## 3 System Architecture of the DSS
### Model Management
#### 3.3.1 Selection of an Optimal Product Mix under the AHP-TOC Heuristic
The criteria resources represent the importance of exploiting total production capacity, and the profit stands for the importance of the margin between sales price and raw material costs for the whole demanded quantity. Through a meticulous process of pairwise comparison, decision-makers attribute relative significance to the two vital elements of resources and profit, reflecting their core considerations. The outcome of the first layer is the priority vector of the resources and profit. The second layer delves into a detailed exploration of the relative importance of each individual resource and each individual SBU's profit, casting light on their contributions within the decision-making process. The second layer entails preliminary computation to obtain the dimensionless decision matrix for SBUs by normalizing their contribution margins, the normalized matrix of the SBU processing times, and the normalized matrix of the actual time and the available time, as well as the normalized matrix of capacity and processing times. Finally, the third layer is dedicated to discerning the hierarchies within SBUs and unraveling their interplay. The layer yields a priority sequence for SBUs, computed by multiplying the normalized contribution margin for each SBU by the weighted vector of profit and subsequently adding the order of priority of the resources. This resource priority is determined by the product of the resultant vector of resources and that of the normalized matrix of capacity and processing times obtained from the second layer. For handling more complex decision-making structures, we propose the implementation of a comprehensive strategy informed by established methodologies. Drawing from the works of [PERSON] [55] and [PERSON] [56], our proposition aligns with the \"divide and conquer approach\" recommended in the literature. This approach involves segmenting the elements into coherent clusters, enabling more focused pairwise comparisons and alleviating the computational burden associated with employing a large number of elements [57]. Additionally, inspired by the principles of continual improvement advocated by [PERSON] and [PERSON] [58], we emphasize the integration of \"iterative refinement\", enabling the continual reassessment and adjustment of pairwise comparisons to accommodate the evolving perspectives and insights. The result, derived from the AHP, yields a provisional product mix, highlighting the necessity for a more refined optimization approach. To that end, we introduced a TS algorithm aimed at identifying optimal product-mix solutions. TS is a metaheuristic search method designed to address complex optimization problems by navigating through a diverse solution space. Introduced by [PERSON] [59] in the 1980s, TS draws inspiration from the concept of memory, incorporating a dynamic mechanism to avoid revisiting previously explored solutions. By employing a strategic memory-based approach, TS effectively  
Figure 2: Main criteria and sub-criteria of AHP for PMP [29]. © 2010 IEEE. Reprinted, with permission, from [PERSON]; [PERSON]; [PERSON] The TOC-based algorithm for solving multiple constraint resources. _IEEE Trans. [PERSON]_**2010**, _57_. balances exploration and exploitation, enabling the efficient exploration of promising solution areas while maintaining the capability to escape local optima. This versatile optimization technique has found applications in various fields, including combinatorial optimization, scheduling, and logistics, demonstrating its robustness and effectiveness in tackling intricate real-world problems. Concerning the requirements of the AHP-TOC heuristic, the following notations are selected. The AHP-TOC heuristic [29], together with the improvements in identifying the problem environment and decrease-increase procedure, is illustrated in Figure 3 and is applied as follows (this section substantially adopts a similar stepping hierarchy and formulations to the original AHP-TOC heuristics of [PERSON] et al.