Integrated order acceptance and inventory policy optimization in a multi-period, multi-product hybrid production system

In today's volatile business environment, manufacturers often face the challenge of making sales and production decisions despite unstable market demand. Companies must strategically determine which customer orders to fulfill or which products to stock under limited resources. This study addresses these challenges by proposing a mixed-integer mathematical programming model to optimize order acceptance/rejection and inventory decisions in a multi-period, multi-product hybrid make-to-order (MTO) and make-to-stock (MTS) system. The model incorporates various factors such as holding costs, production costs, stockout costs, budget constraints, production lead time, labor constraints, and order-specific costs. For each period, the model evaluates resource utilization, production lead times, and stock and stockout costs to decide production for stock or order acceptance/rejection. Additionally, it determines the optimal production quantities for stock and order fulfillment, as well as safety stock levels, all aimed at maximizing profit. To validate the proposed model, a real-life application was conducted using data from a chemical plant, exploring different scenarios to assess the model's sensitivity and capabilities. Furthermore, an experimental study examined the limitations of the mathematical model as the problem size increased, with test problems of varying dimensions developed to measure its effectiveness.