A flexible heuristic for a multi-mode capital constrained project scheduling problem with probabilistic cash inflows

We consider housing projects where an initial capital covers activity expenditures in the starting phase of the project and then, customers who arrive randomly over the project span provide the necessary funds for continuation. The goal is to maximize financial returns, i.e., the project Net Present Value (NPV). Here, capital is considered as a limited nonrenewable resource which is reduced by activity expenditures and augmented by the sales of flats. Activities may be carried out in different operating modes with different durations. The total cost of an activity is fixed irrespective of its operating mode. Thus, the rate of activity expenditures differs from mode to mode. As the previous scheduling decisions are the only controllable factors affecting the available capital at any period, it is important to adjust the speed of expenditures, namely, to select the correct activity modes. The contractor, never sure of the timing of the cash inflows, has to schedule the activities in modes which do not lead to financial bottlenecks and at the same time he has to deliver the project on time. The contractor may also borrow capital from an external source. We propose a flexible heuristic algorithm for solving the capital constrained mode selection problem where there exist general precedence relationships among activities and the magnitude of precedence lags depends on the specific activity mode selected. The algorithm is flexible in the sense that different mode selection criteria are utilized at different decision times depending on the cumulative progress of the project and on some parameters controlled by the contractor. The proposed algorithm may be used as a simulation tool to adjust parameters before the project starts or it may be used as a scheduler during the progress of the project given the current financial situation and cumulative project work done. We test the algorithm by using a typical housing project with real data and also by using hypothetical test problems. The results indicate that the schedules generated are satisfactory with regard to meeting the target project due date and maximizing NPV.