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

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 I1 = 0, n2 ~ n may be selected such that the optimal solutions and corresponding rewards for the n 2 _ stage problem from stage I + ~ - n to stage n2 coincide with those of the revised base problem with any batch of feasible nonzero starting ages in stage 1 + n2 - n of the n, _ stage problem. By an appeal to the structure of the states at each stage and the deployment of the preliminary starting age t 1 = 0 master stroke in the n2 - stage problem, the optimal policy prescriptions and rewards for the base problem for the full set {1,2, ... ,m} of feasible starting ages coincide with those of the ~- stage problem from stage l+n2 -n to stage n2, resulting in m different problems being solved at once. The paper concludes that, ifn < n such that n - n > m thenD'(s) F(s)are stage j optimal decisions and rewards from the template with horizon lengthn for 2' 2 -, J } ,j J J 2' j E {n + 1- n.i->, n } if and only if D' (s ) and r (s ) are the corresponding optimal decisions and rewards in stage J' + n - n: for the 2 2 j+n-nl j J t-r-«. j . ~l template with the horizon length n and revised set {I, 2,"" m} , of starting ages. Moreover, the optimal decisions and corresponding rewards for the base problem are immediate from the choice n2 = n.