An Algorithm for Global Optimal Strategies and Returns in One Fell Swoop, for a Class of Stationary Equipment Replacement Problems with Age Transition Perspectives, Based on Nonzero Starting Ages

Abstract

Aim: This research article aimed at formulating and designing an Excel automated solution-based algorithm for the optimal policy prescriptions and the corresponding returns for all feasible nonzero starting ages in one fell swoop, for a class of equipment replacement problems with stationary pertinent data. Methodology: The aim was achieved by the exploitation of the structure of the states given as functions of the decision periods, and the use of starting age index one, in age-transition dynamic programming recursions, combined with dexterous reasoning regarding the implicit dependence of the dynamic programming recursions on stage numbers. Finally, the article deployed the template to obtain alternate batch optimal replacement strategies for some problem instances, with horizon lengths of 2 to12 years, and the full set of nonzero starting ages. Results: The investigation revealed that  if   is a fixed replacement age in a base problem with horizon length and a single starting age  then the optimal solutions and corresponding rewards for the  stage problem from stage  to stage  coincide with those of the base problem, not only for the single starting age, but for the entire set of feasible nonzero starting ages in stage  of the  stage problem. By an appeal to the structure of the states at each stage and the deployment of  the preliminary starting age  master stroke  in the stage problem, the optimal policy prescriptions and rewards for the base problem for the full  set  of feasible starting ages coincide with those of  the  stage problem from stage  to stage  resulting in  different problems being solved at once. Conclusion: If  then are stage  optimal decisions and  reward from the template with horizon length  if and only if   are the corresponding optimal decisions  and reward  in stage  for the template with  the horizon length .