Integrating efficient resource optimization and linear schedule analysis with singularity functions

Resources perform or enable physical operations and thus are vital on construction projects, yet are subject to various constraints. Their use within a project schedule must therefore be carefully planned. A major objective is optimizing when they are active within the float of noncritical activities to avoid disruptive and costly fluctuations. This paper builds on analyzing criticality of linear schedules with the unique singularity functions. The new approach keeps resources intact and derives one flexible equation for the complete resource profile of a schedule, including any timing or resource rate changes. Another equation models its first moment of area to minimize the objective function toward a level profile. A genetic algorithm is suitable for an iterative optimization. The parameters of its chromosomes are recombined evolutionarily and can model any permutation. Analyzing a road project illustrates how singularity functions integrate resource optimization with its linear schedule and facilitate a subsequent optimization.