Hybrid Make-to-Order/Make-to-Stock (MTO/MTS) production systems have attracted increasing attention from industry and the scientific community in recent years as a solution to the challenges of managing variable demand and reducing inventory costs. In these systems, standard products are manufactured based on demand forecasts MTS, while customized products are manufactured based on customer orders MTO. This combination provides greater flexibility compared with traditional production systems. However, one of the key challenges in these environments is optimizing production scheduling so that production resources, such as machinery and raw materials, are utilized as efficiently and effectively as possible. This challenge becomes more complex in systems involving demand for semi-finished components, as these components are not only used in the production of final products but may also have independent demand. Failure to manage this flexibility can lead to resource waste or missed revenue-generating opportunities. Although numerous studies have been conducted on production scheduling in MTO and MTS systems, most of them have focused solely on optimizing the production process of final products and have not considered the possibility of selling semi-finished components in a hybrid environment. This research gap provides an opportunity to develop a mathematical model that can simultaneously manage this flexibility in hybrid systems. This paper aims to develop a production scheduling model that, in addition to reducing production time and operating costs, provides accurate planning of production machine activities. The proposed model in this paper is a Mixed-Integer Linear Programming (MILP) framework that addresses the optimization of production scheduling in a hybrid MTO/MTS environment. The main novelty of this model lies in integrating flexibility into the decision-making process, such that semi-finished components not only serve as intermediates in the production of final products but can also be sold independently when separate demand exists. The model incorporates this flexibility by simultaneously optimizing total production time and operating costs, including setup costs, machine idle costs, and inventory holding costs, and ultimately provides detailed operational outputs, such as the start and completion times of operations on each production machine. This innovative approach has broad applications in industries such as automotive and electronics, where the multiple-use management of semi-finished components can improve resource utilization, reduce costs, and increase revenue through the direct sale of components. For example, in an automotive factory, a semi-finished engine can either be used in the production of a customized vehicle (MTO) or sold as an independent component when market demand exists, thereby providing significant operational and revenue flexibility.

Hybrid MTO/MTS production systems have been widely recognized in both industry and the research literature over recent decades as a response to the challenges of managing variable demand and reducing inventory costs. By combining the advantages of MTS and MTO production strategies, these systems provide greater flexibility and efficiency compared with traditional production systems. Existing research has primarily focused on three main areas: production strategy design, inventory control, and production scheduling. In a systematic review, Peters and van Oijen [1] proposed a framework for classifying hybrid systems and identified three main types of production control: sequential, parallel, and floating. This classification provided an important foundation for understanding the different structures of these systems. Rafiei and Rabbani [2] also addressed capacity coordination in hybrid production environments and highlighted the importance of decision-making regarding the Customer Order Decoupling Point (CODP). In inventory control and production planning, numerous studies have investigated optimal policies. Beemsterboer, Land, and Teunter [3], in an exploratory study, examined hybrid MTO/MTS production planning and proposed various strategies for simultaneously managing MTO and MTS demands. Subsequently, Beemsterboer et al. [4] investigated the optimization of production batch sizes in hybrid MTO/MTS systems. This study addressed the problem of determining batch sizes for products in both customized and standard production systems. By focusing on flexibility in batch sizes, they demonstrated that the use of hybrid approaches can increase production efficiency while reducing inventory costs, and that flexibility in batch sizes under uncertain conditions can contribute to improved productivity. This paper primarily considered systems comprising only one MTO product and one MTS product and focused on a model that incorporates flexibility in production batch sizes under fixed and predefined conditions; therefore, the current model may not be able to adapt to larger market fluctuations and unforeseen changes in demand. Kuthambalayan and Bera [5] also developed a zero-one integer nonlinear programming model for managing product variety in hybrid systems, in which decisions regarding the production mode (MTS or MTO) and the inventory level of semi-finished components are made at the first stage. In the area of production scheduling, various models have been proposed to optimize the performance of hybrid systems. Kusuma et al. [6] proposed a hybrid MTO/MTS scheduling model for multi-product systems and demonstrated that the hybrid (s,Q)-SPT model performs better in reducing lead time and inventory levels compared with traditional models.

Furthermore, Altendorfer and Minner [7] showed that hybrid MTO/MTS systems generally outperform pure MTS or MTO strategies under most conditions and can serve as an optimal solution. The choice between these two strategies is significantly dependent on system parameters; specifically, the MTO system is more desirable when inventory holding costs are high, customer lead times are longer, or the production rate increases. In contrast, the MTS system performs better under conditions of high demand rates and short lead times. In other studies, Beemsterboer et al. [8] specifically addressed the operational aspects and production scheduling in job-shop environments and the management of workflow. However, a careful review of the existing literature reveals two important research gaps that the present study addresses. The first gap is the lack of attention to the direct sale of semi-finished components. Although several studies have addressed the management of semi-finished components in hybrid systems, such as Tiagarajan and Kothambalayan [5], none has explicitly considered the possibility of selling these components directly as an independent revenue-generating option, separate from their internal use in the production of final products. This aspect, which is common in industries such as automotive and electronics, represents an overlooked opportunity for improving strategic decision-making and increasing profitability. The second gap is the limitation of existing models in managing complex multi-product systems. Many studies, particularly earlier studies or those focusing on simpler systems, consider MTS systems with a limited number of products. This assumption limits the applicability of these models to real-world industries that deal with a high variety of products and components. Therefore, the present study is conducted to address these research gaps by developing a production scheduling framework that considers both the direct sale of semi-finished components and the complexity of multi-product hybrid MTO/MTS production environments.

In this section, the modeling framework for the production scheduling problem in a hybrid MTO/MTS environment is first presented in detail, and its key challenges are examined. Subsequently, a mathematical model is developed to formulate the key decisions, including production scheduling, batch size determination, and decision-making regarding the destination of semi-finished components. Finally, the efficiency and validity of the proposed model are evaluated by analyzing numerical results under several scenarios.

The analysis of the results in Table 4 shows that the model intelligently balances competing costs (setup, holding, and tardiness). Scenario 2, with the highest tardiness cost (CZ=1), has the highest total cost (15759.7), whereas Scenario 3, with the lowest CW and CZ and the highest warehouse capacity, achieves the lowest total cost (3851.8). The proposed model effectively manages hybrid MTO/MTS production policies. For MTS components, considering setup and holding costs, the model determines whether production should take place before demand or not. For MTO components, the model flexibly utilizes inventories of semi-finished components and final components. This capability makes it possible to generate additional revenue from semi-finished components and creates added value in the production system. In Scenario 1, with limited warehouse capacity (CAP=50), the model is required to manage inventory very carefully. This constraint results in production being carried out approximately in proportion to demand, and the holding cost (84.6 units) reaches its minimum possible level. However, this strategy requires frequent production, which increases the setup cost to 990 units. In addition, to prevent tardiness, the model schedules production such that the production of initial components (such as component 2) begins at the beginning of the first period (x2,1=0), so that the production chain of dependent components (5, 6, and 8) is not delayed.

In contrast, Scenario 4, with the highest warehouse capacity (CAP=2000) and a more balanced combination of CW and CZ costs, adopts a different strategy. In this scenario, by utilizing the abundant warehouse space, the model moves toward mass production and reduces the number of setups, resulting in a setup cost of 670 units. For example, component 2, which has low demand in the first period, is produced in the second period (x2,2=0) and its inventory is held for the third period, demonstrating the model's focus on reducing setup costs and utilizing warehouse capacity. This comparison shows that the model dynamically responds to changes in system capacity and determines the optimal production strategy based on resource constraints. Finally, the comparison of the scenarios shows that reducing tardiness costs and increasing warehouse capacity can lead to a significant reduction in total cost, even if this results in increased inventory. Overall, the model is capable of effectively and intelligently balancing the competing objectives of production, inventory management, and scheduling. These results highlight that the proposed model has successfully satisfied demand, such that all MTO and MTS demands have been fulfilled on time, no machine has remained idle in any period, and the production resources have been fully optimized. Inventory levels have been optimally managed and holding costs have been controlled; furthermore, all precedence and scheduling constraints have been successfully satisfied. These findings clearly demonstrate that the developed mathematical model is capable of solving real-world problems with considerable complexity and providing precise and applicable operational outputs for production management decision-making.

In this study, a novel mathematical model was developed for production scheduling in hybrid MTO/MTS environments that integrally incorporates the possibility of directly selling semi-finished components as a strategic decision-making option. The main innovation of this model is the modeling of flexibility in determining the final destination of semi-finished components, which is introduced for the first time in the production management literature as an integrated optimization problem. This approach enables intelligent decision-making between using components as intermediates in the production of final products or selling them as independent products. The proposed model simultaneously optimizes total production time, operating costs (including setup, machine idle time, and inventory holding costs), and revenue from the sale of semi-finished components by combining multi-objective optimization. Numerical results under four different scenarios show that the model is capable of satisfying all MTO, MTS, and semi-finished component demands without delay, minimizing the total system cost, and providing detailed planning of machine scheduling. These outputs are highly applicable to the operational implementation of production. The practical applications of this model are extensive in industries such as automotive, electronics, and industrial machinery, where intelligent management of semi-finished components can lead to improved resource utilization, cost reduction, and the generation of additional revenue. This approach not only enables production managers to make better strategic decisions but also increases organizational profitability through value creation. However, this study has certain limitations that can shape future research directions: 1) the uncertainty in demand and processing times is not considered, which can be addressed using stochastic or robust models, 2) the model is limited to a single-job-shop environment, 3) there is a need to develop metaheuristic algorithms for solving large-scale problems, and 4) operational parameters such as quality and maintenance scheduling are not considered. This research confirms that integrating flexibility in the sale of semi-finished components can lead to improved efficiency of hybrid production systems and create added value for them.

The authors are grateful to all individuals who contributed to the completion of this study through their assistance and constructive input.

The authors declare that this study was conducted without financial support from any external organization.

The datasets generated and analyzed during the current study are available from the corresponding author upon reasonable request.