In this case, each warehouse is modeled as a G/G/m queue system, where m represents the number of doors. Issues such as warehouse location will also be considered during modeling. In spite of the fact that cross-docks attracted much attention in a practical approach, the main reason behind the existence of these shortcomings is the complexity in solving the problem and improving the solution methods to enhance the quality of the solution and the solution time. Therefore, in this paper, we aim to minimize operational time \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Authors** & **Year** & **Objectives** & **Objective** & **Metaheuristic Method** & **Exact Solution, Software** & **Multi- Suppliers** & **Multi- Products** & **Time** & **Case** \\ \hline [PERSON] et al. & 2019 [34] & Time, Cost & Multi- & - & LINGO & ✓ & ✓ & ✓ & ✓ \\ \hline \multirow{4}{*}{[PERSON] and [PERSON]} & \multirow{2}{*}{2019 [35]} & \multirow{2}{*}{Cost, Energy} & \multirow{2}{*}{Multi-} & Multi-objective & \multirow{2}{*}{GAMs} & \multirow{2}{*}{✓} & \multirow{2}{*}{✓} & \multirow{2}{*}{✓} & \multirow{2}{*}{✓} & \multirow{2}{*}{✓} \\  & & & & algorithm (MOICA), & & & & & & \\  & & & & Multi-objective grey & & & & & & \\  & & & & (MOCOV) & & & & & & \\ \hline \multirow{2}{*}{[PERSON] et al.} & \multirow{2}{*}{2020 [36]} & \multirow{2}{*}{Time, Cost} & Multi- & Multi- & Multi-objective & \multirow{2}{*}{GAMs} & \multirow{2}{*}{✓} & \multirow{2}{*}{✓} & \multirow{2}{*}{✓} & \multirow{2}{*}{✓} \\  & & & & evolutionary algorithm & (MOEA) & & & & & \\ \hline [PERSON] and & \multirow{2}{*}{2020 [37]} & \multirow{2}{*}{Time, Cost} & Multi- & - & GAMs & ✓ & ✓ & ✓ & - \\  & & & & & & & & & \\ \hline [PERSON] and & \multirow{2}{*}{2020 [38]} & \multirow{2}{*}{Cost} & Multi- & \multirow{2}{*}{Memetic algorithm} & \multirow{2}{*}{GAMs/CPLEX} & ✓ & ✓ & - & - \\  & & & & & Heuristic algorithm & GAMs & ✓ & ✓ & ✓ & - \\ \hline [PERSON] et al. & \multirow{2}{*}{2020 [40]} & \multirow{2}{*}{Time} & Single & Constructive heuristic & CPLEX & ✓ & ✓ & ✓ & - \\ \hline Núkazmir and & \multirow{2}{*}{2020 [41]} & \multirow{2}{*}{Time} & Cost, Emission & \multirow{2}{*}{Multi-objective water} & \multirow{2}{*}{MATLAB} & \multirow{2}{*}{✓} & \multirow{2}{*}{✓} & \multirow{2}{*}{✓} & \multirow{2}{*}{✓} \\  & & & of & & flow algorithm & (MOWFA) & & & & \\ \hline Shahabi-Shahmir & \multirow{2}{*}{2021 [42]} & \multirow{2}{*}{
\begin{tabular}{} \end{tabular} } & \multirow{2}{*}{Multi-} & - & GAMs & ✓ & ✓ & ✓ & ✓ \\  & & & & & & & & \\  & & & & & & & & \\ \hline [PERSON] et al. & 2021 [43] & Cost & Multi- & - & GAMs & ✓ & ✓ & ✓ & - \\ \hline [PERSON] et al. & \multirow{2}{*}{2021 [44]} & \multirow{2}{*}{Cost} & Multi- & Lagrangian relaxation algorithms & \multirow{2}{*}{GAMs/CPLEX} & ✓ & ✓ & - & ✓ \\ \[PERSON] [PERSON] et al. & \multirow{2}{*}{2021 [45]} & \multirow{2}{*}{Cost} & Multi- & Genetic algorithm (GA) & GAMs & ✓ & - & - & ✓ \\ \[PERSON] et al. & \multirow{2}{*}{2021 [46]} & \multirow{2}{*}{Cost} & Multi- & Adaptive neighborhood & \multirow{2}{*}{C\#} & \multirow{2}{*}{✓} & \multirow{2}{*}{✓} & \multirow{2}{*}{✓} & \multirow{2}{*}{✓} \\  & & & simulated annealing algorithm & & & & & \\ \[PERSON] et al. & \multirow{2}{*}{2021 [47]} & \multirow{2}{*}{Cost} & Multi- & Evolutionary algorithm & GAMs & ✓ & ✓ & ✓ & - \\ \hline [PERSON] et al. & \multirow{2}{*}{2021 [48]} & \multirow{2}{*}{Cost} & Multi- & Branch-and-cut algorithm & \multirow{2}{*}{CPLEX} & ✓ & ✓ & - & - \\  & & & & algorithm & & & & \\ \hline [PERSON] et al. & \multirow{2}{*}{2022 [49]} & \multirow{2}{*}{Time, Vehicles} & Multi- & Multi-objective ant & \multirow{2}{*}{CPLEX} & ✓ & ✓ & - & ✓ \\  & & & colony optimization & & & & & \\  & & & & (MACO) algorithm & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(Cont.\)and cost simultaneously and use metaheuristic algorithms to overcome these deficiencies. Thus, this paper is trying to present an analytical model for the cross-docking concept using queue theory.