## 1 Introduction
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Article** & **Model Category** & **Objective Function** & **Considerations** & **Solving Approaches** \\ \hline \hline \multirow{8}{*}{[PERSON] et al. [13]} & \multirow{8}{*}{Multi-objective optimization model} & The profit by improving learning and reducing the failure cost of the system; the costs associated with repairs and deterioration & The market demands; the machine capacity; the limitation on the total quantity produced; the workforce levels of labor groups; inventory capacity & Subpopulation genetic algorithm; genetic algorithm; weighted sum multi-objective genetic algorithm and nondominated sorting genetic genetic algorithm algorithm II & The multiple criteria \\ \cline{1-1}  & & A framework based on a set of stochastic, nonlinear, multi-objective optimization models & The total revenue; total production costs; utilization of production resources and capacity & The production capacity; the product demand; workforce & decision-making methods Additive value function, TOPSIS and VIKOR \\ \cline{1-1}  & & & The total cost of machine maintenance and overhead, inter- and intra-cell material handling, inventory holding, subcontracting, and backordering & The production-inventory balance; production consistency; the lower and upper bounds for the production level; the capacity limits; the machine balance; the storage space limits; the maximal backordering level & Linearized \\ \cline{1-1}  & & & The total costs composed of regular time labor costs, overtime labor costs, hiring costs, layoff costs, and product-related costs that include producing, holding inventory, backlogging, and subcontracting costs & The workforce level; the production capacity; the production balance; overtime labor limit & Bi-level particleswarm optimization \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._As a major factor determining the production capacity of enterprises, labor costs account for an increasing proportion. Therefore, decision makers pay great attention to the impact of labor changes, and the stability of workers has become more important than ever. Furthermore, the fluctuation of demand will lead to a change in enterprise employment. So, the stability of employment is extremely important to the APP problem. Therefore, in the objective function, the sum of the changes in the number of workers is used to measure its stability. In reality, due to the decline of actual production capacity caused by the change of workers, equipment maintenance or damage, holidays and sudden epidemic situations, or due to the shortage of production materials, production enterprises may produce products in advance or be backordered. Both of these situations will affect the cost of the enterprise. In order to improve the adaptability of enterprises and reduce production costs, it is necessary to properly arrange the production plan to improve the production management level of the enterprise. In considering the situation of production in advance or backorder, this paper analyzes the impact of backorders and determines the cost of backorder and loss of sales. Furthermore, a bi-objective optimization model for an APP problem of multi-product, multi-stage with early and late delivery minimizes total production costs and instability in the workforce, considering the balance equation for production, product demand, labor, inventory and production capacity, and different worker types. In order to improve the efficiency of solving large-scale multi-objective APP problems, a local search (LS) algorithm is based on the minimum cost flow (MCF). Further, in order to improve the speed of solving APP problems, hybrid strategies based on local search-based GA (LS-GA), hybrid genetic algorithm-particle swarm optimization based on stages (HGA-PSO1) and multi-population strategy (HGA-PSO2) are adopted to solve this model. Finally, the performances of the proposed evaluation of the multi-objective algorithm are selected to compare and analyze each algorithm.