joint work with Geert-Jan van Houtum
We analyze robust location-transportation problems with uncertain integer demand. The goal is to select locations of the warehouses and determine their stock levels while considering the optimal policy to satisfy the demand of customers. In this presentation, we consider the integer transshipments between customers and local warehouses. We provide theoretical and numerical results on how to solve or approximate a multi-stage robust location-transportation problem. The numerical experiments will show the efficiency of our methods.
joint work with Dick den Hertog, Ruud Brekelmans
The Chebyshev inequality and its variants provide upper bounds on the tail probability of a random variable. While it is tight, it has been criticized for only being attained by pathological distributions that abuse the unboundedness of the support. We provide an alternative tight lower and upper bound on the tail probability given a bounded support, mean and mean absolute deviation. This fundamental result allows us to find convex reformulations of single and joint ambiguous chance constraints with right-hand side uncertainty and left-hand side uncertainty with specific structural properties.
joint work with Ali Ajdari, Thomas Bortfeld, Dick den Hertog
Technological advancements in radiation therapy (RT) allow for the collection of biomarker data on individual patient response during treatment, and subsequent RT plan adaptations. We present a mathematical framework that optimally adapts the treatment-length of an RT plan, focusing on the inexactness of acquired biomarker data. We formulate the adaptive treatment-length optimization problem as a 2-stage problem in terms of Biological Effective Dose (BED). Using Adjustable Robust Optimization (ARO) techniques we derive explicit stage-2 decision rules and solve the optimization problem.