# Integrating Simulation-Based Optimization for Lean Logistics: A Case Study
## 2 Literature Review
### Techniques for Optimization in Logistics
The objective was to minimize the sum of the total weighted inventory cost and transport cost. They provided Fully Polynomial-Time Approximation Schemes (FPTAS) algorithm without considering the weight of the inventory cost for each for four cases of the batching and scheduling problem that considers the job. In comparison, they first introduced the weighted parameter in this weighted inventory cost. They concluded the transport cost is related to the number of batches created. [PERSON], [PERSON] and [PERSON] [25] improved a distribution plan supporting an urban distribution center (UDC) to solve the last mile problem of urban freight. They defined a mathematical model for searching the best distribution and maintenance plans using a subcontracting strategy; they considered delay for the next periods with an expensive penalty. This approach is based on a mathematical model for a distribution plan with economic and environmental criteria; this model considers also available capacities and allocation constraints for the maintenance strategy. The choice of UDC to subcontract depends on the service cost, environmental cost and on the available capacities. On that course, [PERSON] [26] proposed a standardized simulation method for intermittent production systems with the aim of improve it. He elaborated and introduced a decision support simulation method based on him practical experience. He asseverated the realization of the simulation investigational model can take less time than in earlier methods and it is possible to examine every complex intermittent production system using the elaborated investigational method. Regarding to product allocation to different types of distribution center in retail logistics networks, [PERSON] et al. [27] considered the problem of assigning stock keeping units to distribution centers (DCs) belonging to different DC types of a retail network, for example, central, regional and local DCs. The problem was solved by an MIP (Mixed Integer Programming Problem) solution approach. The application of the new approach results in cost savings of 6% of total operational costs compared to the initial assignment. An AHP-based framework for logistics operations in distributions centers was proposed by [PERSON] et al. [28]. This research presented a framework for designing operations in DCs based on a joint study of three elements: distribution strategy, internal activities and the characteristics of the distribution operations. The methodology was based on theory-building research using three case studies. The data collection was performed by three top managers at large logistics providers (LPs). The analytic hierarchy process (AHP) method was applied and the framework was validated by the LPs. This framework was then applied to a sports fashion retail operation and was reported to enable the decision-making process regarding operations at DCs, creating scenarios for evaluation. [PERSON] et al. [29] proposed two mixed integer linear programming model for two aspects of integrated production-distribution scheduling: order acceptance and batch direct delivery. The aim of this research was trading off among the revenue of accepted orders, costs of delivery and penalties for tardiness incurred in an integrated production-distribution in a supply chain to maximize the total of benefit. Additionally, since the problem was strongly NP-hard, an adaptive genetic algorithm was used to solve large-scale instances in this regard that use the adaptive search approach. For the initial population, four heuristics were developed. To explore and locate the algorithm in a better neighborhood, a local search was made use of. Taguchi experimental design was applied to set the appropriate parameters of the algorithms. Moreover, to verify the developed model and evaluate the performance of algorithm against the exact solution, a commercial solver is used. The effect of different parameters and factors of the proposed model on the profit shows that the order acceptance and the more vehicles of the company improve the profit.