Resource-constrained project scheduling problem under uncertainty of cash flows

Investment project scheduling problem is an important problem in the field of production management. Determining the optimal start time for activity allows ensuring a higher level of project's profit. The article considers an investment project that involves the implementation of a given number of activities for a certain period of time. Each of the activities is characterized by the duration of its implementation, the cost of resources and the income that it provides. In addition, the technological and organizational relationships between the activities are known. This, in particular, can be expressed in the need to complete one activity before doing another. The sources of project financing are the organization's own funds, as well as income received when performing activities. The article considers a situation when all project resources can be presented in monetary form. The project budget is assumed to be known in advance. The planning of the budget, as well as income and expenses for the project, is carried out by years. The net present value (NPV) was used to evaluate the results of the project implementation. This indicator represents the value of the profit from all planned activities, discounted to the time the investment started. Thus, the investment project scheduling problem that we are considering is to find the optimal start time for each of the activities, at which the restrictions on the sufficiency of funds, the interconnection of activities are met and the maximum NPV is ensured. In the proposed statement of the resource-constrained project scheduling problem, the only parameters expressing the uncertainty of the conditions for the implementation of the project are the components of the payment flow. We considered a situation in which the timing of the project and individual activities, as well as the company's own funds, are not subject to fluctuations. Random project parameters were considered independent. The article presents an overview of approaches to project risk assessment for different ways of taking into account the uncertainty factor. In particular, options for scenario analysis, outcome tree construction and simulation were considered. Using the genetic algorithm developed by the authors, a series of computational experiments was carried out. The analysis was carried out for cases of discrete and continuous distribution of project parameters. Based on the results of the experiments, schedules were found that are optimal for various values of random project parameters. For each schedule, the risk of stopping the project due to lack of funds was determined. The found schedules were compared by average NPV values, as well as by risk level. Conclusions were drawn about the choice of schedule, taking into account the cost of raising borrowed funds.

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