Chapter 3
Sensitivity Analysis in Discrete-Event Simulation Using Design of Experiments
José Arnaldo Barra Montevechi, Rafael de Carvalho Miranda and Jonathan Daniel Friend
Additional information is available at the end of the chapter http://dx.doi.org/10.5772/50196
1. Introduction
The use of discrete-event simulation as an aid in decision-making has grown over recent decades [1, 2, 3, 4]. It is already used as one of the most utilized research techniques for many sectors due to its versatility, flexibility and analysis potential [5, 6]. However, one of simulation’s greatest disadvantages is that, on its own, it does not serve as an optimization technique [7]. This forces simulation practitioners to simulate multiple system configurations and choose the one which presents the best system performance. Computational development has helped alter this scenario due to the increasing availability of faster computers and ever improving search and heuristic optimization techniques. Simulation optimization can be defined as the process of testing different combinations of values for controllable values, aiming to find the combination of values which offers the most desirable output result for simulation models [8].
In support of this claim, [1, 9, 10, 11] assert that using optimization along with simulation has been continuously increasing due to the emergence of simulation packages which possess integrated optimization routines. The overarching idea of including these routines is to search for improved definitions for the system parameters in relation to its performance. However, according to [10], at the end of optimization, the user has no way of knowing if an optimal point was truly reached. Despite the fact that simulation has been around for more than half a century, until quite recently, the scientific community was reluctant to use optimization tools in simulation. The first time the subject emerged in two renowned simulation books, [12] and [13], was at the close of the 20th century [9]. This resistance has begun to diminish with the convent of meta- heuristic research, along with strides being made in statistic analysis [14].
© 2012 Montevechi et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
64 Discrete Event Simulations – Development and Applications
According to [15], verification of system performance for a determined set of system parameters with reasonable precision using simulation, demands a considerable amount of computational potential. In order to find the optimal or near-optimal solution, one needs to verify a large number of parameter values, thus, optimization via simulation is normally exhaustive from a computational standpoint.
Having highlighted the computational strains, [8] states that despite the evolution of optimization software, a common criticism made about such commercial packages is that, when more than one variable is manipulated at a time, the software becomes very slow.
Considering that not all decision variables are of equal importance in respect to the response variable that one desires to optimize [16, 17], a sensitivity analysis may be carried out on the simulation model in order to select the variables which will compose the optimization search space in order to limit the number of variables and, in turn, make the search faster.
Thus, in order to proceed to the variable selection, screening can be done in order to separate the most important variables from those which may be eliminated from consideration [16, 17]. The same author presents some examples of experimental design utilized in screening experiments:
2n factorial design; 2n-p fractional factorial design; Supersaturated designs; Groups screening designs.
The current chapter presents an application of Design of Experiments (DOE), specifically fractional factorial design, in order to select the significant input variables in a simulation model, and thus accelerate the optimization process. For information about experimental design, the reader can consult [1, 4, 18, 19]. Fractional factorial design is a DOE technique in which only a fraction of the total number of experiments is executed, thus realizing fewer experiments than full factorial design. Throughout this chapter, it is shown that the use of such a design serves to reduce the search space in the optimization phase of simulation studies. In this chapter, real examples of how to conduct sensitivity analysis with factorial design are given. In order to reach this goal, two study objects are presented, comparing the optimization carried out without previous investigation of input variable significance, with the optimization carried out in reduced search space. Finally, a comparison is made of the results of the optimization, with and without the sensitivity analysis.
2. Simulation optimization
A simulation model generally includes n input variables (x1, x2,...,xn) and m output variables (y1, y2, ..., ym) (Figure 1). The optimization of this simulation method implies finding the optimal configuration of input variables; that is, the values of x1, x2, …, xn which optimize the response variable(s) [20].
Sensitivity Analysis in Discrete-Event Simulation Using Design of Experiments 65
Input Output
x1 y1 x2 Simulation y2 ... Model ... xn ym
Figure 1. Simulation Model [20]
Optimization helps respond to the following questions: What are the optimal adjustments to the input variables (x) which maximize (or minimize) a given simulation model output? The objective is to find an optimal value which maximizes or minimizes a determined performance indicator [11].
According to [21], simulation optimization is one of the most important technologies to come about in recent years. These authors recall that previous methodologies demanded carrying out complex changes to the simulation model, thus consuming time and computational potential and, in many cases, not even being economically viable for real cases due to the large number of decision variables.
A traditional simulation optimization problem (minimization of a single objective) is given in Eq. 1 [22]:
min (1)