Contractual agreements have assumed significant complexity in recent times because of the emergence of strategies like outsourcing and partnering in the successful completion of large software development, manufacturing, and construction projects. A client and contractor enter into an agreement for a project either by bidding or negotiation. Effective and efficient bidding, negotiation, and subsequent monitoring are hindered by the lack of appropriate decision support tools for the management of project finances. Progress payments to the contractor are an important issue in project management because of their potential impact on project finances and activity schedules. In this paper, we consider the problem of simultaneously determining the amount, location, and timing of progress payments in projects from a client's perspective. We develop three mixed-integer linear programming models, based on some practical methods of determining payment schedules from different types of project contracts. We discuss properties of the models and draw insights about the characteristics of optimal payment schedules obtained with each model by an experimental study on a sample of 10 small projects. Our analysis shows that, contrary to current practice, the client obtains the greatest benefit by scheduling the project for early completion such that the payments are not made at regular intervals. It is also cost effective for the client to make payments either in the early stages of the project or toward the end, even though this causes considerable variation in the time gap between payments. We also evaluate the impact of the client's preferred payment schedules on the contractor's finances and activity schedules, and draw some conclusions on the interdependence of payment and project parameters on the objectives of both parties entering the contractual agreement.
