Abstract: Except for labor, equipment, materials resources, space is an important resource for construction activity execution. Space resource required by construction activity means the occupation of two-dimensional or three-dimensional space in construction site during the execution of construction activity. Since the construction site is often fixed and space is limited, space interferences among activities often happen in construction practice, which would reduce productivity, lead to construction delay and cost overrun. Therefore, more and more researchers in construction management field have paid great attention on space interference. When scheduling a construction project, construction project manager should try to prevent or mitigate space interference among activities, which is of great significance to construction practices.
Previous studies have indicated that space interference can decrease resource productivity which leads to a longer actual duration than expected. Therefore, the influence of space interference on productivity is taken into account in this paper. The construction scheduling problem with variable duration under the influence of space interference is studied. The problem is to optimize two goals simultaneously:project makespan and total cost. To be more specific, the degree of space interference is measured and the productivity function of space interference is proposed. Then, a bi-objective programming model is established. The solution of the model conclude two parts:1) the execution time of each activity; 2) mode selection for each activity. In terms of execution time, the model should determine not only the start time but also the actual duration for each activity, since the actual duration is variable in this problem. In order to solve the problem efficiently, the NSGA-II is adopted where a specific encoding method based on relative delay time and the corresponding decoding mechanism are designed. Finally, the model and the algorithm are verified by analyzing a construction project case. By comparing with the traditional scheduling method, the experimental results show that NSGA-II can reduce the space interference more effectively and improve both two objectives. For the construction case used here, the Pareto solutions saves 3.09% on project makespan and 1.01% on total cost when mode selection being fixed. Comparison experiments are also conducted to explore the influence of critical parameter——maximal relative delay time on the performance of NSGA-II. The experimental results indicate that when the maximal relative delay time be set as 40, the NSGA-II has the best performance on solving the case.
This research has a certain practical guidance for construction management in reality. It can provide a scientific and reasonable decision support for project managers. It also enriches the theoretical study in the field of construction management and resource-constrained project scheduling problem.

Key words: construction scheduling, workspace interference, productivity, time-cost optimization, NSGA-II