Production equations for unsteady-state construction processes

The production equation called Little's law has been applied to construction data recently. However, Little's law was derived for steady-state conditions assuming constant input and output rates and long production runs. Production in construction is inherently temporary, and learning curves and environmental influences often render input and output rates unequal and nonlinear. Starting with a conservation of mass formulation, general equations for work-in-process and cycle time for unsteady-state conditions and limited run production are developed. The motivation behind these equations is to explain common trends in production variables seen on construction projects. Previous studies have shown that when output from a construction production system is drastically increased, a significant upward impact is also seen on cycle time and work-in-process, and this work provides underlying theory and equations to explain these trends. Cycle time and work-in-process equations are presented as functions of time and on average. Data from construction activities are used to show that unsteady-state conditions commonly occur. Reasonable simplifications of the general equations provide guidelines for buffer sizing and resource allocation decisions.