Activity Modes Selection in Project Management

In this paper, we consider the activity modes selection problem in the project management, which is also called time-cost tradeoff problem. This problem is known as strongly NP-hard. We provide a lower bound on this problem by combing the dynamic programming method and the Lagrangian relaxation. Furthermore, we develop a method to obtain an upper bound by leverage the greedy algorithm. Later on, we combine the lower bound and upper bound method together to propose a feasible solution. In most of the problems generated in our experiments shows, the gap between the proposed solution and the exact solution (got by solving integer problem) is less than 1 percent