Minimum Cut in the Project Network to Solve Time Cost Trade - Off Problem Using Renewable and Non Renewable Resources

The time cost trade off problem is one of the most important aspects of construction of project planning, scheduling and controlling. There are trade-offs between time and cost to complete the activities of a project. In general, the less expensive the resources used, the longer it takes to complete an activity. Using critical path method the overall project cost can be reduced by using less expensive resource for non-critical activities without impacting the project duration. Here a new solution procedure is introduced to solve the trade off problems by using minimum cut or maximal flow concept. We find the minimum cuts for a acyclic graph which represents the critical path of the project by using the Kargers fast algorithm of randomized minimum cut. The minimum cuts so obtained are used to trace the project activities which are to be reduced, in order to reduce the total project duration. The concept of renewable and non-renewable resources are used to minimize the project duration. The applicability of the proposed solution procedure is illustrated by an example.