Optimum present value scheduling based on synthetic cash flow model with singularity functions

Contractors may increase their profit by rescheduling noncritical activities within their floats. Based on this hypothesis, new theory is explored to optimize the present value of the project balance (PVbal) with singularity functions in a synthetic cash flow model. Its contribution to the body of knowledge is threefold: First, PVbal is expanded to a function of activity shifts in analogy to resource leveling. Second, it is found that intuitive front-shifting may not maximize PVbal because of a trade-off between changes in pay (inflow) and interest (outflow). Conditions for front-shifting and back-shifting and the newly discovered phenomenon of scalloping are derived by exploring monotonicity, periodicity, and concavity of the PVbal function. Monotonicity controls front-shifting or back-shifting; periodicity and concavity control if scalloping can exist, whereby shifting a fractional period gives a local optimum of PVbal. It repeats periodically until all float is exhausted. Third, combinations of financial parameters (markup, interest, retainage, and bill-to-pay delay) are examined on how they impact shift decisions to optimize cash flow.