A transformation for solving a pattern sequencing in the wood cut industry

Consider a wood cutting setting where different panels have to be cut from large boards. Each cut panel size is put into a stack which remains opened until the last panel of that size is cut. The minimization of open stack problem (MOSP) is the problem of sequencing the cutting patterns in order to minimize the maximum number of open stacks during the production run. It is shown that an optimal solution to any MOSP can be obtained from an optimal solution of a corresponding MOSP where all patterns have at most two different panel types.