I am currently working on a project concerning optimal replacement strategies for sows with Erik Jørgensen. The problem is modelled using a multi-level hierarchic Markov decision process. The original model was developed by Anders Ringgaard Kristensen (KVL) whom I have had fruitful discussions with. I have realized that directed hypergraphs actually can be used to model finite-horizon Markov decision processes. They provide us with an efficient way of storing the process and by finding the shortest hyperpath we actually can fnd the optimal policy. Moreover, it should be possible the find the K best policies.
Submitted a draft of the working paper “Bicriterion shortest hyperpaths in random time-dependent networks”. Currently working on a improved branching rule for bi-SBT when two distance functions are considered. Started to work on my thesis. Teaching: Student assistant in “Mathematical Programming I” (1 class).
Finished a draft on bricriterion shortest hyperpaths in random time-dependent networks (see publications). Summer School: “Nordic Summer School on Applied Optimization and Modelling”, Sandvig, Bornholm, Denmark, May 5 – 11, 2002. Conferences: “MCDM Winter Conference 2002”, Semmeing, Austria, February 18-22, 2002. “IFORS 2002”, Edinburgh, Scotland, July 8 – 12, 2002. Teaching: Student assistant in “Mathematical Programming I” (1 class).
I started on completing the papers in my progress report so that they can be submitted to a journal. Professor Daniele Pretolani visited me from September 23 to October 23 where a draft of the paper “Finding the K shortest hyperpaths: algorithms and applications” was made and submitted (see publications). I was so lucky that my girlfriend gave birth to a beautiful boy “Mads” on 3650 grams 🙂 Conferences: “Nordic MPS 2001”, University of Copenhagen, Denmark, November 15-17, 2001. Teaching: Student assistant in “Mat alpha” (2 classes).
Wrote my progress report for my midterm exam (23 May.). Courses: “Logic-based methods for optimization” – Study group about how to use logic-based methods to solve mathematical programming models. “Ph.D. course in scientific writing”, University of Aarhus. Summer School: “Donet Summer School – Integer and Combinatorial Optimization”, Utrecht, The Netherlands, June 11 – 12, 2001. Conferences: “IPCO 2001 – Eighth Conference on Integer Programming and Combinatorial Optimization”, Utrecht, The Netherlands, June 13 – 15, 2001. Teaching: Student assistant in “Management Science and Operations Research 4” (Drøk 4 – 1½ classes).
I have been staying in Camerino, Italy for 3 months where I have visited professor Daniele Pretolani. During my stay, we developed procedures to solve the k’th shortest hyperpath problem and the bi-SBT problem. The k’th shortest hyperpath problem is solved using a new branching rule which divides the hypergraph into subhypergraphs. The bi-SBT problem is solved using different methods which are tested against each other (simple k’th method, two-phases method and k’th diagonal method). During my stay I also found a small error in the definition of a hyperpath which has been used in many papers. I therefore wrote a short note with a new definition (see publications).