Time compression of network-based scheduling systems using the time value of money

Abstract

The primary objective of this research is to develop a network planning model which considers the time value of money. Heretofore, time-cost trade-off procedures have not considered the impact of compounding the cumulative investment of a network-based scheduling system over time. This method of analysis considers the affects of interest on the optimal schedule and optimal cost of the system. The common assumption that activities within a network are independent has been omitted in this investigation. The necessary computational procedures and techniques are first developed to solve a simple system of serial activities. These procedures are then augmented to form a step-by-step algorithm for determining the unconstrained and constrained optima for a parallel system. The basic algorithm is then extended to provide a means of determining an optimal time-cost schedule for a generalized network containing crossed paths. In addition to the conventional constraint of a project due date, the algorithm is amenable to other constraints such as total project cost and minimum activity durations. The inclusion of interest as a direct component of the activity utility function complicates the time compression routine; however, some interesting results are noted and discussed when the time value of money is considered as an integral part of the total project cost function. For example, using the operational logic of this investigation, slack cannot appear in an optimal solution and it is shown that the optimal solution depends to a great extent upon the assumed effective interest rate. Finally, a number of example problems are presented and solved using various optimization techniques. The limitations of the algorithm are described and a number of problems associated with the general area of network-based systems are reviewed. In addition, several problem areas deserving additional research are discussed.