A mathematical model for optimal order acceptance/rejection and inventory policies in multiperiod, multi-product manufacturing systems and its application

Manufacturers often have to make sales and production decisions based on unstable market demand in today's business environment. In this production environment, companies may need to determine which customer orders to fulfill or which products to stock under limited resources. To achieve this objective, this study proposes a mixed-integer mathematical programming model to determine optimal order acceptance/rejection and inventory decisions using in a multi-period and multi-product hybrid maketo-order (MTO) and make-to-stock (MTS) system. The model considers inventory costs, production costs, stockout costs, budget constraints, production lead time, labor constraints, and costs for each order. For each period, the model considers resource utilization, production lead times, stock costs, and stockout costs when making decisions on production for stock or order acceptance/rejection. Additionally, the model determines the production quantities for stock and order, and safety stock levels, optimizing them based on the ultimate profit objective. The study extensively discusses production strategies, stock costs, and types of inventory. A series of analyses are conducted to validate the accuracy of the proposed mathematical model. Firstly, a real-life application is performed using data obtained from a chemical plant. The problem is investigated under different scenarios to test the model's sensitivity and capabilities. Furthermore, an experimental study is conducted to investigate the limitations of the mathematical model as the problem size increases. For this purpose, test problems of different sizes are developed to measure the effectiveness of the proposed mathematical model.