On modelling payments in projects
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On modelling payments in projects N Dayanand1 and R Padman2 1
Thinking Machines Corporation, Bedford, MA and 2 Carnegie Mellon University, USA
Projects are often evaluated on ®nancial performance. The net present value (NPV) has long been established as a highly relevant criterion in the management and control of projects. Research in this area has emphasised scheduling of activities in projects to maximise the contractor's NPV assuming that cash ¯ows (both positive and negative) that occur over the duration of the project are known. In practice, however, the contractor usually knows the expenses associated with project activities. He can use this information combined with the knowledge of other project parameters such as activity durations to negotiate the payments received for completed work so that the project achieves the maximum level of ®nancial returns. Extending previous research, this paper examines the problem of simultaneously determining the amount, location and timing of progress payments. We present several models and their solutions for an example problem. Based on the assumptions made, the models are applicable in different project environments. The problem and models presented here can be used by the contractor and client for managing cash ¯ows, setting milestones, and negotiating critical contract parameters, in addition to identifying the location, timing, and amount of progress payments. They also contribute to the body of research on formulating and solving dif®cult combinatorial optimisation problems. Keywords: cash ¯ow modelling; project management; scheduling
Introduction Financial planning is a vital component of project management since it determines the pro®tability of projects. In order to survive in a competitive environment, project contractors must negotiate payment terms that maximise cash ¯ow. Research in project management has long recognised the net present value (NPV) criterion as highly relevant in the management and control of projects.1 The NPV can be evaluated by considering the amount and timing of cash ¯ows that occur over the duration of the project. Negative cash ¯ows represent expenses and positive cash ¯ows represent progress payments for completed work. Project schedules are signi®cantly affected by these cash ¯ows, which in turn, affect the NPV of the project. Several models have been proposed for projects with ®xed cash ¯ows. In his pioneering work, Russell2 presented a model and an iterative algorithm for solving the problem. In the Russell model, cash ¯ows occurring over the duration of the project are discounted continuously to the start of the project and his work showed that the NPV objective results in an optimal schedule that is quite different from the time critical path. Grinold3 added a project deadline to the model and used a transformation of variables to show that the project scheduling problem with NPV objective is, in fact, a linear program with the structure of a weigh
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