### The Economic Efficiency of the \"Pull\" and \"Push\" Strategy and Optimization Models
In order to solve this problem, [PERSON] and [PERSON] built a simple model-based procedure to determine delivery times using the throughput diagram with early available information [29]. This problem has been addressed by many authors over the years. For example, [PERSON] et al. [30] proposed the delivery date decision support system which integrated the marketing and production planning functions with a consideration of the current capacity and workload smoothing. The system has been implemented in a rotating machinery shop in South Korea. In the MTO strategy, the accurate estimation of processing time is very important. To solve this problem, tools like workload control (WLC) are developed [31]. Capacity planning is important for efficient production planning in Make-to-Order (MTO) and Assemble-to-Order (ATO). [PERSON] and [PERSON] [32] proposed a linear programming model to plan the operations using annualized hours (AH). This model has been implemented in a company that produces agricultural implements. A management system that takes into account possible disruptions in the production system may also be necessary. To solve this problem, [PERSON] et al. (2024) [33] proposed a prediction method based on the spatial and temporal (ST) characteristics of the production process. The problem of the risk of there being a reduced quality of service in an MTO strategy is highlighted by, for example, [PERSON] et al. [26], who have developed a model to calculate the profitability of this strategy for the case of a company that orders raw material after receiving orders from customers. The lead time is very long, making it impossible for the company to fulfill the customer's order in time and they have to give a discount of 25-30% of the value of all purchases. Models have also been developed that take into account the complexity of supply chains or networks. For example, [PERSON] et al. (2022) [34] have developed a model of a two-stage decentralized supply chain for customized production in a stochastic environment. The model was developed to find the optimal strategy, taking into account the relationship between local delivery times, total delivery times, prices, demand and profits, and the impact of firms' production capacity. [PERSON] [35] developed a model distinguishing between functional and innovative products and between physically efficient and market-responsive supply chains. Products characterized by, among other things, a constant (predictable) demand pattern and long product life cycles require cost minimization and high resource utilization, while innovative products characterized by demand variability and short life cycles should respond to the market with a supply chain that has additional capacity and is more flexible. This model has been empirically tested and has found some validation [36]. There is abundant research concerning the problems of managing and optimizing hybrid systems combining Pull (Make-to-Order) and Push (Make-to-Stock) strategies and models [37]. And also, models have been developed for evaluating hybrid versions of MTO and MTS strategies in specific cases and specific sectors of the economy. For example, [PERSON] et al. developed just such a model for production planning in the garment industry [38]. Specific problems are related to the size of the company, and therefore, [PERSON] et al. [39] developed a model to support inventory management decisions in an MTO-MTS context implemented in small- and medium-sized enterprises (SMEs). Combining strategies raises new decision-making problems and the need to develop new tools and methods for solving decision-making problems and calculating the profitability of the solutions used. In the case of combined MTS and MTO strategies, in order to optimally position inventories, strategic as well as tactical decoupling points should be identified [40]. To optimize a hybrid \"Make-to-Stock-Make-to-Order\" environment, [PERSON] et al.