Elimination Properties for a Probabilistic Scheduling Problem

Abstract

In many areas of the economy, we deal with random processes, e.g., transport, agriculture, trade, construction, etc. Effective management of such processes often leads to optimization models with random parameters. Solving these problems is already very difficult in deterministic cases, because they usually belong to the NP-hard class. In addition the inclusion of the uncertainty parameters in the model causes additional complications. Hence these problems are much less frequently studied. We propose a new customized approach to searching the solutions space for problems with random parameters. We prove new, strong properties of solutions, the so-called block elimination properties, accelerating the neighborhood search. They make it possible to eliminate certain subsets of the solution space containing worse solutions without the need to calculate the value of the criterion function. Blocks can be used in the construction of exact and approximate algorithms, e.g., metaheuristics such as tabu search, significantly improving their efficiency.