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ABSTRACT: Many everyday tasks in Operations Research involve solving complicated optimisation problems. These can range from combinatorial optimisation problems (COPs) such as the Travelling Salesman Problem (TSP), the Quadratic Assignment Problem (QAP) and the Max-Cut problem, to "noisy" estimation problems such as the Bu er Allocation Problem (BAP), in which the objective function is unknown and needs to be estimated, e.g., by using discrete event simulation. The purpose of this tutorial is to show that the Cross-Entropy (CE) Method provides a simple, efficient, and general method for solving such problems. Moreover, we wish to show that the CE method is also valuable for rare eventsimulation, where very small probabilities need to be accurately estimated - for example in reliability analysis, or performance analysis of telecommunication systems. This tutorial is intended for a broad audience of Operations Research specialists, Computer Scientists, Mathematicians, Statisticians, an...