The impact of contractor behavior on the client's payment-scheduling problem

Recent approaches to modeling the client's payment-scheduling problem allow the client to control both the timing of payments and the completion times of activities. In practice, the activity schedule is typically determined by the contractor rather than the client. This paper addresses this drawback by considering a model in which the client selects the payment activities and the contractor selects the activity schedule, each to maximize his own net present value (NPV). In addition, the contractor has the option to reject the project if it does not provide a minimum NPV. The new model is shown to be NP-hard in the strong sense and a branch-and-bound procedure is provided for its solution. Results are obtained for the new model that contradict those of the older models. The benefits to the client are no longer increasing with retention and no longer decreasing with the number of payments. Furthermore, it is no longer ideal for the client to focus payments at the beginning and end of the project. Empirical evidence based on a randomly generated data set suggests that the market for the contractor's services, the timing of benefits received by the client, and the project duration drive these new results.