Abstract
This paper presents an instance of the rectangular packing problem which arises in the implementation of a graphical user interface in a windows environment. The problem consists of a single, containing rectangle of finite dimension and an ordered collection of rectangular objects to be packed in the rectangle. The size of the containing rectangle is dynamic, and restrictions are placed on the subset of the objects that can be packed in the rectangle at any given instance. A detailed description of the general problem is provided and a mathematical formulation is presented. A specific, real-world application is then introduced and modeled as an integer linear programming problem. Finally, due to the intractability of a direct solution of the mathematical model, a network representation of the problem is derived from which an efficient branch-and-bound solution algorithm is developed. The performance with respect to execution time of the branch-and-bound algorithm is analyzed for various instances of the problem and the quality of solution with respect to objective value is compared with that of an ad hoc method.
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