Multi-Item Production Smoothing Models with Almost Closed Form Solutions

Computational efficiency in solving large-scale multi-item production smoothing models with quadratic costs is the chief concern of this paper. We consider two multi-item versions of the HMMS model and show that their optimal solutions can be obtained in "almost" closed form. Numerical inversion of large matrices is therefore not necessary and considerable savings in terms of storage requirements are also possible. The existence of unique optimal solutions depends in a very simple way on the model parameters.