Capital- and resource-constrained project scheduling with net present value optimization

In this paper, we study the capital-constrained project scheduling problem with discounted cash flows (CCPSPDC) and the capital- and resource-constrained project scheduling problem with discounted cash flows (CRCPSPDC). The objective of both problems is to maximize the project net present value (NPV), based on three cash flow models. Both problems include capital constraints, which force the project to always have a positive cash balance. Hence, it is crucial to schedule activities in such an order that sufficient capital is available.The contribution of this paper is threefold. First, we propose three distinct cash flow models, which affect the capital availability during the project. Second, we introduce two new schedulers to improve capital feasibility, one for the CCPSPDC and one for the CRCPSPDC. The schedulers focus on delaying sets of activities, which cause cash outflows to be received at later time instances, in order to reduce capital shortages. Both schedulers are implemented as part of three metaheuristics from literature, in order to compare the metaheuristics' performance. Two penalty functions have been included, one to improve capital feasibility and another to improve deadline feasibility. Third, the proposed procedure has been tested on a large dataset and the added value of the schedulers has been validated. Managerial insights are provided with respect to the impact of key parameters