Design and Full Automation of Excel Solution Templates for a Time-perspective Class of Machine Replacement Problems with Pertinent Dynamic Data
Ukwu Chukwunenye *
Department of Mathematics, University of Jos, P.M.B. 2084, Jos, Plateau State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Aim: The aim of this paper is to design and automate optimal policy prescriptions and returns for a time perspective class of machine replacement problems with pertinent dynamic data.
Methodology: The aim was achieved by the exploitation of the structure of the states in time-perspective dynamic programming recursions and the coding functionality in Microsoft Excel.
Results: The paper designed and fully automated the solution templates for the determination of the optimal time replacement policies in machine replacement problems, with pertinent data given as dynamic functions of new machine purchase year and machine age.
Conclusion: The automation of these templates obviates the need for manual inputs of the states and stage numbering as well as the inherent tedious and prohibitive manual computations associated with dynamic programming formulations and may be optimally appropriated for sensitivity analyses on such model, ensuring that problems that could take days to solve are solved in a matter of just a few minutes.
Keywords: Dynamic programming recursions, excel solution templates, full automation, machine replacement, pertinent dynamic data, time optimal policy.