A framework for solving the optimal display quantities with equality constraint

This paper proposes a framework for determining optimal display quantities in shelf space for SPA (Specialty store retailer of Private label Apparel) retailers. In a field of inventory control in terms of optimization, a considerable number of previous researches focus on cases where there is a gap between the original demand and available shelf space. In this paper, we mainly consider a case where the gap is not great and examine the behavior of optimal solution for display quantities. In the formulation, we organize a multi-item newsvendor problem with an equality constraint for shelf space. By solving this problem, an analytical solution for optimal display quantities can be obtained, which would provide useful guidelines for practitioners.