Ε-Constraint Procedures for Pareto Front Optimization of Large Size Discrete Time/Cost Trade-Off Problem

Abstract

The discrete time/cost trade-off problem (DTCTP) optimizes the project duration and/or cost while considering the trade-off between activity durations and their direct costs. The complete and non-dominated time-cost profile over the set of feasible project durations is achieved within the framework of Pareto front problem. Despite the importance of Pareto front optimization in project and portfolio management, exact procedures have achieved very limited success in solving the problem for large size instances. This study develops exact procedures based on combinations of mixed-integer linear programming (MILP), epsilon-constraint method, network and problem reduction techniques, and present new bounding strategies to solve the Pareto problem for large size instances. This study also provides new large size benchmark problem instances aiming to represent the size of real-life projects for the DTCTP. The new instances, therefore, are generated to include up to 990 activities and nine execution modes. Computational experiments reveal that the procedures presented herein can remarkably outperform the state-of-the-art exact methods. The new exact procedures enabled obtaining the optimal Pareto front for instances with serial networks that include more than 200 activities for the first time.