Cost-Time Trade off for Projects with Nonlinear Cost Functions

Project planning, scheduling and control are activities that are frequently encountered by managers and engineers. Project time cost trade-off is an essential activity for every project in order to assess the impact of project crashing. It is extremely important to assess cost trade-off for large projects such electric power generation, mass transportation oil facilities or sophisticated weapons systems. Algorithms for finding project durations versus direct cost are useful in providing managers and decision makers with valuable information for decision making. This paper presents a new algorithm that provides an optimal solution to the problem of crashing projects with activity duration having nonlinear cost functions. The algorithm is based on a reduced enumeration scheme. It attempts to reduce the search for the optimal solution. The objective is to find the minimum cost of a project having a nonlinear cost function for specified project duration. As a result, the optimum duration for all activities is determined. Different specified project durations would result in different project costs. Hence, the trade off between project cost and duration is established. A set of theorems that characterize and illustrate the properties of the algorithm have been stated and proven. The significance of the algorithm and the theories is to provide some insight to this difficult problem of time cost trade-off in project scheduling to elicit further research. Additionally, the user of the algorithm needs not to be familiar with scientific tools such as Linear Programming (LP). An example is solved using LP and the developed algorithm. The usefulness of this work is to enable managers obtain optimal solutions for such problems without resorting to sophisticated techniques that do not even provide exact solutions due to the common practice of approximating nonlinear cost functions by linear functions.

Keywords:

Project Scheduling , Nonlinear Cost , Critical Path , Linear Programming