Production equilibrium point in multi-unit manufacturing systems and the vertical linear complementarity problem

A model that selects and produces products at an equilibrium point in multi-unit manufacturing systems is presented. It enables each business subsystem in the company to select and produce products so that the whole organization meets both internal and external demands at minimum inventory cost. Unlike previously proposed models, this model does not place any restrictions on the number of products or services that each business subsystem can provide. Proofs are provided to show existence of solutions and solvability, and a numerical example is given to demonstrate the utility of the model.