Optimal project deadlines for mean-variance incentive contract designs

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This paper studies contracts that incorporate incentives in the form of bonuses and penalties on top of the contract’s fixed payment and investigates their impact on the project completion time. Its aim is to derive an optimal deadline that maximizes the mean-variance utility function for a risk-averse contractor. By maximizing his payoff utility function, the contractor becomes more motivated to bid for the project, as well as to meet its deadline. It is shown in this paper that under appropriate risk-aversion levels for the contractor, and when the bonus rate in the contract is bigger than that of the penalty, then an optimal deadline that maximizes the risk-averse mean-variance utility function of the contractor exists and is less than the expected mean of the project random duration. This result is in line with many empirical studies and research reports found in the literature which concluded that the bonus in the contract works better than the penalty to incite the contractor to complete the project earlier than planned. In the other case where the bonus rate is less than or equal to the penalty rate, the utility payoff function for the risk-averse contractor is shown to be strictly increasing in terms of the deadline, and therefore, there exists no limit for it. The latter fact cannot therefore work in favor to the contractor. Special cases of famous probability distributions for the project duration were also investigated and their optimal deadlines were derived either in a closed form formula or computed numerically.