An algorithm for identifying the ergodic subchains and transient states of a stochastic matrix is presented. Applications in Markov renewal programming and in the construction of variable length codes are reviewed, and an updating procedure for dealing with certain sequences of stochastic matrices is discussed. Computation times are investigated experimentally and compared with those of another recently proposed method.
One-constraint optimization problems are approached via Lagrange multipliers. Sequential search schemes for generating suitable trial multiplier values are compared, and it is shown that, in general, the minimax sequential search is bisection. For certain applications, it pays to design search procedures that take advantage of special structure, such as recursively defined functions. An efficient, one-pass search procedure based on bisection for a multi-item, multi-echelon inventory problem is also presented.
A linear, fixed-interval stock replenishment policy that achieves an optimal cost balance between inventory and order-level variances is derived in this paper. The reorder rule relies on an exponentially weighted moving average to smooth random components of the demand sequence, which are assumed to be pairwise uncorrelated with mean zero and variance that either grows or decays geometrically, or remains constant in time.
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