An inventory model with constrained newsboy under renting-warehouse

Nowadays, people have higher requirements for the varieties and personalities of commodities with the gradual improvement of their living standard, and more and more commodities have the characteristics of single-period or short-life cycle, so the coordination of supply chain on newsboy-type products becomes an important issue in supply chain management. In this paper, we address the challenge in dealing with the inventory model under limited warehouse and renting warehouse. First, we develop a general profit maximization model for the case that the retailer has limited warehouse capacity and outsourcing warehouse may be required, and prove that expected profit function is concave. Then, we derive the closed-form expressions of order quantities for several cases with the Kuhn-Tucker method to solve this nonlinear optimization problem, and further analyze the optimal solutions. Finally, we conclude that the classical newsboy model is a special case of the problem studied in this paper.