Interruptability analysis for linear scheduling with singularity functions

It is a widely held assumption in the construction industry that activities, especially those that involve labor crews, should be scheduled to perform continuously until they are completed. However, in certain scenarios, depending on the production rates of their adjacent activities, a strategic intentional interruption of activities can create opportunities to improve the schedule by reducing the total duration of the project. This paper analyzes the possibility of interrupting activities with either constant or variable production rates toward the objective of minimizing the total project duration. For activities that exhibit a constant production rate, a heuristic approach determines the feasibility of interrupting activities based on scenario analysis and application of geometry to attain the objective. For activities that exhibit a variable production rate, a mathematical model is developed, extending the geometric approach with singularity functions. A genetic algorithm (GA) is applied in the computer implementation to achieve the objective. Using singularity functions allows modeling complex activities, including all changes in production rates and work breaks, with a single functional expression, greatly reducing the number of constraints that must be implemented for optimization. A complex schedule example is presented to illustrate how the new model can be applied to intentionally interrupt activities to gain a large reduction in total project duration.