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ORDER SPREAD AND ORDER SPLITS IN THE CUTTING STOCK PROBLEM

Authors
Adolf Diegel (Cutline Research), Olaf Diegel (Auckland University of Technology), Edouard Montocchio and Sias van Schalkwyk (Mondi Business Paper South Africa).

ABSTRACT
We use "order spread" for the number of orders within a cutting pattern, horizontally. Spread may be limited by various factors, from favoring prompt delivery or reducing knife changes to few packing stalls: reels coming off a winder need a stack, one for each size, to be packed and labelled, so one faces "MOSP, the Minimization of Open Stacks Problem". We include spread in an LP-table to enforce an absolute limit, or else to reduce the number of open stacks in the context of other objectives.

Further restrictions arise in "OCSP, the Ordered Cutting Stock Problem". It goes beyond a 1-stack case: orders are listed by client name rather than by size and each order must be done before other orders may enter the last pattern needed for the active order.

Beyond the horizontal spread of orders within patterns, we have "order splits", the split of orders between patterns, vertically, from pattern to pattern. Ideally, one has zero splits, each order being filled by one pattern. Conversely, as an order appears in two or more patterns, there are as many splits: stacks must remain open until the order is filled.

We count the number of splits in a cutting plan, generate new patterns or adapt old ones to reduce splits, then consider how splits relate to order spread and other objectives.

Keywords:
Cutting stock, Order spread, Order splits

order splits

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