Severe competition, environmental changes which take place very rapidly, and the dramatic technological innovation will demand increasing quality managerial know-how. A manager in the process of his managerial decision making, often meets complex environmental problems and its complete internal and external relations. In order to solve the problems, how ever will require an ability to make an abstraction of the mentioned problems in the form of models. A manager will meet problems which mainly concern the restriction of time and the demand for making decisions in a rapid, accuarate, and manner. This thesis has investigated an optimization of time related costs of resources allocation to activities using the Crashing Method with the aim of providing tools for a manager to over come the various difficulties of the future. The crash ing method as a method to achieve completion of a project in an optimum timely manner to minimize total cost has been formulat ed into linear and non-linear programming models. In spite of extensive research and aplication results of linear based models of the crashing method as reported for current litera ture, the thesis finds that the non-linear approach more accu rately models the actual conditions of construction of another widely known major case study of the crashing method as report ed. Finally the non-linear model of the crashing method was fully developed, tasted and validated for formulation of the gener a1gorjtje for optimization of cost in relation to project activity duration.