On the block upper-triangularity of undiscounted multi-chain markov decision problems

Authors:
Norihiro Mizuno
Affiliations:
Graduate School of Business Administration, New York University, 90 Trinity Place, New York, NY 10006, U.S.A.
Venue:
Operations Research Letters
Year:
1983

Citing 1
Cited 1

Finite State Markovian Decision Processes

Finite State Markovian Decision Processes

Linear programming with multiple choice constraints for single chain undiscounted Markov decision problems

Operations Research Letters

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Abstract

We show that the LP formulation for an undiscounted multi-chain Markov decision problem can be put in a block upper-triangular form by a polynomial time procedure. Each minimal block (after an appropriate dynamic revision) gives rise to a single-chain Markov decision problem which can be treated independently. An optimal solution to each single-chain problem can be connected by auxiliary dual programs to obtain an optimal solution to a multi-chain problem.