ABSTRACT
In management, the quantitative analysis of time related activities is accomplished by substituting dynamic modes of analysis for static ones. Quantitative tools of analysis are required when the complexity of certain problems preclude any organization and solution. For simplification purposes, all functions are assumed to admit first and second continuous derivatives, unless otherwise stated. Such assumptions will be sufficient to validate our results. For further theoretical treatment, the reader is referred to the extensive bibliographical list as well as to the appropriate appendixes. Using a control theory approach and the assumption of convexity of the reachable set of final states, H. Halkin derived a maximum principle for discrete time systems. In discrete time systems for example when the reachable set is non-convex, the variational approach breaks down while the dynamic programming approach applies. For this reason, dynamic programming is often the only available method for the numerical solution of discrete time problems.
