Ierapetritou⁹ was used to test the accuracy of the surrogate model. Furthermore, to test the effectiveness of the surrogate model, the integrated planning and scheduling problem is solved using the surrogates as aggregates of the feasible space. This integrated planning problem was solved and compared with the solution from the simultaneous method. This methodology is extended to solve high-dimensional problems since it reduces the model complexity by avoiding non-linearities.

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