An ε-constraint method with adaptive mode elimination scheme for multi-objective mixed integer programming

Abstract

The significance of time-cost trade-off is well recognized for over five decades ever since the development of the critical path method. This trade-off originates from the fact that faster accomplishment of project activities, and thereby the project as a whole, is possible should there be more productive resources assigned. Increasing productivity, on the other hand, typically comes at a cost but possibly helps avoid incurrence of additional overhead and/or penalty expenses. The precise determination of the balance between the planned productivity and the aforesaid costs often poses a tough decision to make by the management. The process of finding the proper combination of execution modes gets particularly complex and computationally expensive for real-scale projects. Accordingly, to help set the proper balance between the time and cost of large projects, an ε-constraint method is presented in this study featuring a clever adaptive mode elimination scheme. The proposed approach involves the iterative optimal solution of the trade-off problem over the feasible project durations. For each project realization, the complexity of the optimization problem is first reduced with the aid of the adaptive mode elimination by discarding the redundant execution mode(s). This study uses mixed integer linear programming for formulation and development of the proposed model and uses a project example borrowed from the literature to experiment its usefulness.