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
Issue: 2016 - Volume 7 [Issue 4]
Ukwu Chukwunenye *
Department of Mathematics, University of Jos, P.M.B 2084, Jos, Plateau State, Nigeria
*Author to whom correspondence should be addressed.
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 .
Keywords: Age transition diagrams, age transition dynamic programming recursions, batch automation of optimality results, decision period, decision symbols, equipment replacement problems, one fell swoop, pertinent data, set of feasible nonzero starting ages, sensitivity analyses