The LP/IP hybrid method for construction time-cost trade-off analysis

Construction planners face the decisions of selecting appropriate resources) including crew sizes, equipment, methods and technologies, to perform the tasks of a construction project. In general, there is a trade-off between time and cost to complete a task - the less expensive the resources, the longer it takes. Using Critical Path Method (CPM) techniques, the overall project cost can be reduced by using less expensive resources for non-critical activities without impacting the duration. Furthermore, planners need to adjust the resource selections to shorten or lengthen the project duration. Finding the optimal decisions is difficult and time-consuming considering the numbers of permutations involved. For example, a CPM network with only eight activities, each with two options, will have 2⁸ alternatives. For large problems, exhaustive enumeration is not economically feasible even with very fast computers. This paper presents a new algorithm using linear and integer programming to obtain optimal resource selections efficiently that optimize time/cost of a construction project.