An Inverse Optimal Value Approach for Synchronously Optimizing Activity Durations and Worker Assignments with a Project Ideal Cost

Abstract

Most companies survive the pain of cost and schedule overruns because of inaccurate project activity time settings. In order to deliver a project with a target cost and on schedule, this research proposes an inverse optimal value approach to optimize activity durations and the corresponding worker assignments synchronously to make the optimal project cost infinitely close to an ideal cost. The leader model reflects cost orientation and adjustability of activity durations, the follower model reflects the complexity of activity sequence, critical path completion time, cost pressure, skill matching, energy consumption, and other costs. Through upper-level and lower-level feedback and interaction of activity durations and worker assignments it is possible to deliver a project with an ideal cost. With considerations of the mathematical model characteristics of bi-level programming, nonlinearity, NP hard, and MAX functions, an improved genetic algorithm combining adaptive artificial fish swarms is designed. From the comparison results of random examples and an actual example, the error rate of the optimal value of the improved algorithm is acceptable. Numerical experiments show that the inverse optimal approach can deliver a project without delay and with an ideal cost. The inverse optimization method is more in line with the idea of target management, and can help managers achieve the purpose of cost control.