In this talk, we will discuss two integer programming problems and how different methods can treat them efficiently. In the first part of the talk, we will look into the classical multi-item lot-sizing problem, for which a substantial literature exists since 1950's. We will discuss the problem with big-bucket capacities, i.e., items competing for same resources, and present where the complexities lie. Then, we will present a novel methodology that generates cutting planes using the convex hulls of the key subproblems and different distance functions. We will discuss theoretical properties of the methodology, as well as present preliminary computational results.
In the second part of the talk, we will present the radiation treatment optimization problem for Volumetric Arc Therapy (VMAT). VMAT is a recently introduced cancer treatment technology offering more efficient solutions for doctors and patients. The problem is highly complex and naturally very large in size, and moreover, doctors need fast solutions due to time limitations. We will present a basic formulation and discuss some improvements on it including valid inequalities. Then, we will present a number of methodologies based on Lagrangian relaxation, heuristics and constraint programming, and conclude with preliminary computational results.
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