Application of non-deterministic uncertainty models to improve resource constraint optimal scheduling

Scheduling under non-deterministic uncertainty is a highly complicated problem. It is commonly known and observed that these type of projects can be late and over budget. It has been pointed out that the main reason is that the uncertainty is not, realistically, taken into account in any form of scheduling methods. We propose a modification of the common method for automated optimal scheduling under non-deterministic uncertainty by use of a realistic non-deterministic uncertainty model and by taking this explicitly into account in the optimization. Furthermore, as the non-deterministic nature of the uncertainty results in the need for frequent rescheduling in the future, it is proposed to take this into account explicitly as well. Incorporating more realistic uncertainty models into the decision making process enables (i) a more realistic projection of the project objectives, and (ii) the possibility to make decisions while realistically balancing risks and rewards. Numerical simulations compare the classic method based on stochastic uncertainty, the proposed method with interval uncertainty, and the proposed method with p-box uncertainty, for an industrial reference case and a dataset obtained from a manufacturing plant in Flanders. The results illustrate the improved performance and relevance of the proposed method. This paper uses state of art branch and bound optimization algorithms and adapts those where necessary to incorporate non-deterministic descriptions.