ABSTRACT
Monte Carlo simulation is a very general tool (Bratley and Fox, 1987)(Fishman, 1996), with applications in various fields including statistics, finance, and engineering. In brief, a Monte Carlo study uses random sampling to approximate a mathematical expression. In logistics, it is mainly used to analyze stochastic simulation models using computers. To be more specific, let us narrow the scope of this presentation to the problem of evaluating the expectation E(X) of a real random variable X in a stochastic model. If X takes its values in a given domain Dx R , we have
For example, such an expectation could denote the average time required to manufacture an object on a production line, the probability for a firm to run out of stock of a given product, or the average number of deliveries a haulage company performs every day. Unfortunately, in most applications, we cannot compute the above expression because the domain is too large or complicated (in the discrete case) or because integration is analytically intractable (in the continuous case). Moreover, for most problems, distribution px or density fx is not explicitly available. Usually, variable X is implicitly given as a result of the interaction of numerous stochastic sub-processes of the model. Furthermore, the rules modeling these interactions usually include resolution of an optimization sub-problem or application of a heuristic strategy we intend to test or calibrate.
