Decomposition principles applied to the dynamic production and work-force scheduling problem

One of the most important problems in the production and inventory planning field, is the scheduling of production and work force in a dynamic environment. Although this problem can be formulated as a linear program, it is often quite difficult to solve directly, due to its large scale. Instead, it might be fruitful to use a decomposition approach. Decomposition, in general, means decomposing a difficult problem into several easier, or a sequence of easier problems which are later coordinated to reconstruct the original problem. In this report we discuss several possibilities of applying the most common decomposition principles, namely Benders (primal) and Datnzig-Wolfe (dual), as well as a relatively new decomposition method, called cross decomposition, to the dynamic, multiproduct production and employment planning problem. A number of special cases are also presented.