The aim of this study is to propose an optimization methodology to determine the values of the key decision parameters of an injection molding machine such that the desired quality criteria are met in a shorter production cycle time. The proposed robust parameter design and optimization approach utilizes the Taguchi methodology to find critical parameters for use in the optimization, and it utilizes robust optimization to immunize the obtained solution against estimation errors. The `optimal' designs found by the robust parameter design and optimization approach are implemented in real-life.
joint work with Wolfram Wiesemann
We study a variant of the capacitated vehicle routing problem (CVRP), where demands are modelled as a random vector with ambiguous distribution. We require the delivery schedule to be feasible with a probability of at least 1 - ε, where ε is the risk tolerance of the decision maker. We argue that the emerging distributionally robust CVRP can be solved efficiently with standard branch-and-cut algorithms whenever the ambiguity set satisfies a subadditivity condition. We derive efficient cut generation schemes for some widely used moment ambiguity sets, and obtain favourable numerical results.
joint work with Wolfram Wiesemann, Chin Pang Ho
Robust Markov decision processes (RMDPs) are a promising framework for reliable data-driven dynamic decision-making. Solving even medium-sized problems, however, can be quite challenging. Rectangular RMDPs can be solved in polynomial time using linear programming but the computational complexity is cubic in the number of states. This makes it computationally prohibitive to solve problems of even moderate size. We describe new methods that can compute Bellman updates in quasi-linear time for common types of rectangular ambiguity sets using novel bisection and homotopy techniques.