The use of integer linear programming for modelling project control information

The time and cost parameters are considered to he of paramount importance in the management of construction projects. This paper is concerned with the problem of optimizing the relationship between time and cost thus determining the minimum project and activity costs associated with each feasible duration of a multiactivity project. The problem is considered in two parts. The first part explores methods of finding minimum project cost associated with given project duration, when the time-cost relationship for each activity is only assumed to be continuous and totally defined in the feasible interval but not necessarily linear. A mathematical solution is explored relating earlier work of Meyer and Shaffer (1965), based on integer linear programming, to the analysis of precedence networks. In the second part the methods of integer linear programming are also used to consider the more general problem of finding minimum cost for a project when, for some of the activities, the time-cost relationship may only be partially defined.