Allocative control Data Envelopment Analysis (DEA) model to evaluate inventory control systems when there is a relationship among variables

The purpose of this paper is to present an allocative control Data Envelopment Analysis (DEA) model to measure the efficiency of systems with variables that have a relationship to each other, such as inventory control systems. The static model includes intermediate variables (a common variable class in dynamics models). It is applied to 647 companies (Decision Making Units – DMU) from South and North America (mainly USA, Brazil, and Chile), considering their production inventory systems with data from accounting variables. The model minimizes the inventory and production costs to calculate allocative efficiency. The output is demand, the input is production, and the intermediate variable is inventory. Their costs are in the objective function. There is a variational constraint from Optimal Control Theory (OCT) to describe the relationship between demand, production, and inventory. In summary, the model calculates the efficiency preventing the possibility of a projection that ignores the relationship between these variables. The proposed model is relevant because this relationship always occurs in a practical sense in inventory control systems.