Zero-based batch starting age algorithm for global optimal strategies and returns for a class of Stationary equipment replacement problems with age transition perspectives

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Ukwu Chukwunenye

Abstract

This research article conceptualized, formulated and designing an Excel automated solution-based algorithm for the optimal policy
prescriptions and the corresponding returns for all batches of feasible starting ages for a class of equipment replacement problems with stationary
pertinent data. The tasks were accomplished by the exploitation of the structure of the states given as functions of the decision periods, and the
use of starting age index zero, in age-transition dynamic programming recursions. The investigation revealed that if m is a fixed replacement
age in a base problem with horizon length n, and a single starting age 1 t  0, 2 n  n may be selected such that the optimal solutions and
corresponding rewards for the 2 n - stage problem from stage 2 1 n  n to stage 2 n coincide with those of the revised base problem with any
batch of feasible nonzero starting ages in stage 2 1 n  n of the
2 n - stage problem. By an appeal to the structure of the states at each stage and
the deployment of the preliminary starting age 1 t  0 master stroke in the 2 n - stage problem, the optimal policy prescriptions and rewards for
the base problem for the full set ï»1, 2,ïŒ,mï½ of feasible starting ages coincide with those of the 2n - stage problem from stage 2 1 n  n to stage
2 n , resulting in m different problems being solved at once. The paper concludes that,
if 2 2 n  n , such that n  n  m, then *( ), ( ) j j j j D s f s are stage j optimal decisions and rewards from the template with horizon length 2n , for
2 2 j {n 1 n,ïŒ, n } if and only if
2
* ( ) j n n j D s   2
and ( ) j n n j f s   are the corresponding optimal decisions and rewards in stage 2 j  n  n for the
template with the horizon length n and revised set {1, 2,ïŒ,m} , of starting ages. Moreover, the optimal decisions and corresponding rewards
for the base problem are immediate from the choice 2 n  n.

Keywords: Dynamic programming recursions, Age transition diagrams, Batch Automation of optimality results, Decision symbols, Decision
period, Equipment Replacement Problems, One fell swoop, Pertinent Data, Sensitivity Analyses.

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