A mathematical model for fixed-price-incentive-firm contracts

Abstract

This research focuses on a mathematical model for Fixed-Price-Incentive-Firm (FPIF) type contracts. The model revolves around the concept of a balanced trade-off among different options available to the user. At one extreme, the model develops a FPIF arrangement that gives the contractor a strong incentive to underrun costs, but strict penalties if he overruns. At the other extreme, the model develops a FPIP arrangement that gives the contractor minimal incentive to underrun, yet significant protection against an overrun. The mathematics of the model uses integral calculus to balance each of the options such that both the expected profit for the contractor and the expected cost to the Government do not change as the user selects different options. In this computation, the subjective probability density function for the cost is assumed to remain constant. This process attempt to accommodate the contractor based on his composite attitude toward risk and utility, yet does not obstruct the Government's objective to minimize cost.