# Integrating Simulation-Based Optimization for Lean Logistics: A Case Study
## 2 Literature Review
### The Selected Approach  
In today's manufacturing environment, there is a wide range of methods, techniques and tools for optimization purposes as seen in Section 2.1; but although these have become universal application in many areas [30]. However, those have been few applied for optimization purposes in logistics processes [31]. It has been identified with the literature review that simulation in combination with other methods is a very powerful method for optimization purposes; by this reason, simulation and response surface methodology were considered to be applied for this research. According to [PERSON] [26], the improvement of complex production systems can be realized efficiently only through simulation modeling. Simulation refers to a broad collection of methods and applications to mimic the behavior of real systems, where a system is defined as a facility or process, either actual or planned. This method has been effectively applied by several researchers for process optimization [32]. Other studies utilized a process simulator developed in MATLAB for optimization of Generalized Predictive Control (GPC) tuning parameters [33]. [PERSON] and [PERSON] were able to specify the optimal number and location of distribution centers to determine the allocation of customer demand to DC with a model based on Monte Carlo Simulation [34]. [PERSON] use a discrete event simulation model to evaluate order picking performance in a warehouse operation and propose a new picking design process to improve performance [35]. The aim of development in the long term-not achievable in many cases-is the realization of unique production, with mass production's productivity and lower cost. The improvement of complex production systems can be realized efficiently only through simulation modeling. A standardized simulation method for intermittent production systems has not been elaborated so far. In this paper, I introduce a simulation method for system improvement and present its application possibilities and a practical example. [PERSON] and [PERSON] state that RSM is a method that can interact with simulation models for optimization purposes [36]. RSM can be defined as an experimental and modeling strategy to find the optimal operation conditions of a process [37]; the first-degree model (Equation (2)) and the second-degree model (Equation (3)) are commonly used in RSM [38]. \[Y=\beta o+\sum_{i=1}^{k}\beta i\;Xi+\epsilon \tag{2}\]  
where:  
\(Y=\) Predicted or expected value of the dependent variable  
\(Xi=\) Independent or predictor variables  
\(\beta o=\) Value of \(Y\) when all of the independent variables \((Xi)\) are equal to zero  
\(\beta i=\) Estimated regression coefficient \(i=\ 1\) to k independent variables in the model  
\(\epsilon=\) Random error variable  
\[Y=\ \beta o+\sum_{i=1}^{k}\beta i\ Xi+\sum_{i=1}^{k-1}\sum_{j=2\ \ i<j}^{K}\ \beta ij\ XiXj+\sum_{i=1}^{k}\beta iXi^{2}+\epsilon \tag{3}\]  
where:  
\(Y=\) Predicted or expected value of the dependent variable  
\(Xi,\)\(Xj=\) Independent or predictor variables  
\(\beta o=\) Value of \(Y\) when all of the independent variables \((Xi)\) are equal to zero  
\(\beta i=\) Estimated regression coefficient for first order \(Xi\) variable  
\(\beta ij=\) Estimated regression coefficient for interaction first order \(Xi\)_and_\(Xj\) variable  
\(\beta ii=\) Estimated regression coefficient for second order \(Xi\)_and_\(Xj\) variable  
\(i=1\) to k independent variables in the model  
\(j=2\) to k independent variables in the model  
\(\epsilon=\) Random error variable  
RSM uses different techniques for optimization purposes, such as the contour plots, which allows to visually identify an area of compromise among the response variables. In Figure 1, it shows as an example for this technique a simultaneous optimization; the green region in the plot is the feasible region that satisfies the criteria for Strength value between 24 and 28 and VarStrength value between 0 and 1.