arises because the machinery in the second stage is narrower than the primary. Efficient utilisation of both stages of production is important (from an energy or material use perspective) and what is efficient for the primary stage may be inefficient for the secondary, leading to trade-offs. Metallised film (used in packaging of snacks), and plastic extrusion on paper (used in liquid packaging, e.g. juice cartons) are further examples of such a process. Winder constraints where the slitting process has physical or logical constraints: a very common constraint is that only a certain number of slitting knives are available, so that feasible patterns should not contain more than a maximum number of rolls. Because winder machinery is not standardised, very many other constraints are encountered. An example of a customer requirement is when a particular order cannot be satisfied from either of the two edge positions: this is because the edges of the sheet tend to have greater variations in thickness and some applications can be very sensitive to these. An example of a quality issue is when the master roll contains defects that have to be cut around. Expensive materials with demanding quality characteristics such as photographic paper or Tyvek have to be carefully optimised so that the wasted area is minimised. Multi-machine problems arise when orders can be produced on more than one machine and these machines have different widths. Generally availability of more than one master roll width improves the waste considerably; in practice however additional order splitting constraints may have to be taken into account. There is also a semi-continuous problem, where the produced rolls do not have to be of the same diameter, but can vary within a range. This typically occurs with sheet orders. This is sometimes known as a 1½ dimensional problem. This variant also occurs in the production of corrugated fiberboard, where it is called, somewhat confusingly, the corrugator scheduling problem. Because some paper machines are relatively narrow compared to the demanded items, some companies have invested in a skiving (also known as a web-welding) secondary process, whereby two reels (produced by slitting the initial jumbo reels) are joined side-by-side (with a little overlap) to make up a wider roll. Producing narrower reels in the primary process leads to lower overall waste. In the metals industry one key difference is that typically the master rolls are produced earlier and are generally different from