Resource leveling of linear schedules with singularity functions

This paper builds on a new methodology of modeling linear schedules with singularity functions. These unique functions have been used successfully for criticality and float analyses. The approach is extended to deriving one flexible equation for the complete resource profile of a schedule, including any changes in the resource rates of activities. A subsequent equation describes the first moment of area of the resource profile. Minimizing the moment is the objective function for leveling the resource profile. A genetic algorithm with inverse ranking is computerized to perform successive iterations. Chromosomes contain different permutations resource rates at which the activities can be performed. Probabilistic reproduction, crossover, and mutation steps mimic a biological selection process. Step-by-step descriptions of the calculations and a detailed example of a construction project illustrate how singularity functions can provide a powerful model that integrates the linear schedule with its resource profile and facilitates the overall optimization process.