Geometric Programming Approximation to Dynamic Programming

Abstract

Abstract In this paper, we have developed a geometric programming approximation to dynamic programming. The method has additional advantages of providing the cost involved in decision making and also eliminates the course of dimensionality which restricted the application of dynamic programming to small problems. We also obtained the optimal dual decision variables. We stated two lemmas, and through them, we proved that the optimal allocation policy is the same as the optimal primal decision variables and that the sum of cost matrix in Dynamic programming is the same as the cost coefficient in Geometric programming. We applied the method on a problem and obtained the optimal cost for decision making to be ₦97.30 and optimal decision policy to be (0.1, 0.2, 1, 3). This policy means that lecturers should combine to teach courses in year two and year three but each lecturer handles one course in year four and three courses in year five.