We consider the problem of fair division of a two dimensional heterogeneous good among several agents. Applications include division of land as well as ad space in print and electronic media. Classical cake cutting protocols either consider a one-dimensional resource, or allocate each agent several disconnected pieces. In practice, however, the two dimensional shape of the allotted piece is of ...

The 1-dimensional Cutting Stock Problem (1-CSP) seeks to fulfill with a minimum trim loss the demand of parts of various lengths by cutting them out from a given stock size. In the Pattern Minimization Problem (1-PMP) one wants an optimal 1-CSP solution that uses a minimum number of distinct cutting patterns. We discuss two formulations of 1-PMP: (1) introduced by Vanderbeck, and (2) obtained b...

One of the factors that add to the complexity of the cutting stock problem is the large number of the cutting patterns that may be encountered. When the cutting stock problem is expressed as an integer-programming problem, the large number of cutting patterns involved generally makes computation infeasible. However, if the linear programming formulation of the cutting stock problem is free of i...

Cutting stock problem (CSP) is a of cutting an object into several smaller objects to fulfill the existing demand with minimum unused remaining. Besides minimizing remaining object, sometimes there another additional in CSP, namely number different patterns. This happens because setup cost for each pattern. study shows way obtain patterns (CSP). An example modeled linear programming and then so...