# Integrating Simulation-Based Optimization for Lean Logistics: A Case Study
## 1 Introduction  
Besides high product quality, total cost and response time seem to be the key success factors to be optimized in Logistics Process (LP) in order to be more competitive in the global markets [1]. Therefore, in today environment the organizations cannot afford to keep the LP within traditional frameworks, which consider a high Finished Good (FG) inventory level and slow response times [2]. Consequently, organizations should consider and incorporate strategies to improve organizational performance by reducing costs and achieving excellence in the LP [3]. Lean manufacturing tools and techniques used to reduce waste in the processes, such as just-in-time and inventory management [4]. Logistics cost has an important role in the organizations, being that worldwide cost of LP represents between 9% and 20% of Gross Domestic Product; the variation depends on the region where the process is carried out [5]. As shown by research conducted by [6], the average cost to carry out LP in Latin America is 18.6% of the total cost of sales. However, some Latin America countries are above average, as is the case of Mexico, where the average cost constitutes a 21%. Therefore, it can be concluded that there is a great opportunity to optimize LP in the Mexican enterprises, because on average, almost a quarter of the selling price to the consumer is used in this activity [6]. The inventory management and transportation are two of the main logistical costs in the electronics industry [7]. In logistics, optimization is used for different purposes, such as minimizing Total Logistics Cost (TLC). For the case study presented in this paper, which was implemented in the electronic industrial cluster, the purpose is to improve TLC. In the other hand, constraints to achieve this objective are: Inventory Carrying Cost (ICC), which is related to the storage and maintenance of the inventory during a certain period of time; Response Time Cost (RTC), this is associated with the fulfillment of the committed customer service response time in order to avoid penalties; and Lost Sales Cost, it is a profit or income foregone due to customer orders could not be fulfilled (LSC), [1]. Therefore, Minimizing TLC is a balance achieved among the ICC, RTC and LSC, where define optimal inventory level is key in order to achieve this activity, TLC is represented by the mathematical Equation (1). \[\text{Min TLC}=\text{ICC}+\text{RTC}+\text{LSC} \tag{1}\]  
Optimization of TLC can be achieved with the application of analytical models and simulation. However, LP is categorized as a complex system and it is difficult to study it via analytical models. On the other hand, simulation is considered a powerful tool for comparing alternatives for decision-making; and due to the stochastic nature of this technique, an efficient comparison needs to consider the application of statistical techniques for a better analysis [8]. Those concepts are presented in a friendly manner in this study with the application of commercial software to design the simulation model that represents virtually the real life of LP and to run the statistical analysis with the RSM technique. The present case study, considers LP is performed under traditional framework; where, the majority of FG inventory is concentrated in a Distribution Center (DC) in Mexico City, which is 1750 miles from the manufacturing plant, in order to supply product to wholesale customers located in different cities of Mexico. Therefore, this study aims to test the following hypothesis: \"stochastics tools can be used to define strategies that help to improve TLC without affecting customer service.\"  
Logistics and the TV Manufacturing Industry in the Northern Border of Mexico  
Despite the logistics hurdles, the Mexican TV manufacturing role has been in constant evolution since the first Asian-owned factories began operations. About 1.7 million TV sets for the U.S. market were produced in Mexico in 1987 [9]. By 1998, the output was 19.1 million, about 25.