## 1 Introduction  
Optimal production, safety inventory, and manpower are concurrently determined given a set of manufacturing resources and limitations, [PERSON] [1] mentioned; the APP spans the production planning time to a range of 2 to 18 months, during which the planners may take into consideration each product category the overall production levels to meet predictable fluctuating demands, which is justified from an aggregate point of view [2]. At the same time, such APP can provide production information to effectively utilize an organization's resources to satisfy various demands. Aggregate production planning determines not only which output levels have to be met and what appropriate input mix of resources should be used, but also how to meet prescribed requirements at minimum cost without violating capacity limits [3]. It is essential to aggregate the information for it is almost impossible to consider every detail related to the production planning without sacrificing its effectiveness in the long run. This planning approach can calculate an aggregate number of production problems, such as average item, weight, volume, production time, or dollar value. Productionquantities for each item or item group can be specifically determined upon the creation of the aggregate production plan that includes anticipated constraints. One of the benefits of an APP is that it provides multiple selections of mixes that contains either one or a combination of strategies to respond to demand fluctuation, such as overtime/idle time production rate adjustment, workforce size regulation, level production plus inventory policy, or sales shortfalls [4; 5; 6]. In addition, managers may have the option of using subcontracting as a suitable alternative for part of the production schedule to reduce internal capacity shortages. This work proposes a multi-objective planning (MOP) method to determine the most effective means of satisfying forecast demand by adjusting production rates, hiring and layoffs, inventory levels, overtime work, back orders, and other controllable variables. The objective functions of this APP decision problem are to minimize total production costs, carrying and backordering costs, also changing workforce levels under production constraints. While pervasive approaches-such as global criteria methods, goal programming, fuzzy programming and interactive approaches-consider only the single criterion of shortest distance from goal(s) or the positive ideal solution (PIS), the technique for order preference via the similarity ideal solution (TOPSIS) provides a broader principle of compromise for solving multiple criteria, decision-making problems. The compromise control (ideal solution) minimizes the distance measure, provided that the nearest solution has the shortest distance to the positive ideal solution (PIS) and the longest distance to the negative ideal solution (NIS). The proposed method transforms multiple objectives into two objectives. The bi-objective problem can then be solved by balancing satisfaction through a max-min operator to resolve the conflict between the new criteria based on PIS and NIS. The development of the proposed approach is motivated by the following facts: (1) it combines MOP and TOPSIS to provide an easy way to solve a complex APP problem; (2) it can be efficiently coded when the problem is large in scale; and (3) this combined decomposition-based method gives better results than traditional methods for solving MODM problems [7]. The efficiency of the decomposition-based method increases sharply with the size of the problem. This work is organized as follows. First, Section 2 presents some approaches to solving APP problems. Section 3 presents the formulation of the model. Section 4 provides a guide for developing the optimal overall production plan using ideal-solution principles. A case study in Section 5 demonstrates the applicability of the proposed model to practical APP decision problems for developing the optimal overall production plan. Finally, conclusions are drawn in Section 6.