# A Survey of the Literature on Order-Picking Systems by Combining Planning Problems
## 5 Discussion
### Research and Solution Methods  
In this section, all the reviewed articles were classified according to the solving methods used in the reviewed articles. The following research methods have been proposed in the literature to analyze interactions of order-picking policies or to integrate multiple order-picking planning problems: analytical models, simulation experiments, and mathematical programming. Analytical models refer to a set of mathematical equations that approximate the performance of a system by relating the performance variable to multiple system parameters. Simulation experiments are defined as methods to imitate the system's operations or characteristics with the purpose of conducting numerical experiments to provide insights into the behavior of the system. Mathematical programming models refer to the set of mathematical expressions that describe the problem consisting of an objective function and constraints to define the overall structure of the problem. Figure 10 shows the distribution of these research methods in the scientific literature.  
According to Figure 10, it can be seen that the mathematical programming method has been the most commonly used solution in the research works. The use of simulation and analytical models as a research method to integrate different order-picking planning problems are limited. Thirteen studies used the simulation method, and 11 studies used analytical models. Table 10 shows the frequency of the solution methods used in the articles.  
According to Table 10, it can be seen that most of the research works (51 articles) focused on mathematical programming methods. In addition, the Variable Neighborhood Search Algorithm and Genetic Algorithm are by far the most popular method to analyze combinations of order-picking planning problems.  
Figure 10: Solving methods used in Studies.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Auditors** & **Assignment** & **Routing** & **Batching** & **Sequencing Tardiness** & **Others** \\ \hline [PERSON] et al. [46] & ✓ & ✓ & ✓ & ✓ & \\ [PERSON] et al. [12] & ✓ & ✓ & ✓ & ✓ & \\ [PERSON] et al. [5], [PERSON] [37], [PERSON] \& [PERSON] [23] & & ✓ & & \\ [PERSON] \& [PERSON] [82] & & ✓ & & \\ \hline \hline \end{tabular}
\end{table}
Table 9: Overview of the reviewed articles on Minimization of Makespan.  
In this review article, papers on OPS published from 2010 to 2021 with scientific degrees shown in Figure 4 were comprehensively studied. First, the articles, according to Table 2, examined the warehouses mentioned in the papers, and then it was found that that parallel aisles, with 14 cases, were the most studied warehouses. Next, the picking order problems were investigated (Figure 7 and Table 3). Then, the combinations of order-picking problems were surveyed (Table 4). Afterward, the objectives of the articles were addressed, and the reviewed articles were classified in terms of minimizing tardiness (Table 5). Moreover, articles on cost minimization were addressed (Table 6). Later, studies on maximum productivity and storage space improvement were addressed (Tables 7 and 8, respectively). Finally, the objectives of articles on minimizing makespan were provided (Table 9) and the research methods used in the reviewed papers were presented in Table 10.