#### 2019 CSCE Annual Conference - Laval (Greater Montreal) Conference

Mr. Kareem Mostafa, University of Waterloo (Presenter)

Almost all infrastructure projects are repetitive in nature and require repetition of a set of identical or non-identical tasks along a number of units (e.g., sections of a linear highway, floors or a vertical high-rise, etc. ). Scheduling of these repetitive projects uses the project deadline to determine the tasks’ delivery rates and the necessary number of crews to achieve these rates. Efficient scheduling requires the crews to move from one unit to the other uninterrupted to minimize idle time and to maximize learning curve effects. While an ideal schedule would have all tasks following the same delivery rate, any rounding or use of pre-set crew limit disturbs the synchronized delivery rates and produces a schedule with intermittent delays. For example, in the case the successor task is faster than its predecessor, the successor task is given a later start date to maintain its work continuity, thus delaying the start of all the following tasks and possibly extending the project duration. In this case, researchers often introduce a designed task interruption to improve the synchronization of tasks’ delivery speeds, and help reduce project duration. Hence, optimal repetitive scheduling needs to strike the right balance between maintaining crew-work continuity to achieve cost savings (e.g., learning curve effect) and introducing task interruptions to achieve shorter project duration. Such a compromise motivated many researchers to consider work interruption as a variable in the larger scheme of schedule optimization, as opposed to having work continuity as a hard constraint. Because schedule optimization problems already have a high number of variables (e.g., construction options, number of crews, etc.), they are classified as NP-hard problems where the increase in variables produces an exponential increase in the number of possible solutions. Conversely, reducing the number of variables would substantially decrease problem size and increase the possibility of finding near optimum solutions to problems. This paper, therefore, aims to developing and testing a general mathematical formulation to compute the optimal work interruptions scheme (in magnitude and frequency) without incorporating them as variables in schedule optimization. The paper starts with a literature review of existing studies on interruption time for repetitive projects, followed by a generic mathematical formulation of interruption time, given the tasks’ delivery speeds and permissible number of interruptions. Experimentation with a spreadsheet program is then presented to demonstrate the use of the proposed formulation and its benefits in facilitating schedule optimization for variety of project sizes.