A New Multi-objective Model for Multi-mode Project Planning with Risk

The purpose of this problem is to choose a set of project activities for crashing, in a way that the expected project time, cost and risk are minimized and the expected quality is maximized. In this problem, each project activity can be performed with a specific executive mode. Each executive mode is characterized with four measures, namely the expected time, cost, quality and risk. In this paper, linear relationships between time and cost, and between time and quality are omitted and the problem of the expected time-cost-quality tradeoff is considered in a probabilistic and discrete state. Then, to make the problem more real, the combination of four measures are considered as uncertain for each executive mode. It means that time, cost, quality or risk (or all of them) of each activity in each executive mode is considered as the expected numbers (probabilistic means). After modeling three objective problems, a test problem with nine activities is presented and solved by the NSGA-II algorithm. In order to improve the results and speed of the proposed algorithm in accessing Pareto solutions, a new hybrid algorithm, called MEM-NSGA, is presented that gives better solutions than the NSGA-II algorithm in the same conditions.