The effect of risk aversion on the optimal project resource rate

Under resourcing a project increases the probability of a time overrun. Consequently, project contracts should be designed to encourage an appropriate allocation of resources to the project. A common way to encourage timely completion is to use contracts with time penalties and incentives linked to the completion time. If there are a number of competing contractors, then the project manager can employ a take it or leave it approach in designing the contract. However, where there are very few possible contractors, then a bargaining approach is more appropriate for the contract's construction. Therefore, this paper investigates how close the resource rate stemming from the Nash bargaining contract is to the optimal rate. Risk neutral and risk averse project managers and contractors are considered. It is found that when the contractor is risk neutral, the chosen resource rate is independent of the project completion time distribution no matter whether the project manager is risk neutral or risk averse, and it coincides with the optimal, i.e. centrally coordinated, rate. When the contractor is risk averse, the resource rate is dependent on the project completion time distribution. However, the results indicate that if the contractor is less risk averse than the project manager, then the resource rate is approximately the optimal one. Hence a time based contract designed using Nash bargaining is particularly suitable when the number of possible contractors is small and they are large enough with regard to the project size to be less risk averse than the project manager.