DA Stochastic Dynamic Programming, Stochastic Dynamic Distance Optimal Partitioning Problems and Partitions-Requirements-Matrices

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This book consists of, apart from the introduction, the chapters- DA Stochastic Dynamic Programming with Random Disturbances, - The Problem of Stochastic Dynamic Distance Optimal Partitioning(SDDP problem), - Partitions-Requirements-Matrices (PRMs).DA ("decision after") stochastic dynamic programming with random disturbances"is characterized by the fact that these random disturbances are observedbefore the decision is made at each stage. In the past, only very moderateattention was given to problems with this characteristic.In Chapter 2 specific properties of DA stochastic dynamic programming problemsare worked out for theoretical characterization and for more efficientsolution strategies of such problems.The (DA) Stochastic Dynamic Distance Optimal Partitioning problem(SDDP problem) is an extremely complex Operations Research problem. Itshows several connections with other problems of operations research andinformatics such as stochastic dynamic transportation and facility locationproblems or metric task systems and more specific k-server problems.Partitions of integers as states of SDDP problems require an enormousamount of storage space for the corresponding computer programs. Investigationsof inherent characteristic structures of SDDP problems are also importantas a basis for heuristics.Partitions-requirements-matrices (PRMs) (Chapter 4) are matrices of transitionprobabilities of SDDP problems which are formulated as Markov decisionprocesses. PRMs "in the strict meaning" include optimal decisions ofcertain reduced SDDP problems, as is shown (in many cases) toward the endof the book.PRMs (in the strict meaning) themselves represent interesting (almost selfevident)combinatorial structures, which are not otherwise found in literature.In order to understand the investigations of this book, previous knowledgeabout stochastic dynamic Programming and Markov decision processes isuseful, however not absolutely necessary since the concerned models aredeveloped from scratch.