A Scenario-Based Nonlinear Programming Model for a Two-Level Inventory Control Problem: A Case in Dairy Product Industry

In this paper, a novel scenario-based two-level inventory control model with a limited budget is formulated. The demand during the selling period is considered to follow a uniform probability distribution. In addition, it is assumed that there will be some customers who are willing to wait for their demands to be satisfied; thus a service level is considered for these customers. The aim is to find the optimal order quantities of the products and the required raw materials such that the relevant expected total profit obtained during the period is maximized. After proving the convexity of the proposed formulation, a penalty function and the Barrier method is proposed to solve the developed nonlinear stochastic programming problem. The problem is solved under different demand scenarios defined in three states of good, fair, and low. Finally, a case study in a dairy manufacturing company is provided to illustrate the application of the proposed methodology in real-world inventory control systems.