Interruptability analysis for linear scheduling with singularity functions

It is a widely held assumption in the construction industry that activities, especially those involving labor crews, should be scheduled to be performed continuously until they are completed. In certain scenarios, however, depending on the production rates of the adjacent activities, a strategic intentional interruption of an activity can create opportunities to improve the overall schedule by reducing the overall duration of the project. This paper analyzes the possibility of intentionally interrupting activities with either constant or variable production rates, in order to minimize the project duration; the objective. For activities exhibiting a constant production rate, a heuristic approach which allows for the feasibility of interrupting activities to be determined based on scenario analysis, and thru application of geometry, attainment of the objective. For activities exhibiting a variable production rate, a mathematical model employing singularity functions is developed, extending the previous geometrical approach and allowing for computer implementation. Genetic algorithms (GA) are applied in order to achieve the objective. The use of singularity functions allows for complex activities to be modeled, including all changes in production rates and work breaks, with a sole functional expression, greatly reducing the number of constraints that need to be implemented in the optimization model. A complex case example is presented, illustrating how the model can be applied to intentionally interrupt activities allowing for a large reduction in overall project duration.