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This research includes modeling and decision support for three important applications. The first is police districting, in which our approach offers benefits in solution quality through. including higher than previous levels of spatial resolution. The second relates to assigning home health care workers to shift slots for a nationwide network of care providers. In this model, we consider provider preferences, which is apparently novel. Third, we consider the problem of assigning airplanes with demanded flights for the world's largest private air services company. Our formulation includes novel elements related to accommodating the challenge of small airports and individual customer needs. Despite the novel elements of our formulations, we have observed similar optimization formulations in the related domains being applied and at least three cases. In case 1, the decision-makers apply the solution with no or few changes. In case 2, the decision-makers depart manually from the generated solution. In case 3, the decision-makers develop a more accurate model as we have done.
More generally, a traditional approach in the field of operations research when applying mathematical optimization-based methods typically follows a sequential process: processing input data, formulating and solving a single reasonably desirable optimization model, and getting and implementing an optimal or near-optimal solution. The cases 2 and 3 mentioned above potentially apply also. Whether the model is abandoned or not, the results can generate poor quality solutions if realistic assumptions and objectives are ignored. Our proposed research offers a novel framework for "Mixed-Initiative Planning" (human decision-makers supported by optimization solvers) that considers a collaborative system between humans and the optimization engine. In this approach, the system can dynamically switch between models of varying fidelity while humans provide feedback on preferences, input data, or adjusted solutions.
The proposed framework, in turn, helps determine whether it is worth waiting for optimization or using faster solutions based on low-fidelity models, or heuristics. The user may choose to pick between two or more low-fidelity model recommendations, wait for the more accurate model to solve, or lead manual solution generation supported by guidance from one or both models. This framework is tested preliminary in one numerical example related to private aviation operations. The proposed framework is expected to lead to practical benefits for the real-world cases considered through anticipating and complimenting the approaches that the human decision-makers are likely to apply the developed models.