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@Article{Kristensen03,
  Title                    = {A general software system for {M}arkov decision processes in herd management applications},
  Author                   = {Kristensen, A.R.},
  Journal                  = {Computers and Electronics in Agriculture},
  Year                     = {2003},
  Number                   = {3},
  Pages                    = {199--215},
  Volume                   = {38},

  Abstract                 = {A general software system for construction, editing and optimization of Markov decision processes ranging from traditional models and hierarchical Markov processes to multi-level hierarchical processes is presented. The software is designed to be multipurpose, to meet the needs of students and young scientists for demonstration of methods and concepts as well as the needs of a professional user, building real world models. A short description of the system is given and its facilities are illustrated through a sow model defined as a three-level hierarchical Markov process combining decisions on two time scales. Emphasis is put on modeling devices that may simplify the structure or speed up the calculations, which in real world models are of vast dimensions. (C) 2002 Elsevier Science B.V. All rights reserved.},
  Doi                      = {10.1016/S0168-1699(02)00183-7},
  File                     = {kristensen03.pdf:kristensen03.pdf:PDF},
  Keywords                 = {Optimal Replacement}
}

@Article{Kristensen00,
  Title                    = {Multi-level hierarchic {M}arkov processes as a framework for herd management support},
  Author                   = {Kristensen, A. R. and Jørgensen, E.},
  Journal                  = {Annals of Operations Research},
  Year                     = {2000},
  Pages                    = {69--89},
  Volume                   = {94},

  Abstract                 = {A general problem in relation to application of Markov decision processes to real world problems is the curse of dimensionality, since the size of the state space grows to prohibitive levels when information on all relevant traits of the system being modeled are included. In herd management, we face a hierarchy of decisions made at different levels with different time horizons, and the decisions made at different levels are mutually dependent. Furthermore, decisions have to be made without certainty about the future state of the system. These aspects contribute even further to the dimensionality problem. A new notion of a multi-level hierarchic Markov process specially designed to solve dynamic decision problems involving decisions with varying time horizon has been presented. The method contributes significantly to circumvent the curse of dimensionality, and it provides a framework for general herd management support instead of very specialized models only concerned with a single decision as, for instance, replacement. The applicational perspectives of the technique are illustrated by potential examples relating to the management of a sow herd and a dairy herd.},
  Doi                      = {10.1023/A:1018921201113},
  File                     = {kristensen00.pdf:kristensen00.pdf:PDF},
  Keywords                 = {ANIMAL REPLACEMENT-PROBLEM; DAIRY-COWS; RANKING}
}

@Article{Relund06,
  Title                    = {Finding the {$K$} best policies in a finite-horizon {M}arkov decision process},
  Author                   = {Nielsen, L.R. and Kristensen, A.R.},
  Journal                  = {European Journal of Operational Research},
  Year                     = {2006},
  Number                   = {2},
  Pages                    = {1164--1179},
  Volume                   = {175},

  Abstract                 = {Directed hypergraphs represent a general modelling and algorithmic tool, which have been successfully used in many different research areas such as artificial intelligence, database systems, fuzzy systems, propositional logic and transportation networks. However, modelling Markov decision processes using directed hypergraphs has not yet been considered. \par In this paper we consider finite-horizon Markov decision processes (MDPs) with finite state and action space and present an algorithm for finding the K best policies. That is, we are interested in ranking the first K policies in non-decreasing order using an additive criterion of optimality. The algorithm uses a directed hypergraph to model the finite-horizon MDP. It is shown that the problem of finding the optimal policy can be formulated as a minimum weight hyperpath problem and be solved in linear time, with respect to the input data representing the MDP, using different additive optimality criteria.},
  Doi                      = {10.1016/j.ejor.2005.06.011},
  File                     = {relund06.pdf:relund06.pdf:PDF},
  Institution              = {Danish Informatics Network in the Agriculture Sciences (DINA), The Royal Veterinary and Agricultural University},
  Keywords                 = {Relund Hypergraphs MDP}
}

@Book{Puterman94,
  Title                    = {Markov Decision Processes},
  Author                   = {M.L. Puterman},
  Publisher                = {Wiley-Interscience},
  Year                     = {1994},
  Series                   = {Wiley Series in Probability and Mathematical Statistics},

  Keywords                 = {MDP}
}

@Book{Tijms03,
  Title                    = {A first course in stochastic models},
  Author                   = {Tijms, Henk. C.},
  Publisher                = {John Wiley \& Sons Ltd},
  Year                     = {2003},

  ISBN                     = {978-0-471-49880-3}
}

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