Journal of the Operational Research Society

, Volume 66, Issue 8, pp 1297–1311 | Cite as

A heuristic for the Minimum Score Separation Problem, a combinatorial problem associated with the cutting stock problem

  • Kai Helge Becker
  • Gautam Appa
General Paper


The Minimum Score Separation Problem (MSSP) is a combinatorial problem that was introduced in JORS 55 as an open problem in the paper industry arising in conjunction with the cutting stock problem. During the process of producing boxes, flat papers are prepared for folding by being scored with knives. The problem is to determine whether and how a given production pattern of boxes can be arranged such that a certain minimum distance between the knives can be kept. Introducing the concept of matching-based alternating Hamiltonian paths, this paper models the MSSP as the problem of finding an alternating Hamiltonian path on a graph that is the union of a matching and a type of graph known as a ‘threshold graph’. On this basis, we find a heuristic that can quickly recognize a large percentage of feasible and infeasible instances of the MSSP. Detailed computational experiments demonstrate the efficiency of our approach.


cutting stock problem bin packing heuristics networks and graphs Travelling Salesman Problem alternating Hamiltonian path threshold graph 


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Copyright information

© Operational Research Society Ltd. 2014

Authors and Affiliations

  • Kai Helge Becker
    • 1
  • Gautam Appa
    • 2
  1. 1.Queensland University of Technology (QUT)BrisbaneAustralia
  2. 2.London School of Economics and Political ScienceLondonUK

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